Nuclear Power Plant

**Chapter 6**

**Abstract**

public individuals dose

the more severe accidents.

pressure vessel [13].

**89**

**1. Introduction**

Plant, Brazil

Calculation of the Dose for Public

Accident at the Angra 2 Nuclear

*André Silva de Aguiar, Seung Min Lee and Gaianê Sabundjian*

Through a severe accident at nuclear power plant Angra 2, the whole body dose

effective of the individuals members of the public located in the Emergency Planning Zones (EPZs) will be calculated, and later, the protective actions in these EPZs will be analyzed. Two different scenarios of radionuclide release into the atmosphere will be considered. In the first scenario, 2 h of the release of Xe, Cs,

**Keywords:** MELCOR, CALPUFF, atmospheric dispersion, nuclear power plant,

From the nuclear accidents that occurred in the world [1–3], the International Atomic Energy Agency (IAEA), together with the licensing bodies of countries that use nuclear energy, requested that they carry out computer simulations of some accidents that are considered credible for their facilities, in order to verify their

These accidents are known as the design basis, in other words, accidents of loss of primary coolant by large or small ruptures at points in the primary circuit, whose probability of occurrence is critical to the system. It was after the accident at Unit 2 of the Three Mile Island Nuclear Plant (TMI) in 1979 that it was necessary to study

These severe accidents are those in which substantial damage is expected in the reactor core [4]. The knowledge of accidents with core meltdown is based on the simulations with computer programs of the type MARCH [5], APRIL [6], MELCOR [7–9], SCADAP/RELAP5 [10–11], and MAAP4 [12]. Among these programs, MELCOR, SCDAP/RELAP5, and MAAP4 are widely used for the integral analysis of the melted material in the core and the consequences in the lower part of the

In the event of a severe accident, followed by successive failures of physical barriers and problems in the control and protection systems of the reactor, the release of radioactive material into the atmosphere may become significant. The problems generated by these catastrophic events can lead to an increase in levels of

Ba, and Te, and the second scenario, 168 h of release.

integrity when subjected to such events.

Individuals Due to a Severe

#### **Chapter 6**

## Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear Plant, Brazil

*André Silva de Aguiar, Seung Min Lee and Gaianê Sabundjian*

### **Abstract**

Through a severe accident at nuclear power plant Angra 2, the whole body dose effective of the individuals members of the public located in the Emergency Planning Zones (EPZs) will be calculated, and later, the protective actions in these EPZs will be analyzed. Two different scenarios of radionuclide release into the atmosphere will be considered. In the first scenario, 2 h of the release of Xe, Cs, Ba, and Te, and the second scenario, 168 h of release.

**Keywords:** MELCOR, CALPUFF, atmospheric dispersion, nuclear power plant, public individuals dose

#### **1. Introduction**

From the nuclear accidents that occurred in the world [1–3], the International Atomic Energy Agency (IAEA), together with the licensing bodies of countries that use nuclear energy, requested that they carry out computer simulations of some accidents that are considered credible for their facilities, in order to verify their integrity when subjected to such events.

These accidents are known as the design basis, in other words, accidents of loss of primary coolant by large or small ruptures at points in the primary circuit, whose probability of occurrence is critical to the system. It was after the accident at Unit 2 of the Three Mile Island Nuclear Plant (TMI) in 1979 that it was necessary to study the more severe accidents.

These severe accidents are those in which substantial damage is expected in the reactor core [4]. The knowledge of accidents with core meltdown is based on the simulations with computer programs of the type MARCH [5], APRIL [6], MELCOR [7–9], SCADAP/RELAP5 [10–11], and MAAP4 [12]. Among these programs, MELCOR, SCDAP/RELAP5, and MAAP4 are widely used for the integral analysis of the melted material in the core and the consequences in the lower part of the pressure vessel [13].

In the event of a severe accident, followed by successive failures of physical barriers and problems in the control and protection systems of the reactor, the release of radioactive material into the atmosphere may become significant. The problems generated by these catastrophic events can lead to an increase in levels of radioactivity in the vicinity of the plant, representing a threat to the society and local life.

These conditions are conventionally known as boundary conditions. The postulated

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

d. Injection of the Emergency Core Cooling System – ECCS from Refueling Water Storage Tank – RWST by Safety Injection Pump – SIP e do RHR

These boundary conditions, together with the primary circuit breakage, are sufficient to result in total core melting. Two mitigating measures were modeled in this study: Passive Autocatalytic Recombiner – PAR and Filtered Containment

**Simulation time Xe-133 m Bq Cs-137 Bq Ba-133 m Bq Te-127 Bq** C1 – 2 h 2,11E+10 5,28E+01 1,40E+04 3,65E+06 C2 – 168 h 8,17E+19 1,56E+07 7,39E+10 2,00E+12

c. Loss of suction from sump and residual heat removal – RHR;

conditions are as follows:

available; and

*Source term for scenarios C1 and C2.*

**Table 1.**

**Figure 2.**

**91**

*Flow path (CV990 and CV991) of the radionuclides to the atmosphere.*

a. Turbine bypass unavailable;

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

e. All accumulators are available.

b. Condenser not available;

Therefore, the dispersion study can generate results with impacts on the occupation and dimensioning of the site. Also in this context, it is important to remember that the severity of a possible accident associated with nuclear facilities in general is strongly linked to population density of the regions around the facility, as well as, evacuation policy, medical treatment, and other health measures which should be taken to mitigate its radiological consequences.

#### **2. Description of the accident**

A typical PWR modeling was developed by the German company, GRS (Global Research for Safety), and supplied to CNEN, as shown in **Figure 1**. This modeling was chosen, in this study, for the purpose of performing an independent analysis of severe accidents in ANGRA 2 nuclear power plant (NPP). However, although this typical PWR of the GRS is similar to ANGRA 2 NPP, they are not identical, so that an adaptation of the modeling was necessary in order to apply it for analysis of severe accidents in NPP, ANGRA 2. For this reason, a considerable part of this study was dedicated for the adaptation of the modeling.

#### **2.1 Description of the simulated accident scenario**

In this study is presented a loss of coolant accident, in other words, Small Break LOCA (SBLOCA), in the hot leg. In this case, it is postulated that the rupture occurs in loop 1. The area of the rupture in the hot leg is 380 cm<sup>2</sup> . The total flow area of the piping connected to the pressure vessel is 4418 cm<sup>2</sup> , so that the area of the rupture is less than 10% of the piping area; reason why the rupture of 380 cm<sup>2</sup> is considered small.

The SBLOCA alone would not be sufficient to result in a severe accident, as long as the various plant safety systems were available. It was, therefore, necessary to add some aggravating conditions in order to cause the mentioned severe accident.

**Figure 1.** *PWR primary and secondary circuit modeling.*

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*

These conditions are conventionally known as boundary conditions. The postulated conditions are as follows:


These boundary conditions, together with the primary circuit breakage, are sufficient to result in total core melting. Two mitigating measures were modeled in this study: Passive Autocatalytic Recombiner – PAR and Filtered Containment


#### **Table 1.**

radioactivity in the vicinity of the plant, representing a threat to the society and

should be taken to mitigate its radiological consequences.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

was dedicated for the adaptation of the modeling.

**2.1 Description of the simulated accident scenario**

**2. Description of the accident**

is considered small.

**Figure 1.**

**90**

*PWR primary and secondary circuit modeling.*

Therefore, the dispersion study can generate results with impacts on the occupation and dimensioning of the site. Also in this context, it is important to remember that the severity of a possible accident associated with nuclear facilities in general is strongly linked to population density of the regions around the facility, as well as, evacuation policy, medical treatment, and other health measures which

A typical PWR modeling was developed by the German company, GRS (Global Research for Safety), and supplied to CNEN, as shown in **Figure 1**. This modeling was chosen, in this study, for the purpose of performing an independent analysis of severe accidents in ANGRA 2 nuclear power plant (NPP). However, although this typical PWR of the GRS is similar to ANGRA 2 NPP, they are not identical, so that an adaptation of the modeling was necessary in order to apply it for analysis of severe accidents in NPP, ANGRA 2. For this reason, a considerable part of this study

In this study is presented a loss of coolant accident, in other words, Small Break

the rupture is less than 10% of the piping area; reason why the rupture of 380 cm<sup>2</sup>

The SBLOCA alone would not be sufficient to result in a severe accident, as long as the various plant safety systems were available. It was, therefore, necessary to add some aggravating conditions in order to cause the mentioned severe accident.

. The total flow

, so that the area of

LOCA (SBLOCA), in the hot leg. In this case, it is postulated that the rupture

occurs in loop 1. The area of the rupture in the hot leg is 380 cm<sup>2</sup>

area of the piping connected to the pressure vessel is 4418 cm<sup>2</sup>

local life.

*Source term for scenarios C1 and C2.*

#### **Figure 2.**

*Flow path (CV990 and CV991) of the radionuclides to the atmosphere.*

Venting System – FCVS, with the purpose of evaluating their validity and efficiencies.

The inputs of the simulations performed for this work were elaborated using the input provided by GRS. This original input was modified according to the imposed conditions. It was assumed that the rupture occurs only in the Control Volume (CV) number 200, that is, in CV200 of loop 1, shown in **Figure 1**.

The flow path, given by FL070, has its opening and closing controlled by a CF660 control function. The setpoint for the valve opening is 7.0 bar and occurs after 168 h of simulation, but the setpoint for closing has not been implemented. It should be noted that the opening of the CV990 flow path, see **Figure 2**, occurs only after 168 h of simulation.

The flow path CV990 and CV991, see **Figure 2**, contains filters for aerosols and for fission products vapors so that some fraction of radionuclides are withdrawn through these filters when the vapors and aerosols are transported along of the flow path. A single filter can remove only one type of fission products, whether aerosols or vapors, but not both.

The radionuclide package of the MELCOR code contains a simple filter model which efficiency is defined by the global decontamination factor (DFG) determined by the user. The decontamination value assumed for aerosol filter was 1000, and for vapors of fission products, vapors were 100, which equated to 99.9 and 99.0% filtration, respectively.

#### **2.2 Source term**

The source term represents the radioactive inventory located in a system, equipment or component, which serves as a reference to evaluate the safety aspects in different conditions of operation of the reactor. It also represents one of the most important design bases for the study of installation performance, distribution of fission products in reactor systems, and in the environment in case of accidents.

**4. Methodology**

*Topography of the study area.*

**Figure 3.**

atmosphere.

**93**

**4.1 Atmospheric model: WRF/CALMET**

concentration and deposition fluxes [15].

The use of mathematical models facilitates the simulation process of transport

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

The WRF – Weather Research and Forecasting, is a numerical modeling system,

The CALMET – California Meteorological Model, is a three-dimensional meteo-

The CALMET is classified as a diagnostic meteorological model that incorporates meteorological observations and/or outputs of predictive meteorological models to

developed for the weather forecasting and study of atmospheric phenomena of micro and mesoscale. Its development is the result of the collaboration between US research and government agencies centers: National Center for Atmospheric Research (NCAR), National Centers for Environmental Prediction (NCEP), National Oceanic and Atmospheric Administration (NOAA), US Departement of Defense, Oklahoma University, and Federal Aviation Administration (FAA).

rological model that is integrated with the dispersion model – CALPUFF. The CALPOST is a post-processing package that makes possible to calculate the average

mechanisms and pollutant deposition. These models provide a conservative theoretical estimate of the concentration levels of pollutants in the air, making it possible to evaluate the spatial and temporal evolution of these pollutants in the

Knowing the source term, there is the possibility of modeling radionuclide dispersion, calculating radiation concentrations and doses, as well as spatializing affected areas and environments. The source term of the present study is based on the radionuclides used in the MELCOR output, being this Xenon-133 m, Césiso-137, Barium-133 m, and Tellurium-127. **Table 1** shows the activities of the radionuclides for the scenarios C1 – simulation time of 2 h and C2 – simulation time of 168 h.

#### **3. Characterization of the study area**

The study area is placed in the south coast of Rio de Janeiro State, known region as "Costa Verde," in the city of Angra dos Reis, where the CNAAA is placed zone (23 k), latitude-UTM (7455581.00 m S), and longitude-UTM (555471.00 m E). The region geomorphology is extremely hilly, with quite steep slopes, high or negatives steepness and differences in elevations up to 800 m.

The geomorphology has two units of topography, one formed by ridge and scarps, and the other, by lowlands. The scarps has an average gap of 700 m and are dissected by half parallel valleys, which alternate with stretches of deep cutouts, between the rivers that flow down the mountain. **Figure 3** [14] shows the topography of the region.

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*

**Figure 3.** *Topography of the study area.*

#### **4. Methodology**

Venting System – FCVS, with the purpose of evaluating their validity and

number 200, that is, in CV200 of loop 1, shown in **Figure 1**.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

The inputs of the simulations performed for this work were elaborated using the input provided by GRS. This original input was modified according to the imposed conditions. It was assumed that the rupture occurs only in the Control Volume (CV)

The flow path, given by FL070, has its opening and closing controlled by a CF660 control function. The setpoint for the valve opening is 7.0 bar and occurs after 168 h of simulation, but the setpoint for closing has not been implemented. It should be noted that the opening of the CV990 flow path, see **Figure 2**, occurs only

The flow path CV990 and CV991, see **Figure 2**, contains filters for aerosols and for fission products vapors so that some fraction of radionuclides are withdrawn through these filters when the vapors and aerosols are transported along of the flow path. A single filter can remove only one type of fission products, whether aerosols

The radionuclide package of the MELCOR code contains a simple filter model which efficiency is defined by the global decontamination factor (DFG) determined by the user. The decontamination value assumed for aerosol filter was 1000, and for vapors of fission products, vapors were 100, which equated to 99.9 and 99.0%

The source term represents the radioactive inventory located in a system, equipment or component, which serves as a reference to evaluate the safety aspects in different conditions of operation of the reactor. It also represents one of

Knowing the source term, there is the possibility of modeling radionuclide dispersion, calculating radiation concentrations and doses, as well as spatializing affected areas and environments. The source term of the present study is based on the radionuclides used in the MELCOR output, being this Xenon-133 m, Césiso-137, Barium-133 m, and Tellurium-127. **Table 1** shows the activities of the radionuclides for the scenarios C1 – simulation time of 2 h and C2 – simulation

The study area is placed in the south coast of Rio de Janeiro State, known region as "Costa Verde," in the city of Angra dos Reis, where the CNAAA is placed zone (23 k), latitude-UTM (7455581.00 m S), and longitude-UTM (555471.00 m E). The region geomorphology is extremely hilly, with quite steep slopes, high or negatives

The geomorphology has two units of topography, one formed by ridge and scarps, and the other, by lowlands. The scarps has an average gap of 700 m and are dissected by half parallel valleys, which alternate with stretches of deep cutouts, between the rivers that flow down the mountain. **Figure 3** [14] shows the topogra-

the most important design bases for the study of installation performance, distribution of fission products in reactor systems, and in the environment in

efficiencies.

after 168 h of simulation.

or vapors, but not both.

filtration, respectively.

**2.2 Source term**

case of accidents.

time of 168 h.

phy of the region.

**92**

**3. Characterization of the study area**

steepness and differences in elevations up to 800 m.

The use of mathematical models facilitates the simulation process of transport mechanisms and pollutant deposition. These models provide a conservative theoretical estimate of the concentration levels of pollutants in the air, making it possible to evaluate the spatial and temporal evolution of these pollutants in the atmosphere.

#### **4.1 Atmospheric model: WRF/CALMET**

The WRF – Weather Research and Forecasting, is a numerical modeling system, developed for the weather forecasting and study of atmospheric phenomena of micro and mesoscale. Its development is the result of the collaboration between US research and government agencies centers: National Center for Atmospheric Research (NCAR), National Centers for Environmental Prediction (NCEP), National Oceanic and Atmospheric Administration (NOAA), US Departement of Defense, Oklahoma University, and Federal Aviation Administration (FAA).

The CALMET – California Meteorological Model, is a three-dimensional meteorological model that is integrated with the dispersion model – CALPUFF. The CALPOST is a post-processing package that makes possible to calculate the average concentration and deposition fluxes [15].

The CALMET is classified as a diagnostic meteorological model that incorporates meteorological observations and/or outputs of predictive meteorological models to

produce, through objective analysis techniques, velocity, temperature, and other variables necessary for simulations with the CALPUFF model.

The CALMET requires that the meteorological and geophysical data are in specific formats before being used. The processing of these data is then performed with the aid of the preprocessors which prepare the data for assimilation in the CALMET processor.

#### **4.2 Dispersion model: CALPUFF**

The modeling of the atmospheric dispersion is a technique of simulation of the phenomena that occurs in nature, allowing to estimate the concentration of the pollutants in a set of points, based on a set of variables that influence them. The modeling of atmospheric dispersion is useful not only in the identification of emitting sources but also in the management of gaseous effluents and air quality, constituting one of the techniques of evaluation of air quality indicated by the environmental legislation.

The California Puff Model CALPUFF is a non-stationary puff model for dispersion simulations that can be used for a wide variety of applications in air quality modeling studies. The model was proposed and reviewed by Scire et al. [15] and has been adopted by the United States Environmental Protection Agency – EPA as a regulatory model for environmental impact studies covering distances of 50– 300 km and including topography and complex meteorological systems.

The CALPUFF software is entirely public, designed to simulate release into the atmosphere, and is used to predict the effects of an accident, thus enabling effective emergency planning.

*4.4.1 Inhalation dose calculation*

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

document, as observed in Eq. (1).

*Din* = Inhalation dose, Sv;

*4.4.2 Immersion dose calculation*

document, as observed in Eq. (2).

*in* = Immersion dose, Sv;

Where:

P

**Figure 4.**

*i*

pollutant).

Where:

*D* P

**95**

*i*

The inhalation dose calculation was based on the IAEA-TecDoc-1162 [18]

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

*e g*ð Þ*<sup>i</sup>* = Inhalation dose coefficient – Sv/Bq (was used e(g)i for adult e(g) i > 17 years), according to Regulatory Position CNEN 3.01/011:2011 [19];

*T* = Exposure time – h (time the individual of the public will be exposed to the

The immersion dose calculation was based on the IAEA-TecDoc-1162 [18]

*Dim* <sup>¼</sup> <sup>X</sup> *i*

i > 17 years), according to Regulatory Position CNEN 3.01/011:2011 [19]; and

∁*<sup>i</sup>* = Concentration of each radionuclide – Bq/m<sup>3</sup>

*e g*ð Þ*<sup>i</sup>* = Immersion dose coefficient – Sv.m3

∁*<sup>i</sup>* ∗ *e g*ð Þ*<sup>i</sup>* ∗ *Br* ∗ *T* (1)

/h [18]; and

∁*<sup>i</sup>* ∗ *e g*ð Þ*<sup>i</sup>* ∗ *T* (2)

/Bq.h (was used e(g)i for adult e(g)

;

;

*Din* <sup>¼</sup> <sup>X</sup> *i*

*Regions in EPZ that will be considered the dose calculation and measures protective.*

∁*<sup>i</sup>* = Concentration of each radionuclide – Bq/m<sup>3</sup>

*Br* = Breathing rate, whose value considered 1.5 m<sup>3</sup>

#### **4.3 WRF/CALMET coupling**

The choice of the WRF model configuration, as well as the domains, spatial resolution, and grid nesting, were made to obtain necessary meteorological data for the INPUT of the CALMET model. The initial and boundary conditions assimilated by the WRF are derived from the GFS (Global Forecasting System Model) of the National Centers for Environment Prediction (NCEP), whose spatial resolution is 0.5° (55 km) and a time resolution of 3 h. To compose the GFS domain, both horizontally and vertically, a model for interpolation of the data is used. More details about this model can be found in KALNAY et al. [16]. The GFS data can be obtained for free from the electronic address. Link: https://www.ncdc.noaa.gov/da ta-access/model-data/model-datasets.

The meteorological data of the January month of 2009 was used for the simulation with the WRF. The January month data was chosen, due to being the most recent data obtained from Electronuclear for the four Angra towers.

The grid used by CALMET has a domain of 80 km and a cell number of 229 229. In the region of the NPP, the wind field data of the Electronuclear Towers was used, which radius of influence is 5 km.

#### **4.4 Whole body dose calculation**

The whole body dose is the contribution of the internal dose (inhalation or ingestion) added to the external dose (plume immersion) [17]. The calculations of the exposure pathways are in equations (Eqs. (1) and (2)), respectively. For the present study, the whole body dose analysis considered the plume concentration value and exposure time in the Emergency Planning Zones – EPZ, as shown in **Figure 4**.

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*

**Figure 4.** *Regions in EPZ that will be considered the dose calculation and measures protective.*

#### *4.4.1 Inhalation dose calculation*

The inhalation dose calculation was based on the IAEA-TecDoc-1162 [18] document, as observed in Eq. (1).

$$D\_{in} = \sum\_{i} \mathbb{C}\_{i} \ast e(\mathbf{g})\_{i} \ast B\_{r} \ast T \tag{1}$$

Where:

produce, through objective analysis techniques, velocity, temperature, and other

The CALMET requires that the meteorological and geophysical data are in specific formats before being used. The processing of these data is then performed with the aid of the preprocessors which prepare the data for assimilation in the CALMET

The modeling of the atmospheric dispersion is a technique of simulation of the phenomena that occurs in nature, allowing to estimate the concentration of the pollutants in a set of points, based on a set of variables that influence them. The modeling of atmospheric dispersion is useful not only in the identification of emitting sources but also in the management of gaseous effluents and air quality, constituting one of the techniques of evaluation of air quality indicated by the

The California Puff Model CALPUFF is a non-stationary puff model for dispersion simulations that can be used for a wide variety of applications in air quality modeling studies. The model was proposed and reviewed by Scire et al. [15] and has been adopted by the United States Environmental Protection Agency – EPA as a regulatory model for environmental impact studies covering distances of 50– 300 km and including topography and complex meteorological systems.

The CALPUFF software is entirely public, designed to simulate release into the atmosphere, and is used to predict the effects of an accident, thus enabling effective

The choice of the WRF model configuration, as well as the domains, spatial resolution, and grid nesting, were made to obtain necessary meteorological data for the INPUT of the CALMET model. The initial and boundary conditions assimilated by the WRF are derived from the GFS (Global Forecasting System Model) of the National Centers for Environment Prediction (NCEP), whose spatial resolution is 0.5° (55 km) and a time resolution of 3 h. To compose the GFS domain, both horizontally and vertically, a model for interpolation of the data is used. More details about this model can be found in KALNAY et al. [16]. The GFS data can be obtained for free from the electronic address. Link: https://www.ncdc.noaa.gov/da

The meteorological data of the January month of 2009 was used for the simulation with the WRF. The January month data was chosen, due to being the most

The grid used by CALMET has a domain of 80 km and a cell number of 229 229. In the region of the NPP, the wind field data of the Electronuclear Towers was

The whole body dose is the contribution of the internal dose (inhalation or ingestion) added to the external dose (plume immersion) [17]. The calculations of the exposure pathways are in equations (Eqs. (1) and (2)), respectively. For the present study, the whole body dose analysis considered the plume concentration value and exposure time in the Emergency Planning Zones – EPZ, as shown in

recent data obtained from Electronuclear for the four Angra towers.

variables necessary for simulations with the CALPUFF model.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

processor.

**4.2 Dispersion model: CALPUFF**

environmental legislation.

emergency planning.

**4.3 WRF/CALMET coupling**

ta-access/model-data/model-datasets.

used, which radius of influence is 5 km.

**4.4 Whole body dose calculation**

**Figure 4**.

**94**

*Din* = Inhalation dose, Sv;

P *i* ∁*<sup>i</sup>* = Concentration of each radionuclide – Bq/m<sup>3</sup> ;

$$\mathbf{e(g)}\_i = \text{Inhalation dose coefficient - Sv/Bq (was used e(g))}\text{ for adult e(g)}$$

i > 17 years), according to Regulatory Position CNEN 3.01/011:2011 [19]; *Br* = Breathing rate, whose value considered 1.5 m<sup>3</sup> /h [18]; and

*T* = Exposure time – h (time the individual of the public will be exposed to the pollutant).

#### *4.4.2 Immersion dose calculation*

The immersion dose calculation was based on the IAEA-TecDoc-1162 [18] document, as observed in Eq. (2).

$$D\_{im} = \sum\_{i} \mathbb{C}\_{i} \* e(\mathbf{g})\_{i} \* T \tag{2}$$

Where:

*D in* = Immersion dose, Sv;

P *i* ∁*<sup>i</sup>* = Concentration of each radionuclide – Bq/m<sup>3</sup> ;

*e g*ð Þ*<sup>i</sup>* = Immersion dose coefficient – Sv.m3 /Bq.h (was used e(g)i for adult e(g) i > 17 years), according to Regulatory Position CNEN 3.01/011:2011 [19]; and

*T* = Exposure time – h (time the individual of the public will be exposed to the pollutant).

#### **5. Results**

#### **5.1 Pollutant transport model: CALPUFF**

The simulations were performed on CALPUFF assuming a point source of emissions related to the chimney of the NPP Angra 2, which height considered was 155 m. The emission rate will follow scenarios C1 and C2, with the constant release rate of the radionuclides released into the atmosphere.

#### *5.1.1 Radionuclides release for scenario C1*

The simulation was performed from 05/01/2009 to 08/01/2009 at 06:00 h. It was considered that all the radionuclides of **Table 1**, after release, behave according to the region's wind field during the entire simulation period, 72 h. The respective plume concentration periods that were considered: 1, 3, and 72 h, for each EPZ, see **Tables 2**–**5**. **Figure 5** shows the wind field and radionuclides transport from **Table 1** for scenario C1.

#### *5.1.2 Radionuclides release for scenario C2*

The simulation was performed from 05/01/2009 to 08/01/2009 at 06:00 h. It was considered that all the radionuclides of **Table 1**, after release, behave according


#### **Table 2.**

*Radionuclides concentration in EPZ-3 km (Praia Brava).*


#### **Table 3.**

*Radionuclides concentration in EPZ-5 km (Frade).*


to the region's wind field during the entire simulation period, 72 h. The respective plume concentration periods that were considered: 1, 3, and 72 h, for each EPZ, see **Tables 6**–**9**. **Figure 6** shows the wind field and radionuclides transport from

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 5,92E+13 1,11E+01 5,27E+04 1,43E+06 3 h 2,34E+13 4,37E+00 2,07E+04 5,60E+05 72 h 2,18E+12 3,58E-01 1,70E+03 4,60E+04

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 1,09E+03 1,49E-06 3,96E-04 1,03E-01 3 h 8,29E+02 1,16E-06 3,07E-04 8,01E-02 72 h 2,21E+02 2,83E-07 7,51E-05 1,96E-02

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

**Table 1** for scenario C2.

**Table 5.**

**Figure 5.**

**Table 6.**

**97**

*Radionuclides concentration in EPZ-15 km (Angra dos Reis).*

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

**5.2 Whole body dose in EPZ**

*Concentration and wind field for scenario C1.*

• Whole body dose analysis for Scenario C1

*Radionuclides concentration in EPZ-3 km (Praia Brava).*

#### **Table 4.**

*Radionuclides concentration in EPZ-10 km (Mambucaba).*

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*


**Table 5.**

*T* = Exposure time – h (time the individual of the public will be exposed to the

The simulations were performed on CALPUFF assuming a point source of emissions related to the chimney of the NPP Angra 2, which height considered was 155 m. The emission rate will follow scenarios C1 and C2, with the constant release rate

The simulation was performed from 05/01/2009 to 08/01/2009 at 06:00 h. It was considered that all the radionuclides of **Table 1**, after release, behave according to the region's wind field during the entire simulation period, 72 h. The respective plume concentration periods that were considered: 1, 3, and 72 h, for each EPZ, see **Tables 2**–**5**. **Figure 5** shows the wind field and radionuclides transport from **Table 1**

The simulation was performed from 05/01/2009 to 08/01/2009 at 06:00 h. It was considered that all the radionuclides of **Table 1**, after release, behave according

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 1,53E+04 3,76E-05 9,97E-03 2,60E+00 3 h 6,04E+03 1,48E-05 3,92E-03 1,02E+00 72 h 5,64E+02 1,21E-06 3,22E-04 8,39E-02

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 1,00E+04 2,37E-05 6,29E-03 1,64E+00 3 h 4,30E+03 9,22E-06 2,45E-03 6,37E-01 72 h 1,08E+03 2,15E-06 5,71E-04 1,49E-01

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 1,54E+03 3,55E-06 9,41E-04 2,45E-01 3 h 9,34E+02 2,16E-06 5,74E-04 1,50E-01 72 h 1,60E+02 2,92E-07 7,75E-05 2,02E-02

pollutant).

**5. Results**

for scenario C1.

**Table 2.**

**Table 3.**

**Table 4.**

**96**

**5.1 Pollutant transport model: CALPUFF**

*5.1.1 Radionuclides release for scenario C1*

*5.1.2 Radionuclides release for scenario C2*

*Radionuclides concentration in EPZ-3 km (Praia Brava).*

*Radionuclides concentration in EPZ-5 km (Frade).*

*Radionuclides concentration in EPZ-10 km (Mambucaba).*

of the radionuclides released into the atmosphere.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

*Radionuclides concentration in EPZ-15 km (Angra dos Reis).*

**Figure 5.** *Concentration and wind field for scenario C1.*


#### **Table 6.**

*Radionuclides concentration in EPZ-3 km (Praia Brava).*

to the region's wind field during the entire simulation period, 72 h. The respective plume concentration periods that were considered: 1, 3, and 72 h, for each EPZ, see **Tables 6**–**9**. **Figure 6** shows the wind field and radionuclides transport from **Table 1** for scenario C2.

#### **5.2 Whole body dose in EPZ**

• Whole body dose analysis for Scenario C1

#### *Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*


#### **Table 7.**

*Radionuclides concentration in EPZ-5 km (Frade).*


#### **Table 8.**

*Radionuclides concentration in EPZ-10 km (Mambucaba).*


For the dose calculation, were used the equations (Eqs. (1) and (2)), and the exposure time to individual members of the public was 1, 3, and 72 h. It was considered that these individual members of the public are not under any protection and the plume exposure is 100%. **Table 10** shows the dose values for each

**EPZ 5 km Região do Frade (mSv)**

**EPZ 5 km Região do Frade (mSv)**

1 h 2,73E+05 1,79E+05 2,75E+04 1,95E+04 3 h 3,24E+05 2,30E+05 5,00E+04 4,44E+04 72 h 7,25E+05 1,39E+06 2,05E+05 2,84E+05

1 h 7,06E-05 4,63E-05 7,12E-06 5,04E-06 3 h 8,38E-05 5,96E-05 1,29E-05 1,15E-05 72 h 1,94E-04 3,60E-04 5,31E-05 7,35E-05

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

**EPZ 10 km Mambucaba (mSv)**

**EPZ 10 km Mambucaba (mSv)** **EPZ 15 km Angra dos Reis (mSv)**

**EPZ 15 km Angra dos Reis (mSv)**

For the dose calculation, were used the equations (Eqs. (1) and (2)), and the exposure time to individual members of the public was 1, 3, and 72 h. It was considered that these individual members of the public are not under any protection and the plume exposure is 100%. **Table 11** shows the dose values for each

According to the PEE/RJ [20] – External Emergency Plan of the State of Rio de Janeiro, in order to prioritize the risks and facilitate the planning and implementation of protection measures recommended by CNEN, the concept of EPZ was adopted. The Emergency Planning Zones were subdivided into circular crowns as shown in **Figure 4**. According to the PEE/RJ, the preventive evacuation of the population constitutes an effective protection measure up to the distance of 5 km around the plant. From this distance, no additional benefit will be obtained with the preventive evacuation. Thus, to the EPZ 10 km and EPZ 15 km, it is preferable to recommend, in the short term, that the population remains sheltered. In this sense, the existing

EPZ 3 km: circumscribed area from 3 km centered on the nuclear unit of

exposure time, as well as for each EPZ.

**EPZ 3 km Praia Brava (mSv)**

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

**EPZ 3 km Praia Brava (mSv)**

*Whole body dose in EPZ for scenario C1.*

*Whole body dose in EPZ for scenario C2.*

exposure time, as well as for each EPZ.

**6. Conclusions**

**C1 exposure time**

**Table 10.**

**C2 exposure time**

**Table 11.**

rays are classified as follows:

**99**

• Preventive action zones

CNAAA, so the property area of ELETRONUCLEAR.

• Whole body dose analysis for Scenario C2

#### **Table 9.**

*Radionuclides concentration in EPZ-15 km (Angra dos Reis).*

**Figure 6.** *Concentration and wind field for scenario C2.*

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*


**Table 10.**

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 5,97E+12 1,05E+00 4,97E+03 1,34E+05 3 h 3,62E+12 6,39E-01 3,03E+03 8,20E+04 72 h 6,18E+11 8,64E-02 4,09E+02 1,11E+04

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 3,88E+13 7,01E+00 3,32E+04 8,99E+05 3 h 1,66E+13 2,72E+00 1,29E+04 3,49E+05 72 h 4,19E+12 6,36E-01 3,01E+03 8,16E+04

**Simulation time Xe-133 m Bq/m<sup>3</sup> Cs-137 Bq/m3 Ba-133 m Bq/m<sup>3</sup> Te-127 Bq/m<sup>3</sup>** 1 h 4,23E+12 4,42E-01 2,09E+03 5,66E+04 3 h 3,21E+12 3,42E-01 1,62E+03 4,39E+04 72 h 8,57E+11 8,37E-02 3,96E+02 1,07E+04

**Table 8.**

**Table 7.**

**Table 9.**

**Figure 6.**

**98**

*Concentration and wind field for scenario C2.*

*Radionuclides concentration in EPZ-10 km (Mambucaba).*

*Radionuclides concentration in EPZ-5 km (Frade).*

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

*Radionuclides concentration in EPZ-15 km (Angra dos Reis).*

*Whole body dose in EPZ for scenario C1.*


**Table 11.**

*Whole body dose in EPZ for scenario C2.*

For the dose calculation, were used the equations (Eqs. (1) and (2)), and the exposure time to individual members of the public was 1, 3, and 72 h. It was considered that these individual members of the public are not under any protection and the plume exposure is 100%. **Table 10** shows the dose values for each exposure time, as well as for each EPZ.

• Whole body dose analysis for Scenario C2

For the dose calculation, were used the equations (Eqs. (1) and (2)), and the exposure time to individual members of the public was 1, 3, and 72 h. It was considered that these individual members of the public are not under any protection and the plume exposure is 100%. **Table 11** shows the dose values for each exposure time, as well as for each EPZ.

#### **6. Conclusions**

According to the PEE/RJ [20] – External Emergency Plan of the State of Rio de Janeiro, in order to prioritize the risks and facilitate the planning and implementation of protection measures recommended by CNEN, the concept of EPZ was adopted. The Emergency Planning Zones were subdivided into circular crowns as shown in **Figure 4**.

According to the PEE/RJ, the preventive evacuation of the population constitutes an effective protection measure up to the distance of 5 km around the plant. From this distance, no additional benefit will be obtained with the preventive evacuation. Thus, to the EPZ 10 km and EPZ 15 km, it is preferable to recommend, in the short term, that the population remains sheltered. In this sense, the existing rays are classified as follows:

• Preventive action zones

EPZ 3 km: circumscribed area from 3 km centered on the nuclear unit of CNAAA, so the property area of ELETRONUCLEAR.

EPZ 5 km: circular crown, centered on the nuclear unit of CNAAA, with a 5 km outside radius and inner radius of 3 km. This EPZ 5 km is defined as the impact zone.

It is observed in **Table 13** that for the Preventive Action Zones (EPZ 3 km and EPZ 5 km) and Environmental Control Zones (EPZ 10 km and EPZ 15 km), the recommendations of the protective measures that best meet the dose levels is Evacuation. The Scenario C2 is characterized as a General Emergency, having as a

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

• Scenario C1 it is observed the occurrence of an Area Emergency, having as a

• Scenario C2 it is observed the occurrence of a General Emergency, having as a

• The impact zone that is currently 5 km, covering the Preventive Action Zones, for scenario C2, has the extension of this impact zone for distances beyond

• Analyzing the C1 and C2 scenarios, it is inferred that the faster the accident is mitigated, the lower will be the radiological consequences and therefore, the

Advance planning is essential to identify potential problems that may occur in

• Community familiarity with alerting methods, the nature of the hazard and

However, if environmental monitoring confirms that the population's exposure will extend beyond a few days, justifying other protection actions beyond shelter and evacuation, temporary or permanent resettlement should be considered [22].

an evacuation. The NRC case study cites the following aspects of planning as

measure of the local authorities the evacuation of the population in EPZ.

In summary, it is possible to conclude that:

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

protective measure in all EPZ, Evacuation;

5 km; and

protective measure in all EPZ, Sheltered in place.

actions to the protective measures will be lighter.

contributing to efficiency and effectiveness of evacuation [23]:

• Use of multiple forms of emergency communications;

• High level of cooperation among agencies;

evacuation procedures;

**101**

• Community communication; and

• Well-trained emergency responders.

• Environmental control zones

EPZ 10 km: circular crown, centered on the nuclear unit of CNAAA with a 10 km outer radius and inner radius of 5 km.

EPZ 15 km: circular crown, centered on the nuclear unit of CNAAA with a 15 km outer radius and inner radius of 10 km.

According to a CNEN study [21], the protection measures for CNAAA can be divided as follows:


Based on the dose values for sheltered and evacuation of Regulatory Position CNEN 3.01/006: 2011 [22], whose values are 10 mSv for sheltered and 50 mSv for evacuation, will be recommended the protection measures for each EPZ for scenarios C1 and C2, as shown in **Tables 12** and **13**. The recommendations in **Table 12** were based on the projected doses of **Table 10** and the recommendations in **Table 13** were based on the projected doses of **Table 11**.

It is observed in **Table 12** that for the Preventive Action Zones (EPZ 3 km and EPZ 5 km) and Environmental Control Zones (EPZ 10 km and EPZ 15 km), the recommendations of the protective measures that best meet the dose levels is Sheltered in place. The Scenario C1 is characterized as Area Emergency, having as a measure of the local authorities the notification to the population to remain in their residences or workplace, awaiting future instructions.


**Table 12.**

*Recommendations for protection measures in EPZ for scenario C1.*


**Table 13.**

*Recommendations for protection measures in EPZ for scenario C2.*

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*

It is observed in **Table 13** that for the Preventive Action Zones (EPZ 3 km and EPZ 5 km) and Environmental Control Zones (EPZ 10 km and EPZ 15 km), the recommendations of the protective measures that best meet the dose levels is Evacuation. The Scenario C2 is characterized as a General Emergency, having as a measure of the local authorities the evacuation of the population in EPZ.

In summary, it is possible to conclude that:

EPZ 5 km: circular crown, centered on the nuclear unit of CNAAA, with a 5 km outside radius and inner radius of 3 km. This EPZ 5 km is defined as the impact

EPZ 10 km: circular crown, centered on the nuclear unit of CNAAA with a

EPZ 15 km: circular crown, centered on the nuclear unit of CNAAA with a 15 km

According to a CNEN study [21], the protection measures for CNAAA can be

a. Area emergency: EPZ 3 km and EPZ 5 km (notification to the population to remain in residences or workplace, awaiting instructions) and EPZ 10 km and EPZ 15 km (notification to the population to keep on the alert for further

b. General Emergency: EPZ 3 km (population evacuation), EPZ 5 km (keep population sheltered), EPZ 10 km and EPZ 15 km (notification to the population to remain in the residences or workplace, awaiting instructions).

Based on the dose values for sheltered and evacuation of Regulatory Position CNEN 3.01/006: 2011 [22], whose values are 10 mSv for sheltered and 50 mSv for evacuation, will be recommended the protection measures for each EPZ for scenarios C1 and C2, as shown in **Tables 12** and **13**. The recommendations in **Table 12** were based on the projected doses of **Table 10** and the recommendations in

It is observed in **Table 12** that for the Preventive Action Zones (EPZ 3 km and EPZ 5 km) and Environmental Control Zones (EPZ 10 km and EPZ 15 km), the recommendations of the protective measures that best meet the dose levels is Sheltered in place. The Scenario C1 is characterized as Area Emergency, having as a measure of the local authorities the notification to the population to remain in their

> **EPZ 10 km Mambucaba**

> **EPZ 10 km Mambucaba**

**EPZ 15 km Angra dos Reis**

**EPZ 15 km Angra dos Reis**

**EPZ 5 km Frade**

1 h Sheltered Sheltered Sheltered Sheltered 3 h Sheltered Sheltered Sheltered Sheltered 72 h Sheltered Sheltered Sheltered Sheltered

> **EPZ 5 km Frade**

1 h Evacuation Evacuation Evacuation Evacuation 3 h Evacuation Evacuation Evacuation Evacuation 72 h Evacuation Evacuation Evacuation Evacuation

instructions, keeping their normal activities); and

**Table 13** were based on the projected doses of **Table 11**.

residences or workplace, awaiting future instructions.

**EPZ 3 km Praia Brava**

*Recommendations for protection measures in EPZ for scenario C1.*

*Recommendations for protection measures in EPZ for scenario C2.*

**EPZ 3 km Praia Brava**

zone.

• Environmental control zones

10 km outer radius and inner radius of 5 km.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

outer radius and inner radius of 10 km.

divided as follows:

**C1 exposure time**

**C2 exposure time**

**Table 12.**

**Table 13.**

**100**


Advance planning is essential to identify potential problems that may occur in an evacuation. The NRC case study cites the following aspects of planning as contributing to efficiency and effectiveness of evacuation [23]:


However, if environmental monitoring confirms that the population's exposure will extend beyond a few days, justifying other protection actions beyond shelter and evacuation, temporary or permanent resettlement should be considered [22].

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**References**

October 2019]

2003-2005

2012

[1] Corey GR. A brief review of the accident at three mile island. IAEA Bulletin, Vol. 21, no.5. Available from: https://inis.iaea.org/search/search.aspx? orig\_q=RN:11554960 [Accessed: 20

*DOI: http://dx.doi.org/10.5772/intechopen.92200*

[9] Gauntt RO, Cole RK, et al. MELCOR Computer Code Manuals. Vo1. 2: Reference Manuals, Version 1.8.5, Prepared by Sandia National

Laboratories (SNL) for the U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, NUREG/

[10] Allison CM, et al. SCDAP/RELAPS/ MOD3.1 code manual. Volume II: Damage Progression Model Theory, Technical Report NUREG/CR-6150,

[11] Alliso NCM, et al. SCDAP/RELAPS/ MOD3.2 Code Manual. Volume I-V, NUREG/CR-6150, INEL 96/0422,

[12] MAAP4: Modular Accident Analysis Program for LWR Plants. Code Manual Vols. 1–4, Prepared by Fauske &

Associates, Inc., Burr Ridge, IL, USA for the EPRI, Palo Alto, CA, USA; 1994

[13] Lamarsh JR. Introduction to Nuclear Reactor Theory. New york University: Addison-Wesley Publishing Company;

[14] Aguiar AS, Lamego Simoes Filho FF,

Moraes NO. Station Blackout in unit 1 and analysis of the wind field in the region of Angra dos Reis. Annals of Nuclear Energy [Internet]. Elsevier BV; April 2015;**78**:93-103. DOI: 10.1016/j.

[15] Scire JS et al. A user's Guide for the CALPUFF Dispersion Model. (Version 5). Land O'Lakes, Florida, USA: Earth Tech.

[16] Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, et al. The NCEP/NCAR 40-year reanalysis project. Bulletin of the American Meteorological Society. 1996;**77**(3):

Alvim ACM, Pimentel LCG,

anucene.2014.12.010

Inc; 2000

437-470

CR-6119, Vo1. 2, Re'v. 2; 2000

EGG-2720. USA: INEL; 1993

Revision 1; 1997

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear…*

1975

[2] Chernobyl's Legacy. Health, Environmental and Socio-Economic Impacts and Recommendations to the Governments of Belarus, the Russian Federation and Ukraine. Vienna: IAEA;

[3] Gauntt R, Kalinich D, Cardoni J, Phillips J, Goldmann A, Pickering S, et al. Fukushima Daiichi Accident Study. Sandia Report SAND2012–6173;

[4] U.S.NRC – Nuclear Regulatory Commission. Severe Accidents. Available from: http://www.nrc.g ov/reading-rm/doc-collections/nuregs/ staff/sr1793/initial/chapter19.pdf [Accessed: 20 October 2019]

[5] Wooton RO, Cybuiskis P, Quayle SF. MARCH2 (meltdown accident response characteristics). In: Code Description and User's Manual. Washington, D.C.: Nuclear Regulatory Commission; 1984.

[6] Kim SH, Kim DH, Koh BR, Pessanha J, Siahmed EL-K, Podowski MZ, et al. The Development of APRIL.MOD2 – A Computer Code for Core Meltdown Accident Analysis of Boiling Water Nuclear Reactors. NUREG/CR-5157,

(NUREG/CR-3988)

ORNL/Sub/81–9089/3; 1988

NUREG/CR-6119; 1990

1998

**103**

[7] U.S.NRC – Nuclear Regulatory Commission. MELCOR Computer Code Manuals. Sandia National Laboratories.

[8] Gauntt RO, Cole RK, et al. MELCOR computer code manuals. NUREG/CR-6119, Rev. 1. USA: National Laboratory;

#### **Author details**

André Silva de Aguiar\*, Seung Min Lee and Gaianê Sabundjian Nuclear and Energy Research Institute (IPEN/CNEN - SP), São Paulo, SP, Brazil

\*Address all correspondence to: aguiargm@gmail.com

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Calculation of the Dose for Public Individuals Due to a Severe Accident at the Angra 2 Nuclear… DOI: http://dx.doi.org/10.5772/intechopen.92200*

### **References**

[1] Corey GR. A brief review of the accident at three mile island. IAEA Bulletin, Vol. 21, no.5. Available from: https://inis.iaea.org/search/search.aspx? orig\_q=RN:11554960 [Accessed: 20 October 2019]

[2] Chernobyl's Legacy. Health, Environmental and Socio-Economic Impacts and Recommendations to the Governments of Belarus, the Russian Federation and Ukraine. Vienna: IAEA; 2003-2005

[3] Gauntt R, Kalinich D, Cardoni J, Phillips J, Goldmann A, Pickering S, et al. Fukushima Daiichi Accident Study. Sandia Report SAND2012–6173; 2012

[4] U.S.NRC – Nuclear Regulatory Commission. Severe Accidents. Available from: http://www.nrc.g ov/reading-rm/doc-collections/nuregs/ staff/sr1793/initial/chapter19.pdf [Accessed: 20 October 2019]

[5] Wooton RO, Cybuiskis P, Quayle SF. MARCH2 (meltdown accident response characteristics). In: Code Description and User's Manual. Washington, D.C.: Nuclear Regulatory Commission; 1984. (NUREG/CR-3988)

[6] Kim SH, Kim DH, Koh BR, Pessanha J, Siahmed EL-K, Podowski MZ, et al. The Development of APRIL.MOD2 – A Computer Code for Core Meltdown Accident Analysis of Boiling Water Nuclear Reactors. NUREG/CR-5157, ORNL/Sub/81–9089/3; 1988

[7] U.S.NRC – Nuclear Regulatory Commission. MELCOR Computer Code Manuals. Sandia National Laboratories. NUREG/CR-6119; 1990

[8] Gauntt RO, Cole RK, et al. MELCOR computer code manuals. NUREG/CR-6119, Rev. 1. USA: National Laboratory; 1998

[9] Gauntt RO, Cole RK, et al. MELCOR Computer Code Manuals. Vo1. 2: Reference Manuals, Version 1.8.5, Prepared by Sandia National Laboratories (SNL) for the U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, NUREG/ CR-6119, Vo1. 2, Re'v. 2; 2000

[10] Allison CM, et al. SCDAP/RELAPS/ MOD3.1 code manual. Volume II: Damage Progression Model Theory, Technical Report NUREG/CR-6150, EGG-2720. USA: INEL; 1993

[11] Alliso NCM, et al. SCDAP/RELAPS/ MOD3.2 Code Manual. Volume I-V, NUREG/CR-6150, INEL 96/0422, Revision 1; 1997

[12] MAAP4: Modular Accident Analysis Program for LWR Plants. Code Manual Vols. 1–4, Prepared by Fauske & Associates, Inc., Burr Ridge, IL, USA for the EPRI, Palo Alto, CA, USA; 1994

[13] Lamarsh JR. Introduction to Nuclear Reactor Theory. New york University: Addison-Wesley Publishing Company; 1975

[14] Aguiar AS, Lamego Simoes Filho FF, Alvim ACM, Pimentel LCG, Moraes NO. Station Blackout in unit 1 and analysis of the wind field in the region of Angra dos Reis. Annals of Nuclear Energy [Internet]. Elsevier BV; April 2015;**78**:93-103. DOI: 10.1016/j. anucene.2014.12.010

[15] Scire JS et al. A user's Guide for the CALPUFF Dispersion Model. (Version 5). Land O'Lakes, Florida, USA: Earth Tech. Inc; 2000

[16] Kalnay E, Kanamitsu M, Kistler R, Collins W, Deaven D, Gandin L, et al. The NCEP/NCAR 40-year reanalysis project. Bulletin of the American Meteorological Society. 1996;**77**(3): 437-470

**Author details**

**102**

André Silva de Aguiar\*, Seung Min Lee and Gaianê Sabundjian

\*Address all correspondence to: aguiargm@gmail.com

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

provided the original work is properly cited.

Nuclear and Energy Research Institute (IPEN/CNEN - SP), São Paulo, SP, Brazil

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

**Chapter 7**

**Abstract**

optimize a Cherenkov detector.

**1. Introduction**

**105**

Optimization of Cosmic Radiation

Following the interaction of a neutrino with saline environment, the Cherenkov cone will be generated. The electromagnetic effect of the Cherenkov cone is perpendicular to the cone generator and it has the energy directly proportional to the neutrino energy. In the saline environment, neutrinos with very high energies (noise – 115 dBm) can be determined. Investigation of these neutrinos will lead to the construction of a Cherenkov detector. The construction of a Cherenkov detector involves the design and the construction of a very large number of detection elements and of cascade amplifiers. Another necessary condition is to know exactly the distribution of the dielectric parameters of the saline environment. In order to know the distribution of the dielectric parameters of the saline environment, it is necessary to make a map of their distribution. Under these conditions, the number of detection elements will be optimized and also the optimal position of the future Cherenkov detector will be determined. In this chapter, we will present the methodology of calculating the detection elements and a method to determine the dielectric parameters. Measurements of attenuation of the propagation of electromagnetic waves in this environment will be presented. We will detail how to

Following the interaction of a neutrino with saline environment the Cherenkov cone will be generated. This cone has the height in the prolongation of the neutrino's direction and the base of the Cherenkov cone is forming in the continuation of the neutrino's direction, keeping its angle at the top of the cone. The base of the Cherenkov cone moves further in the same direction as the neutrino that produced the Cherenkov Effect. The electromagnetic effect of the Cherenkov cone is perpendicular to the lateral surface of the cone and it has the energy directly proportional to the energy of the neutrino. It is this neutrino that produced this effect. By determining the energy and the direction of the neutrino that produced the electromagnetic effect of the Cherenkov cone, information about the phenomena in the Universe that generated this neutrino is discovered. In the saline environment, neutrinos with very high energies can be determined. These neutrinos provide information about the phenomena in the Universe that occurred at great distances from Earth. These distances are much larger than the distances at which the most efficient telescopes can work, so that the information obtained from neutrinos will

Detection in Saline Environment

*Valeriu Savu, Mădălin Ion Rusu and Dan Savastru*

**Keywords:** netrins, radiation, cone, Cherenkov, electromagnetic

[17] U.S. NRC – Nuclear Regulatory Commission. Dose Standards and Methods for Protection against Radiation and Contamination. USNRC Technical Training Center

[18] IAEA – International Atomic Energy Agency. Generic Procedures for Assessment and Response during a Radiological Emergency. TECDOC-1162

[19] CNEN – Comissão Nacional de Energia Nuclear. Coeficientes de Dose para Exposição do Público. Posição Regulatória; 2011

[20] SESDEC – Secretaria de Estado de Saúde e Defesa Civil. Plano de Emergência Externo do Estado do Rio de Janeiro. Para Caso de Emergência Nuclear nas Instalações da Central Nuclear Almirante Álvaro Alberto (CNAAA); 2008

[21] CNEN – Comissão Nacional de Energia Nuclear. Plano de Emergência Setorial – CNAAA. CGRN/DRS. Seminário Plano de Emergência – Marinha do Brasil; 2011

[22] CNEN – Comissão Nacional de Energia Nuclear. Medidas de Proteção e Critérios de Intervenção em Situações de Emergência. Posição Regulatória; 2011

[23] U.S. NRC – Nuclear Regulatory Commission. Identification and Analysis of Factors Affecting Emergency Evacuations. NUREG/CR-6864. Washington, D.C.; 2005

#### **Chapter 7**

[17] U.S. NRC – Nuclear Regulatory Commission. Dose Standards and Methods for Protection against

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

Radiation and Contamination. USNRC

[18] IAEA – International Atomic Energy

Technical Training Center

Regulatória; 2011

(CNAAA); 2008

2011

**104**

Marinha do Brasil; 2011

Agency. Generic Procedures for Assessment and Response during a Radiological Emergency. TECDOC-1162

[19] CNEN – Comissão Nacional de Energia Nuclear. Coeficientes de Dose para Exposição do Público. Posição

[20] SESDEC – Secretaria de Estado de

Emergência Externo do Estado do Rio de Janeiro. Para Caso de Emergência Nuclear nas Instalações da Central Nuclear Almirante Álvaro Alberto

[21] CNEN – Comissão Nacional de Energia Nuclear. Plano de Emergência Setorial – CNAAA. CGRN/DRS. Seminário Plano de Emergência –

[22] CNEN – Comissão Nacional de Energia Nuclear. Medidas de Proteção e Critérios de Intervenção em Situações de Emergência. Posição Regulatória;

[23] U.S. NRC – Nuclear Regulatory Commission. Identification and Analysis

of Factors Affecting Emergency Evacuations. NUREG/CR-6864.

Washington, D.C.; 2005

Saúde e Defesa Civil. Plano de

## Optimization of Cosmic Radiation Detection in Saline Environment

*Valeriu Savu, Mădălin Ion Rusu and Dan Savastru*

#### **Abstract**

Following the interaction of a neutrino with saline environment, the Cherenkov cone will be generated. The electromagnetic effect of the Cherenkov cone is perpendicular to the cone generator and it has the energy directly proportional to the neutrino energy. In the saline environment, neutrinos with very high energies (noise – 115 dBm) can be determined. Investigation of these neutrinos will lead to the construction of a Cherenkov detector. The construction of a Cherenkov detector involves the design and the construction of a very large number of detection elements and of cascade amplifiers. Another necessary condition is to know exactly the distribution of the dielectric parameters of the saline environment. In order to know the distribution of the dielectric parameters of the saline environment, it is necessary to make a map of their distribution. Under these conditions, the number of detection elements will be optimized and also the optimal position of the future Cherenkov detector will be determined. In this chapter, we will present the methodology of calculating the detection elements and a method to determine the dielectric parameters. Measurements of attenuation of the propagation of electromagnetic waves in this environment will be presented. We will detail how to optimize a Cherenkov detector.

**Keywords:** netrins, radiation, cone, Cherenkov, electromagnetic

#### **1. Introduction**

Following the interaction of a neutrino with saline environment the Cherenkov cone will be generated. This cone has the height in the prolongation of the neutrino's direction and the base of the Cherenkov cone is forming in the continuation of the neutrino's direction, keeping its angle at the top of the cone. The base of the Cherenkov cone moves further in the same direction as the neutrino that produced the Cherenkov Effect. The electromagnetic effect of the Cherenkov cone is perpendicular to the lateral surface of the cone and it has the energy directly proportional to the energy of the neutrino. It is this neutrino that produced this effect. By determining the energy and the direction of the neutrino that produced the electromagnetic effect of the Cherenkov cone, information about the phenomena in the Universe that generated this neutrino is discovered. In the saline environment, neutrinos with very high energies can be determined. These neutrinos provide information about the phenomena in the Universe that occurred at great distances from Earth. These distances are much larger than the distances at which the most efficient telescopes can work, so that the information obtained from neutrinos will

increase the horizon of knowledge and contribute to the improvement of information about the Universe. Thus, we can say that this information makes a significant contribution in the field of astrophysics and astronomy.

the direction and energy level of the neutrinos generating the Cherenkov cone with the same precision level. Considering these aspects, the special importance of designing and realizing a complex system for determining the electrical parameters of the antennas for the detection of Cherenkov cone of electromagnetic radiation in saline environment, is deduced. The determination of the electrical parameters of the antennas for the detection of the Cherenkov cone of electromagnetic radiation in saline environment will be thought out so that it can determine these parameters in such environments. The basic parameters of the antennas [6, 7] will be determined: the radiation diagram, the directivity, the gain, the polarization, the input impedance, the frequency band, the effective surface, and the effective height.

*Optimization of Cosmic Radiation Detection in Saline Environment*

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

In order to determine the Cherenkov cone in saline environment (the noise does not influence the energy measurement because the maximum noise level measured in saline environment is 115 dBm [8]), it is necessary to make a Cherenkov detector in this environment. The implementation of a Cherenkov detector in saline environment involves the design and construction of a very large number of detection elements together with the related devices and a very large number of cascade amplifiers as well [5]. Under these conditions the price of a Cherenkov detector in saline environment is very high. Another necessary condition (it is of particular importance since it can reduce the costs of producing a Cherenkov detector in saline environment) is the accurate knowledge and distribution of the dielectric parameters of the saline environment in the salt volume in which a Cherenkov detector will be made. The realization of a map of the distribution of the dielectric parameters of the saline environment in the entire volume of a salt rock implies the elaboration of a complex system for determining the dielectric parameters of the saline environment for the detection of the Cherenkov cone of cosmic radiation in this environment. With this system, measurements can be made in saline (on-site) environment in order to make this map. The use of this system in the measurements will increase the possibility to implement a Cherenkov detector in saline environment. Until now, this system has not been used in saline environment for the detection of cosmic radiation, which brings a novelty in the field. The novelty in the field of cosmic radiation detection in saline environment has led to patent applications A/00959/05.12.2016 [9], A/00404/07.06.2018 [10] and A/00354/12.06.2019 [11]. So far, a number of studies were carried out in different environments in order to perform a Cherenkov cosmic radiation detector. The studies were conducted in environments such as: air, ice, salt rock [12, 13], limestone rock, etc. For saline environment the SalSA detector is known, under water (ANTARES, Baikal, NEMO,

NESTOR, AUTEC etc.), under ice (AMANDA, ICECUBE and RICE), for atmosphere (ASHRA, AUGER, EUSO and OWR), between soil and air (GLUE, Forte'NuTel and ANITA) [14]. The "Salt Sensor Array" (SalSA) detector has as reference parameters, 10 x 10 rows of square surfaces, placed 250 m horizontally between them for a depth of 2000 m and placed at 182 m vertically between them, with 12 knots per row and for each row 12 detection elements, resulting in 14,400 detection elements. In the SalSA (saline environment) project, a 250 m attenuation

length of the electromagnetic waves was obtained for a frequency band of 100 MHz ÷ 300 MHz using antennas with horizontal and vertical polarity [15]. Cherenkov 3D type detector with a geometry 20 20 20 where the number of sub-bands is 1 and the number of antennas with the same polarization type is 2 has a

block and it uses the neutron electron cosmic radiation detection system [5, 9]. In these studies, there was no question to determine the dielectric parameters of the

In saline environment, two projects were carried that studied the way of detecting the Cherenkov cone of electromagnetic radiation in saline environment,

environments, in which the measurements were performed.

, uses 32,000 detection elements and a number of 400 wells in the salt

size of 500 m<sup>3</sup>

**107**

The study of cosmic radiation began between 1911 and 1913. During this period, the Austrian Physicist Victor Hess, following balloon flights, measured the variation of ionization present in the air with the altitude [1]. The neutrinos carried by cosmic radiation have very high energies of the order (10<sup>15</sup> ÷ 1023) eV, those with energy between (10<sup>15</sup> ÷ 1021) eV can be detected in saline environment and those with energies greater than 10<sup>21</sup> eV cross the terra.

The investigation of the interactions of high-energy neutrinos of cosmic origin in a dense environment (natural salt) will lead to the construction of a cosmic radiation observer in this environment. The phenomenon by which particles charged with high energies are detected due to the interaction with the environment is called the Askaryan effect and consists in the coherent emission of Cherenkov radiations in the radio frequency domain, through an excessive electrical charge that occurs during the development of an electron cascade in that environment. Cherenkov radiation occurs in the case of particles moving through an environment at a speed greater than the speed of light through that environment [2].

An avalanche of relativistic particles [3] represents the interaction between a very high-energy neutrino and a dense and dielectric environment (salt block). For neutrinos with energy greater than 10<sup>15</sup> eV, only about 20% of it appears as a hadronic particles cascade, and this cascade has an electromagnetic component [3]. The electromagnetic cascade consists of electrically charged particles (about 70% of the particles) [4]. These particles contribute to the generation of the total electromagnetic energy of the cascade [4]. Particles with a speed of travel greater than the speed of light through a transparent and dense environment (the salt block) will produce the Cherenkov radiation effect (in our electromagnetic case) in this environment [2].

The phenomenon, by which the interaction with the environment can detect particles charged with high energies, is called the Askaryan effect and consists in the emission of Cherenkov radiation (in the case of particles moving through an environment at a speed greater than the speed of light through that environment) coherent in the radio frequency domain by the excess load that appears during the development of a cascade in that environment [2]. Determination of neutrinos with energies greater than 10<sup>12</sup> eV can lead to the discovery of new astrophysical systems and new physical processes [3]. The direction, from which these very high energy neutrinos come from, is a direct indicator of the source that generates them, thus a cosmic radiation observer from a saline will have to fulfill this goal [3]. The result of the interaction of a very high energy neutrino with a dielectric, transparent and dense environment (salt block), is an avalanche of relativistic particles [3] which by Cherenkov effect will cause the information obtained to generate new aspects about astro-particles and they create the premises for a deeper understanding of the cosmic phenomena of high energy in the Universe [3]. These particles contribute to the generation of total electromagnetic energy in the form of a Cherenkov cone [4]. Knowing the effects related to the propagation of electromagnetic waves in dielectric environments with impurities (saline environment) [5], then, by eliminating the influences of the parameters of the propagation environment (saline environment), one can deduce the basic parameters of the flexible transmitting and receiving antennas. By performing a sufficient number of measurements, these basic parameters of the flexible transmitting and receiving antennas can be determined. Knowing these parameters, the detection of the electromagnetic radiation of the Cherenkov cone (which is known to be perpendicular to the generator of the cone) can be performed with much greater accuracy. Then it will be possible to determine

#### *Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

increase the horizon of knowledge and contribute to the improvement of information about the Universe. Thus, we can say that this information makes a significant

The study of cosmic radiation began between 1911 and 1913. During this period, the Austrian Physicist Victor Hess, following balloon flights, measured the variation of ionization present in the air with the altitude [1]. The neutrinos carried by cosmic radiation have very high energies of the order (10<sup>15</sup> ÷ 1023) eV, those with energy between (10<sup>15</sup> ÷ 1021) eV can be detected in saline environment and those with

The investigation of the interactions of high-energy neutrinos of cosmic origin in a dense environment (natural salt) will lead to the construction of a cosmic radiation observer in this environment. The phenomenon by which particles charged with high energies are detected due to the interaction with the environment is called the Askaryan effect and consists in the coherent emission of Cherenkov radiations in the radio frequency domain, through an excessive electrical charge that occurs during the development of an electron cascade in that environment. Cherenkov radiation occurs in the case of particles moving through an environment at a speed

An avalanche of relativistic particles [3] represents the interaction between a very high-energy neutrino and a dense and dielectric environment (salt block). For neutrinos with energy greater than 10<sup>15</sup> eV, only about 20% of it appears as a hadronic particles cascade, and this cascade has an electromagnetic component [3]. The electromagnetic cascade consists of electrically charged particles (about 70% of the particles) [4]. These particles contribute to the generation of the total electromagnetic energy of the cascade [4]. Particles with a speed of travel greater than the speed of light through a transparent and dense environment (the salt block) will produce the Cherenkov radiation effect (in our electromagnetic case) in this

The phenomenon, by which the interaction with the environment can detect particles charged with high energies, is called the Askaryan effect and consists in the emission of Cherenkov radiation (in the case of particles moving through an environment at a speed greater than the speed of light through that environment) coherent in the radio frequency domain by the excess load that appears during the development of a cascade in that environment [2]. Determination of neutrinos with energies greater than 10<sup>12</sup> eV can lead to the discovery of new astrophysical systems and new physical processes [3]. The direction, from which these very high energy neutrinos come from, is a direct indicator of the source that generates them, thus a cosmic radiation observer from a saline will have to fulfill this goal [3]. The result of the interaction of a very high energy neutrino with a dielectric, transparent and dense environment (salt block), is an avalanche of relativistic particles [3] which by Cherenkov effect will cause the information obtained to generate new aspects about astro-particles and they create the premises for a deeper understanding of the cosmic phenomena of high energy in the Universe [3]. These particles contribute to the generation of total electromagnetic energy in the form of a Cherenkov cone [4]. Knowing the effects related to the propagation of electromagnetic waves in dielectric environments with impurities (saline environment) [5], then, by eliminating the influences of the parameters of the propagation environment (saline environment), one can deduce the basic parameters of the flexible transmitting and receiving antennas. By performing a sufficient number of measurements, these basic parameters of the flexible transmitting and receiving antennas can be determined. Knowing these parameters, the detection of the electromagnetic radiation of the Cherenkov cone (which is known to be perpendicular to the generator of the cone) can be performed with much greater accuracy. Then it will be possible to determine

contribution in the field of astrophysics and astronomy.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

greater than the speed of light through that environment [2].

energies greater than 10<sup>21</sup> eV cross the terra.

environment [2].

**106**

the direction and energy level of the neutrinos generating the Cherenkov cone with the same precision level. Considering these aspects, the special importance of designing and realizing a complex system for determining the electrical parameters of the antennas for the detection of Cherenkov cone of electromagnetic radiation in saline environment, is deduced. The determination of the electrical parameters of the antennas for the detection of the Cherenkov cone of electromagnetic radiation in saline environment will be thought out so that it can determine these parameters in such environments. The basic parameters of the antennas [6, 7] will be determined: the radiation diagram, the directivity, the gain, the polarization, the input impedance, the frequency band, the effective surface, and the effective height.

In order to determine the Cherenkov cone in saline environment (the noise does not influence the energy measurement because the maximum noise level measured in saline environment is 115 dBm [8]), it is necessary to make a Cherenkov detector in this environment. The implementation of a Cherenkov detector in saline environment involves the design and construction of a very large number of detection elements together with the related devices and a very large number of cascade amplifiers as well [5]. Under these conditions the price of a Cherenkov detector in saline environment is very high. Another necessary condition (it is of particular importance since it can reduce the costs of producing a Cherenkov detector in saline environment) is the accurate knowledge and distribution of the dielectric parameters of the saline environment in the salt volume in which a Cherenkov detector will be made. The realization of a map of the distribution of the dielectric parameters of the saline environment in the entire volume of a salt rock implies the elaboration of a complex system for determining the dielectric parameters of the saline environment for the detection of the Cherenkov cone of cosmic radiation in this environment. With this system, measurements can be made in saline (on-site) environment in order to make this map. The use of this system in the measurements will increase the possibility to implement a Cherenkov detector in saline environment. Until now, this system has not been used in saline environment for the detection of cosmic radiation, which brings a novelty in the field. The novelty in the field of cosmic radiation detection in saline environment has led to patent applications A/00959/05.12.2016 [9], A/00404/07.06.2018 [10] and A/00354/12.06.2019 [11].

So far, a number of studies were carried out in different environments in order to perform a Cherenkov cosmic radiation detector. The studies were conducted in environments such as: air, ice, salt rock [12, 13], limestone rock, etc. For saline environment the SalSA detector is known, under water (ANTARES, Baikal, NEMO, NESTOR, AUTEC etc.), under ice (AMANDA, ICECUBE and RICE), for atmosphere (ASHRA, AUGER, EUSO and OWR), between soil and air (GLUE, Forte'NuTel and ANITA) [14]. The "Salt Sensor Array" (SalSA) detector has as reference parameters, 10 x 10 rows of square surfaces, placed 250 m horizontally between them for a depth of 2000 m and placed at 182 m vertically between them, with 12 knots per row and for each row 12 detection elements, resulting in 14,400 detection elements. In the SalSA (saline environment) project, a 250 m attenuation length of the electromagnetic waves was obtained for a frequency band of 100 MHz ÷ 300 MHz using antennas with horizontal and vertical polarity [15]. Cherenkov 3D type detector with a geometry 20 20 20 where the number of sub-bands is 1 and the number of antennas with the same polarization type is 2 has a size of 500 m<sup>3</sup> , uses 32,000 detection elements and a number of 400 wells in the salt block and it uses the neutron electron cosmic radiation detection system [5, 9]. In these studies, there was no question to determine the dielectric parameters of the environments, in which the measurements were performed.

In saline environment, two projects were carried that studied the way of detecting the Cherenkov cone of electromagnetic radiation in saline environment, but in these projects, there was no search for flexibility and adaptability of the antennas for the most accurate detection of the Cherenkov cone of electromagnetic radiation in saline medium.

for such detectors, since it suffers important changes of its electrical properties, based on which, the neutrinos that pass through the block can be detected.

*Optimization of Cosmic Radiation Detection in Saline Environment*

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

conventional receiver.

Cherenkov detector [11].

methods were studied, a direct and an indirect one.

the radiant electromagnetic field [6, 33].

• radiation diagram,

• directivity,

**109**

identical. The basic parameters of the antennas are [6, 7]:

antenna. The antennas will be introduced in saline environment.

antennas [30].

Based on the Askaryan effect [24–26] the radiation that passes through a dense dielectric generates a cone of coherent radiation in the radio or microwave frequency domain, known as Cherenkov radiation [27–29]. In order to detect this radiation, one has to determine the frequency domain in which those radio impulses have maximum intensity and the parameters of an antenna that can be used in a

In an experimental setup with a particular configuration of transmitter and receiver antennas, one can measure the level and the range of the radiation generated and, based on those results, can evaluate the neutrinos energy. The system proposed in this paper consists in an Anritsu MS2690A signal analyzer, with an incorporated signal generator, coupled to the transmitting and receiving

With this system, the dielectric parameters of the saline environment are determined first and, by knowing these parameters, the distance of attenuation of the propagation of electromagnetic waves through the saline environment can be determined (the distance at which the module of the electromagnetic field decreases to 1/e). Thus, it is possible to determine, following a package of measurements for the vertical plane [8], and for the horizontal plane [31], the distribution of the attenuation of the electromagnetic waves through the saline environment (the map of the distribution of the electromagnetic waves in the saline environment leading to the determination of the optimal position of placement in a saline environment of a Cherenkov detector), the determination of the minimum number of detection elements, and the optimal position of their placement in saline environment [10]. Based on the use of dedicated software, one can determine the extreme situations of the generation of the Cherenkov cone outside the volume of the

In order to determine the dielectric parameters of the saline environment, two

*The direct method* involves the injection of a radio frequency signal into the measuring medium (saline medium) in order to determine the electrical parameters of the radio frequency antennas. Thus, this method involves performing a measuring assembly. This will include a radio frequency signal generator nozzle that will inject the signal into an emission antenna, the electrical parameters of which are known, an antenna for the reception of the injected signal, the electrical parameters of which will be determined, a signal analyzer block received from the measuring

According to IEEE standard no. 145–1983 [32], which states that "the antenna is a means of transmitting or receiving radio waves", i.e. the antenna is that part of a radio equipment that, by means of electromagnetic exchange of power with the environment, ensures communication between at least two telecommunication equipments. The antenna can also be regarded as an element that adapts between the environment and the receiver or transmitter. It actually performs a transformation of the power of the electromagnetic field into a signal received as electrical power. Also, the antenna transforms the electric emission power into the power of

The transmitting and receiving antennas, from a constructive point of view, are

The study of the detection of cosmic neutrinos began almost 20 years ago. Several specific telescopes have been developed that have attempted to identify these particles. The results were not the ones expected. On 23-02-1987, a radiation source of cosmic neutrinos was identified for the first time. This was called "Supernova 1987A" and opened a new stage in the theory of cosmos evolution. For ice detectors (ANITA) [16] with an SNR > 1 allowance, all events occurring in the frequency band (100 ÷ 1000) MHz can be considered detectable. In another paper dealing with the detection of cosmic radiation at the ice surface in Antarctica [17], it is mentioned that if SNR = 1 is considered, then the number of events can be estimated. Nor does this work address the reflections, attenuations, and characteristic of the antennas. Another paper dealing with the interaction of neutrinos (UHE) [18] and referring to a constant detector volume, does not take into account the effects related to the signal-to-noise ratio, antennas, propagation through the study environment, aspects that we want to achieve in this project. Due to an inhomogeneous distribution of impurities in the saline environment, a theoretical approach to the propagation phenomenon of electromagnetic waves in this environment cannot be realized [19, 20].

In order to obtain the most accurate dielectric parameters of the saline environment, it is necessary to improve the system of measurement and the determination of these parameters. In order to reach the proposed objective it is necessary to minimize the errors introduced by adapting the detection elements (transmission and reception antennas) to the saline environment (the electrical parameters of the antennas: the working impedances, the directional characteristics in horizontal and vertical plane, the gain, etc. of the transmitting and receiving antennas that are affected by the saline environment), it is necessary to make a band-pass filter with the lowest insertion attenuation resulting in a uniform bandwidth and it is also necessary to make an amplifier with the amplification as much as possible constant in the working band (central frequency 187.5 MHz, amplification band at 3 dB greater than the bandwidth filter by at least 10% and the amplification can compensate for the losses introduced by the connection cables).

The determination of the Cherenkov cone in saline environment presents as a result the determination of the energy, the direction and the sense that the neutrinos, which interact with a saline environment, possess. These neutrinos provide information about the phenomena in the Universe that occurred at great distances from Earth. These distances are much larger than the distances at which the most efficient telescopes can work, so that information obtained from neutrinos will increase the horizon of knowledge and will contribute to the improvement of information about the Universe. Thus, we can say that this information makes a significant contribution in the field of astrophysics and astronomy.

#### **2. Data measurement systems in saline environment**

The generation of radiation pulses that arise from the interaction between high energy neutrinos (Ultra High Energy, UHE) and a dense dielectric medium has been studied first by Askaryan [21], who also presented the first results based on laboratory tests.

Askaryan also identified several natural materials that can be used as neutrinos detectors: the salt blocks present in saline mines, the ice from polar region, and the soil of moon [22, 23]. It was proven that a solid block of salt is a very good candidate

#### *Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

but in these projects, there was no search for flexibility and adaptability of the antennas for the most accurate detection of the Cherenkov cone of electromagnetic

The study of the detection of cosmic neutrinos began almost 20 years ago. Several specific telescopes have been developed that have attempted to identify these particles. The results were not the ones expected. On 23-02-1987, a radiation source of cosmic neutrinos was identified for the first time. This was called "Supernova 1987A" and opened a new stage in the theory of cosmos evolution. For ice detectors (ANITA) [16] with an SNR > 1 allowance, all events occurring in the frequency band (100 ÷ 1000) MHz can be considered detectable. In another paper dealing with the detection of cosmic radiation at the ice surface in Antarctica [17], it is mentioned that if SNR = 1 is considered, then the number of events can be estimated. Nor does this work address the reflections, attenuations, and characteristic of the antennas. Another paper dealing with the interaction of neutrinos (UHE) [18] and referring to a constant detector volume, does not take into account the effects related to the signal-to-noise ratio, antennas, propagation through the study environment, aspects that we want to achieve in this project. Due to an inhomogeneous distribution of impurities in the saline environment, a theoretical approach to the propagation phenomenon of electromagnetic waves in this envi-

In order to obtain the most accurate dielectric parameters of the saline environment, it is necessary to improve the system of measurement and the determination of these parameters. In order to reach the proposed objective it is necessary to minimize the errors introduced by adapting the detection elements (transmission and reception antennas) to the saline environment (the electrical parameters of the antennas: the working impedances, the directional characteristics in horizontal and vertical plane, the gain, etc. of the transmitting and receiving antennas that are affected by the saline environment), it is necessary to make a band-pass filter with the lowest insertion attenuation resulting in a uniform bandwidth and it is also necessary to make an amplifier with the amplification as much as possible constant in the working band (central frequency 187.5 MHz, amplification band at 3 dB greater than the bandwidth filter by at least 10% and the amplification can

The determination of the Cherenkov cone in saline environment presents as a result the determination of the energy, the direction and the sense that the neutrinos, which interact with a saline environment, possess. These neutrinos provide information about the phenomena in the Universe that occurred at great distances from Earth. These distances are much larger than the distances at which the most efficient telescopes can work, so that information obtained from neutrinos will increase the horizon of knowledge and will contribute to the improvement of information about the Universe. Thus, we can say that this information makes a

The generation of radiation pulses that arise from the interaction between high energy neutrinos (Ultra High Energy, UHE) and a dense dielectric medium has been studied first by Askaryan [21], who also presented the first results based on

Askaryan also identified several natural materials that can be used as neutrinos detectors: the salt blocks present in saline mines, the ice from polar region, and the soil of moon [22, 23]. It was proven that a solid block of salt is a very good candidate

compensate for the losses introduced by the connection cables).

significant contribution in the field of astrophysics and astronomy.

**2. Data measurement systems in saline environment**

laboratory tests.

**108**

radiation in saline medium.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

ronment cannot be realized [19, 20].

for such detectors, since it suffers important changes of its electrical properties, based on which, the neutrinos that pass through the block can be detected.

Based on the Askaryan effect [24–26] the radiation that passes through a dense dielectric generates a cone of coherent radiation in the radio or microwave frequency domain, known as Cherenkov radiation [27–29]. In order to detect this radiation, one has to determine the frequency domain in which those radio impulses have maximum intensity and the parameters of an antenna that can be used in a conventional receiver.

In an experimental setup with a particular configuration of transmitter and receiver antennas, one can measure the level and the range of the radiation generated and, based on those results, can evaluate the neutrinos energy. The system proposed in this paper consists in an Anritsu MS2690A signal analyzer, with an incorporated signal generator, coupled to the transmitting and receiving antennas [30].

With this system, the dielectric parameters of the saline environment are determined first and, by knowing these parameters, the distance of attenuation of the propagation of electromagnetic waves through the saline environment can be determined (the distance at which the module of the electromagnetic field decreases to 1/e). Thus, it is possible to determine, following a package of measurements for the vertical plane [8], and for the horizontal plane [31], the distribution of the attenuation of the electromagnetic waves through the saline environment (the map of the distribution of the electromagnetic waves in the saline environment leading to the determination of the optimal position of placement in a saline environment of a Cherenkov detector), the determination of the minimum number of detection elements, and the optimal position of their placement in saline environment [10]. Based on the use of dedicated software, one can determine the extreme situations of the generation of the Cherenkov cone outside the volume of the Cherenkov detector [11].

In order to determine the dielectric parameters of the saline environment, two methods were studied, a direct and an indirect one.

*The direct method* involves the injection of a radio frequency signal into the measuring medium (saline medium) in order to determine the electrical parameters of the radio frequency antennas. Thus, this method involves performing a measuring assembly. This will include a radio frequency signal generator nozzle that will inject the signal into an emission antenna, the electrical parameters of which are known, an antenna for the reception of the injected signal, the electrical parameters of which will be determined, a signal analyzer block received from the measuring antenna. The antennas will be introduced in saline environment.

According to IEEE standard no. 145–1983 [32], which states that "the antenna is a means of transmitting or receiving radio waves", i.e. the antenna is that part of a radio equipment that, by means of electromagnetic exchange of power with the environment, ensures communication between at least two telecommunication equipments. The antenna can also be regarded as an element that adapts between the environment and the receiver or transmitter. It actually performs a transformation of the power of the electromagnetic field into a signal received as electrical power. Also, the antenna transforms the electric emission power into the power of the radiant electromagnetic field [6, 33].

The transmitting and receiving antennas, from a constructive point of view, are identical. The basic parameters of the antennas are [6, 7]:


**The radiation diagram** of the antenna represents the space surface for which the vectors leaving the antenna towards this surface have the module proportional to the intensity of the radiation in the respective direction. The direction, in which the field intensity is zero, is called null. The region between two nulls is called the lob. The maximum of the lobe is called the level of the lobe and the direction, in which it is maximum, is called the orientation of the lobe. If we represent the lobes in relative sizes, then an antenna can have one or more level 1 (0 dB) lobes called main lobes, � and less than 1 level lobes (negative in dB) – named secondary (lateral or auxiliary) lobes. The back lobe of an antenna (180° to the main lobe) is related to the main lobe (in dB) and it is called the front/back ratio of the antenna [6, 7].

We can define the radiation diagram of an antenna if we take into account the electric component module E for the electromagnetic field radiated by the antenna. The other parameters and their definitions are kept. A decrease in 3 dB of the electric field module represents a decrease of its times (1/√2 ≈ 0.707) [6, 7].

The maximum radiation intensity is given by:

$$P\_{\Omega\max} = \left| P\_{\Omega} \left( \theta = \frac{\pi}{2} \right) \right| = \left| \frac{\eta\_0 k\_0^2}{32\pi^2} \left( \sin \frac{\pi}{2} \right)^2 \right| = \frac{\eta\_0 k\_0^2}{32\pi^2} \tag{1}$$

the antenna would radiate isotropically all input power. The radiation intensity, corresponding to the isotropically radiated power, is equal to the ratio of the input power to 4π. For an approximate calculation, the formula [6, 7] can be used:

*Optimization of Cosmic Radiation Detection in Saline Environment*

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

*Gmax* <sup>≈</sup> <sup>3</sup> <sup>∙</sup> <sup>10</sup><sup>5</sup> *θθ*

vectors *E* and *H*.

fied range" [6, 7].

[6, 7]:

**111**

travel of the curve (right or left) [6, 7]*.*

and traveled by a constant current I is as follows [6, 7]:

*Rrad* <sup>¼</sup> *Prad*. <sup>1</sup>

where: and represents the angular openings (in degrees) at 3 dB in the planes of

**The polarization** of an antenna is determined by the polarization of the electromagnetic field radiated by it. The propagation of the electromagnetic field is given by a transverse plane wave (components E and H are perpendicular to each other and in turn are perpendicular to the propagation direction). The polarization of an electromagnetic field is determined by the curve of the vector E described in time at the observation point. This curve can be an ellipse (elliptic polarization), a circle (circular polarization) or a straight line (linear polarization). Apart from linear polarization, the other polarizations are characterized by the direction of

**The input impedance** of an antenna is, in fact, the impedance presented at the antenna terminals. The impedance of the antenna is given by the ratio between the voltage and the current at the terminals or the ratio between the electrical and magnetic components determined at a conveniently chosen point. The formula for calculating the impedance of the dipole antenna of length l is much smaller than λ

> 2 *I* 2 � �

The frequency band is defined as "the frequency range, in which the antenna performance associated with a predetermined parameter, is maintained in a speci-

The actual surface area of an antenna, for a given direction, is represented by the

The effective height of an antenna, with a linear polarization and receiving a plane wave from a given direction, represents the ratio between the voltage determined with the open circuit at the antenna terminals and the intensity of the electric

An issue that interests us is the input resistance of the dipole antenna. This antenna will be calculated to work in a saline environment. In order to determine the parameters of the antenna in saline environment, we must know the input resistance of the dipole antenna in the free space. In order to determine the input resistance of the dipole antenna, we will start from the cylindrical dipole, which is a direct materialization of the concept of thin wire antenna. The parameters of the cylindrical dipole are slightly different from those provided by a theoretical analysis. This fact is given by the condition imposed on the length of the dipole, which must be much larger than the diameter. But this condition is not strictly fulfilled. Considering that the dipole radiates in the free space, we will have approximate formulas for calculating the input resistance. If we make the notation G = nπ, then

ratio of the power available at the antenna terminals, being considered as the receiving antenna and the power density for the plane wave incident in that direction. The electromagnetic wave and the antenna are considered to be adapted from each other in terms of polarization. If no specific direction is indicated, then the

maximum antenna radiation direction is taken by default [6, 7].

field determined by the antenna polarization direction.

<sup>¼</sup> *<sup>η</sup>*0*k*<sup>2</sup> 0*l* 2

<sup>6</sup>*<sup>π</sup>* (5)

(4)

and the relative radiation intensity is given by:

$$P\_{\Omega \text{rel}} = \frac{|P\_{\Omega}|}{P\_{\Omega \text{ max}}} = \frac{\frac{\eta\_0 k\_0^2}{32\pi^2} (\sin \theta)^2}{\frac{\eta\_0 k\_0^2}{32\pi^2}} = (\sin \theta)^2 \tag{2}$$

where: *P<sup>Ω</sup>* represents the radiation intensity,

*θ* represents the angle under which the radiation intensity is determined,

*η<sup>0</sup>* represents the vacuum impedance,

*k0* represents the vacuum propagation constant.

From these equations, the radiation pattern of the antenna can be determined.

*Directivity* is the ratio of radiation intensity in a given direction to the average radiation intensity that is calculated for all directions in space. The average radiation intensity is calculated as the total radiated power divided by 4π. The approximate formula for calculating directivity is as follows [6, 7]:

$$D(\theta, \phi) = 10 \log \left[ 4\pi \frac{P\_{\Omega}(\theta, \phi)}{P\_{rad}} \right] [dB] \tag{3}$$

**The absolute gain** of an antenna, for a given direction, represents the radiation intensity in that direction relative to the radiation intensity that could be obtained if *Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

• gain,

• polarization,

• the input impedance,

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

• the frequency band,

• the effective height.

**The radiation diagram** of the antenna represents the space surface for which the vectors leaving the antenna towards this surface have the module proportional to the intensity of the radiation in the respective direction. The direction, in which the field intensity is zero, is called null. The region between two nulls is called the lob. The maximum of the lobe is called the level of the lobe and the direction, in which it is maximum, is called the orientation of the lobe. If we represent the lobes in relative sizes, then an antenna can have one or more level 1 (0 dB) lobes -

We can define the radiation diagram of an antenna if we take into account the electric component module E for the electromagnetic field radiated by the antenna. The other parameters and their definitions are kept. A decrease in 3 dB of the electric field module represents a decrease of its times (1/√2 ≈ 0.707) [6, 7].

called main lobes, � and less than 1 level lobes (negative in dB) – named secondary (lateral or auxiliary) lobes. The back lobe of an antenna (180° to the main lobe) is related to the main lobe (in dB) and it is called the front/back ratio of

> 2

> > ¼

*η*0*k*<sup>2</sup> 0 <sup>32</sup>*π*<sup>2</sup> ð Þ sin *<sup>θ</sup>* <sup>2</sup> *η*0*k*<sup>2</sup> 0 32*π*<sup>2</sup>

*θ* represents the angle under which the radiation intensity is determined,

*<sup>D</sup>*ð Þ¼ *<sup>θ</sup>*, <sup>ϕ</sup> <sup>10</sup> *log* <sup>4</sup>*<sup>π</sup> <sup>P</sup>*Ωð Þ *<sup>θ</sup>*, *<sup>ϕ</sup>*

**The absolute gain** of an antenna, for a given direction, represents the radiation intensity in that direction relative to the radiation intensity that could be obtained if

*Prad* 

From these equations, the radiation pattern of the antenna can be determined. *Directivity* is the ratio of radiation intensity in a given direction to the average radiation intensity that is calculated for all directions in space. The average radiation intensity is calculated as the total radiated power divided by 4π. The approximate

 <sup>¼</sup> *<sup>η</sup>*0*k*<sup>2</sup> 0 <sup>32</sup>*π*<sup>2</sup> sin *<sup>π</sup>*

 

2

 <sup>¼</sup> *<sup>η</sup>*0*k*<sup>2</sup> 0

<sup>32</sup>*π*<sup>2</sup> (1)

<sup>¼</sup> ð Þ sin *<sup>θ</sup>* <sup>2</sup> (2)

½ � *dB* (3)

<sup>2</sup>

The maximum radiation intensity is given by:

*<sup>P</sup>*<sup>Ω</sup> *max* <sup>¼</sup> *<sup>P</sup>*<sup>Ω</sup> *<sup>θ</sup>* <sup>¼</sup> *<sup>π</sup>*

and the relative radiation intensity is given by:

where: *P<sup>Ω</sup>* represents the radiation intensity,

*k0* represents the vacuum propagation constant.

formula for calculating directivity is as follows [6, 7]:

*η<sup>0</sup>* represents the vacuum impedance,

*<sup>P</sup>*Ωrel <sup>¼</sup> j j *<sup>P</sup>*<sup>Ω</sup>

*P*<sup>Ω</sup> *max*

• the actual area,

the antenna [6, 7].

**110**

the antenna would radiate isotropically all input power. The radiation intensity, corresponding to the isotropically radiated power, is equal to the ratio of the input power to 4π. For an approximate calculation, the formula [6, 7] can be used:

$$G\_{\text{max}} \approx \frac{3 \bullet 10^5}{\theta\_{\text{E}} \theta\_{\text{H}}} \tag{4}$$

where: and represents the angular openings (in degrees) at 3 dB in the planes of vectors *E* and *H*.

**The polarization** of an antenna is determined by the polarization of the electromagnetic field radiated by it. The propagation of the electromagnetic field is given by a transverse plane wave (components E and H are perpendicular to each other and in turn are perpendicular to the propagation direction). The polarization of an electromagnetic field is determined by the curve of the vector E described in time at the observation point. This curve can be an ellipse (elliptic polarization), a circle (circular polarization) or a straight line (linear polarization). Apart from linear polarization, the other polarizations are characterized by the direction of travel of the curve (right or left) [6, 7]*.*

**The input impedance** of an antenna is, in fact, the impedance presented at the antenna terminals. The impedance of the antenna is given by the ratio between the voltage and the current at the terminals or the ratio between the electrical and magnetic components determined at a conveniently chosen point. The formula for calculating the impedance of the dipole antenna of length l is much smaller than λ and traveled by a constant current I is as follows [6, 7]:

$$R\_{rad} = P\_{rad} \Big/ \left(\frac{\mathbf{1}}{2}I^2\right) = \frac{\eta\_0 k\_0^2 l^2}{6\pi} \tag{5}$$

The frequency band is defined as "the frequency range, in which the antenna performance associated with a predetermined parameter, is maintained in a specified range" [6, 7].

The actual surface area of an antenna, for a given direction, is represented by the ratio of the power available at the antenna terminals, being considered as the receiving antenna and the power density for the plane wave incident in that direction. The electromagnetic wave and the antenna are considered to be adapted from each other in terms of polarization. If no specific direction is indicated, then the maximum antenna radiation direction is taken by default [6, 7].

The effective height of an antenna, with a linear polarization and receiving a plane wave from a given direction, represents the ratio between the voltage determined with the open circuit at the antenna terminals and the intensity of the electric field determined by the antenna polarization direction.

An issue that interests us is the input resistance of the dipole antenna. This antenna will be calculated to work in a saline environment. In order to determine the parameters of the antenna in saline environment, we must know the input resistance of the dipole antenna in the free space. In order to determine the input resistance of the dipole antenna, we will start from the cylindrical dipole, which is a direct materialization of the concept of thin wire antenna. The parameters of the cylindrical dipole are slightly different from those provided by a theoretical analysis. This fact is given by the condition imposed on the length of the dipole, which must be much larger than the diameter. But this condition is not strictly fulfilled.

Considering that the dipole radiates in the free space, we will have approximate formulas for calculating the input resistance. If we make the notation G = nπ, then [6, 7]:

$$R\_{\rm in} = \begin{cases} 20G^2 & 0 < n < 1/4 \\\\ 24.7G^{2,5} & 1/4 \le n < 1/2 \\\\ 11.4G^{4,17} & 1/2 \le n < 0.6366 \end{cases} \tag{6}$$

• the propagation of radio waves through a saline environment is not affected by

• no significant dispersion phenomena were observed for the frequency range

• the attenuation length is dependent on the percentage of impurities the salt

To perform the indirect method, the behavior of the antenna, introduced in a saline environment, will be analyzed when we have an interleaved element (air) between the antenna and the medium. By analyzing the following figure, we can determine the influence of the electrical parameters of the radio frequency antennas in saline environment when there is no perfect contact with this environment. **Figure 2** shows a cavity in a dielectric medium (salt), in which an emission or

If we analyze the **Figure 1** where the cavity is cylindrical with the length L and

2 *πb*<sup>2</sup> *L*

(7)

the radius of the base of r = b and considering the continuity of the tangential component of the electric field (*E0* = *E1*), we will find the equation below:

<sup>¼</sup> ð Þ *<sup>ε</sup>*0ð Þ *<sup>ε</sup><sup>r</sup>* � <sup>1</sup> j j *<sup>E</sup>*<sup>00</sup>

4*W*<sup>0</sup>

• no significant phenomena of double salt refraction were reported.

scattering phenomena;

(0.1 ÷ 1) GHz.

**Figure 1.**

block contains;

**113**

• no depolarization phenomena were observed;

*The system of generation and analysis of radio signals in saline environment.*

*Optimization of Cosmic Radiation Detection in Saline Environment*

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

Other empirical properties of salt blocks are [35]:

reception antenna (dipole antenna in λ/2) is introduced.

Δ*ω ω*0

• a decrease in the tangent of the loss angle with frequency;

The behavior of the dipole antenna in dielectric mediums for propagating the electromagnetic waves is similar to the behavior in vacuum or air, except that the impedance and the calculation of the antenna arm lengths change according to the relative permittivity of the environment, in which the antenna is located. If a group of antennas is inserted into a salt block, then the input resistance and the length of the dipole antenna in λ/2 will be changed with the real value of the permittivity of the salt (*ε<sup>r</sup>* = 5.981 + j0.0835) and the penetration depth of the waves. Electromagnetic will depend on tgδ, which is precisely the ratio between the imaginary and the real part of the permittivity.

The antenna parameters are influenced when the antenna passes from work in vacuum or air to work in environment with different permittivity of vacuum. Therefore, in calculating the antennas working in environments with different permittivity than the vacuum (generally higher), the permissibility of the environment, in which the antenna works is taken into account. Averages such as salt constitute an unconventional environment for antennas and therefore the dielectric parameters of the salt, for a frequency range between 100 MHz and 5 GHz, must be known.

The direct method is performed by a system of generation and analysis of radio signals in saline environment and it is made from an emission antenna, a receiving antenna, and a signal analyzer. Two pairs of antennas are used for two working frequencies f1 and f2, in order to determine the dielectric parameters of the salt, in order to determine the transfer of electromagnetic waves through the salt block, and in order to determine the electrical parameters of the radiofrequency antennas in saline environment.

The system is made of two identical antennas of the dipole type in *λ*/2 for the wavelength corresponding to the frequency *f*1 = 450 MHz and *f*2 = 750 MHz, each provided with a symmetrical and an impedance adapter of a transformer type with transmission lines mounted in the immediate vicinity of antenna, coaxial cables with small losses of type RG58LL, an impedance adapter of type CD, connecting cables of type CDF400 with small losses between signal analyzer Anritsu MS2690A (generator part with emission antenna), two antennas (one for transmission and one for reception), and the signal analyzer Anritsu MS2690A (analyzer part with the receiving antenna). The schematic diagram of the system, for generating and analyzing radio signals in saline environment, is shown in **Figure 1** [8].

The indirect method involves the determination of the electrical parameters of the radio frequency antennas in saline environment, knowing the electrical parameters of these radio frequency antennas in air and measuring their parameters introduced in a saline environment when the dielectric parameters of the saline environment are known. This method involves performing a measurement installation of the electrical parameters of the radio frequency antennas in the air and repeating the measurements in a saline environment with the same installation. For this, dielectric parameters of the saline environment must be known.

Knowing the conclusions of the measurements in a saline environment, we can determine the electrical parameters of the radiofrequency antennas in such an environment. Numerous measurements have been made in massive salt blocks by RADAR penetration technology (GPR) [34]. From the conclusions of the measurements, we mention:

#### *Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

**Figure 1.**

*Rin* ¼

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

real part of the permittivity.

in saline environment.

measurements, we mention:

**112**

known.

8 >>><

>>>:

20*G*<sup>2</sup> 0<*n* <1*=*4

24*:*7*G*2, <sup>5</sup> 1*=*4≤*n* <1*=*2

The behavior of the dipole antenna in dielectric mediums for propagating the electromagnetic waves is similar to the behavior in vacuum or air, except that the impedance and the calculation of the antenna arm lengths change according to the relative permittivity of the environment, in which the antenna is located. If a group of antennas is inserted into a salt block, then the input resistance and the length of the dipole antenna in λ/2 will be changed with the real value of the permittivity of the salt (*ε<sup>r</sup>* = 5.981 + j0.0835) and the penetration depth of the waves. Electromagnetic will depend on tgδ, which is precisely the ratio between the imaginary and the

The antenna parameters are influenced when the antenna passes from work in vacuum or air to work in environment with different permittivity of vacuum. Therefore, in calculating the antennas working in environments with different permittivity than the vacuum (generally higher), the permissibility of the environment, in which the antenna works is taken into account. Averages such as salt constitute an unconventional environment for antennas and therefore the dielectric parameters of the salt, for a frequency range between 100 MHz and 5 GHz, must be

The direct method is performed by a system of generation and analysis of radio signals in saline environment and it is made from an emission antenna, a receiving antenna, and a signal analyzer. Two pairs of antennas are used for two working frequencies f1 and f2, in order to determine the dielectric parameters of the salt, in order to determine the transfer of electromagnetic waves through the salt block, and in order to determine the electrical parameters of the radiofrequency antennas

The system is made of two identical antennas of the dipole type in *λ*/2 for the wavelength corresponding to the frequency *f*1 = 450 MHz and *f*2 = 750 MHz, each provided with a symmetrical and an impedance adapter of a transformer type with transmission lines mounted in the immediate vicinity of antenna, coaxial cables with small losses of type RG58LL, an impedance adapter of type CD, connecting cables of type CDF400 with small losses between signal analyzer Anritsu MS2690A (generator part with emission antenna), two antennas (one for transmission and one for reception), and the signal analyzer Anritsu MS2690A (analyzer part with the receiving antenna). The schematic diagram of the system, for generating and

The indirect method involves the determination of the electrical parameters of the radio frequency antennas in saline environment, knowing the electrical parameters of these radio frequency antennas in air and measuring their parameters introduced in a saline environment when the dielectric parameters of the saline environment are known. This method involves performing a measurement installation of the electrical parameters of the radio frequency antennas in the air and repeating the measurements in a saline environment with the same installation. For

Knowing the conclusions of the measurements in a saline environment, we can

determine the electrical parameters of the radiofrequency antennas in such an environment. Numerous measurements have been made in massive salt blocks by RADAR penetration technology (GPR) [34]. From the conclusions of the

analyzing radio signals in saline environment, is shown in **Figure 1** [8].

this, dielectric parameters of the saline environment must be known.

11*:*4*G*4, <sup>17</sup> 1*=*2≤ *n*<0*:*6366

(6)

*The system of generation and analysis of radio signals in saline environment.*


Other empirical properties of salt blocks are [35]:


To perform the indirect method, the behavior of the antenna, introduced in a saline environment, will be analyzed when we have an interleaved element (air) between the antenna and the medium. By analyzing the following figure, we can determine the influence of the electrical parameters of the radio frequency antennas in saline environment when there is no perfect contact with this environment.

**Figure 2** shows a cavity in a dielectric medium (salt), in which an emission or reception antenna (dipole antenna in λ/2) is introduced.

If we analyze the **Figure 1** where the cavity is cylindrical with the length L and the radius of the base of r = b and considering the continuity of the tangential component of the electric field (*E0* = *E1*), we will find the equation below:

$$\frac{\Delta\rho}{\rho\_0} = \frac{(\varepsilon\_0(\varepsilon\_r - 1))|E\_{00}|^2 \pi b^2 L}{4W\_0} \tag{7}$$

**Figure 2.** *Cavity in a dielectric medium (saline medium), in which a dipole antenna is inserted in λ/2.*

where: *E*<sup>00</sup> ¼ 1 and *W*<sup>0</sup> ¼ *πε*0*L* Ð *b <sup>a</sup> J*0ð Þ *k*0*r* 2 *rdr* represents the energy found in the cavity. The resonant frequency of the empty cavity is:

$$a\_0 = k\_0 c = 2.405 \left( \frac{c}{a} \right) \tag{8}$$

or an approximate value:

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

[37, 38]:

or otherwise:

where:

for salt).

**115**

where: *λ<sup>0</sup>* is the wavelength in vacuum.

which they propagate (of the saline environment).

*Optimization of Cosmic Radiation Detection in Saline Environment*

then it will exponentially decrease in time to zero.

*I z*ð Þ¼ <sup>1</sup> 2

(*z* = 0), *β* represents the absorption coefficient.

isotropic environments for the electromagnetic waves [37–39]:

∇ ∙ *<sup>E</sup>* � *μσ*

ffiffiffi *ε μ* r

*<sup>E</sup>*ð Þ <sup>0</sup>ð Þ*<sup>z</sup>*

*L* ffi

*λ*0 <sup>2</sup>*π ε*ð Þ<sup>1</sup>

For the study of the propagation of electromagnetic waves through saline environment it is necessary to know the dielectric parameters of the medium, through

For this we will consider the propagation equation in linear, homogeneous, and

*∂E ∂t* � *με ∂*2 *E <sup>∂</sup>t*<sup>2</sup> <sup>¼</sup> <sup>∇</sup> *<sup>ρ</sup>*

and we consider the dissipative (absorbing) environment in which *σ* 6¼ 0. We can assume that, if the environment contains free electric charge (*ρ* 6¼ 0),

We can determine the intensity of the wave at a certain depth *z,* which will be

*I z*ð Þ¼ *I*0*e*

range and the loss angle tangent between 0.015 and 0.030 at 300 MHz [40].

*I d*ð Þ¼ *I*0*e*

*<sup>d</sup>* <sup>¼</sup> <sup>1</sup>

*<sup>ω</sup>* <sup>≪</sup> <sup>1</sup> and *<sup>v</sup>* ffi

which means that the electromagnetic wave has the same propagation speed for whatever its frequency is. This means that there is no dispersion (this is the case

1 ffiffiffiffiffi

We will consider the case of an almost dielectric environment (*σ* – small, *ε* – big). In this case the ratio (*σ*/*ε*) will be much smaller than the unit [37, 38]:

> *σ εω* <sup>≪</sup> 1, *<sup>ω</sup><sup>c</sup>*

where: *I0* represents the intensity of the wave upon entering the environment

The salt from the mines of North America showed dielectric constants in the 5–7

An important problem is to determine the penetration length of electromagnetic waves in saline environment (attenuation length.) Thus we will define the depth of penetration of the wave into the environment. We will note the distance d as representing this depth. This depth is the decrease of the intensity of the field e times from the initial one. Then the intensity of the wave at depth d becomes:

ffiffiffi *ε μ* r

*<sup>E</sup>*ð Þ <sup>0</sup>ð Þ <sup>0</sup> <sup>2</sup>

*e*

�*β<sup>z</sup>* (16)

�*β<sup>d</sup>* (17)

*<sup>β</sup>* (18)

*εμ* <sup>p</sup> (19)

<sup>2</sup> tan *δ*

*ε*

� � (14)

�*β<sup>z</sup>* (15)

(13)

and *E*<sup>0</sup> ¼ *J*0ð Þ *k*0*r* is the energy in the empty cavity and *J0* represents the Bessel function of the first order for which *r* = *a*. Then, we will obtain:

$$\frac{\Delta a}{a\rho\_0} = 1.856(1 - \varepsilon\_r) \left(\frac{b}{a}\right)^2\tag{9}$$

If we use the last two formulas, then we can deduce the relative dielectric permittivity for the salt measurements:

$$
\epsilon\_r = 5.981 + j0.0835 \,\tag{10}
$$

The loss angle tangent is related to the attenuation coefficient of the field (*α*) and it represents the distance at which the electromagnetic field module decreases to (1/e). The formula, associated with the loss angle tangent, is [36]:

$$\tan \delta = \sqrt{\left[\frac{2}{\varepsilon'} \left(\frac{ac}{2\pi f}\right)^2 + 1\right]^2 - 1} \tag{11}$$

where: *f* represents the frequency and *c* is the speed of light in a vacuum. Then the attenuation length becomes:

$$L = \frac{1}{\alpha} = \frac{\lambda\_0}{2\pi} \sqrt{\frac{2}{\varepsilon' \left(\sqrt{1 + \tan^2 \delta} - 1\right)}}\tag{12}$$

*Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

or an approximate value:

$$L \cong \frac{\lambda\_0}{2\pi (\varepsilon)^{\frac{1}{2}} \tan \delta} \tag{13}$$

where: *λ<sup>0</sup>* is the wavelength in vacuum.

For the study of the propagation of electromagnetic waves through saline environment it is necessary to know the dielectric parameters of the medium, through which they propagate (of the saline environment).

For this we will consider the propagation equation in linear, homogeneous, and isotropic environments for the electromagnetic waves [37–39]:

$$
\nabla \bullet \bar{E} - \mu \sigma \frac{\partial \bar{E}}{\partial t} - \mu \varepsilon \frac{\partial^2 \bar{E}}{\partial t^2} = \nabla \left(\frac{\rho}{\varepsilon}\right) \tag{14}
$$

and we consider the dissipative (absorbing) environment in which *σ* 6¼ 0.

We can assume that, if the environment contains free electric charge (*ρ* 6¼ 0), then it will exponentially decrease in time to zero.

We can determine the intensity of the wave at a certain depth *z,* which will be [37, 38]:

$$I(x) = \frac{1}{2} \sqrt{\frac{\varepsilon}{\mu}} (\bar{E}\_0(x))^2 = \frac{1}{2} \sqrt{\frac{\varepsilon}{\mu}} (\bar{E}\_0(0))^2 e^{-\beta x} \tag{15}$$

or otherwise:

where: *E*<sup>00</sup> ¼ 1 and *W*<sup>0</sup> ¼ *πε*0*L*

**Figure 2.**

permittivity for the salt measurements:

the attenuation length becomes:

**114**

cavity. The resonant frequency of the empty cavity is:

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

Ð *b <sup>a</sup> J*0ð Þ *k*0*r*

*Cavity in a dielectric medium (saline medium), in which a dipole antenna is inserted in λ/2.*

function of the first order for which *r* = *a*. Then, we will obtain:

Δ*ω ω*0

(1/e). The formula, associated with the loss angle tangent, is [36]:

tan *δ* ¼

*<sup>L</sup>* <sup>¼</sup> <sup>1</sup>

*<sup>α</sup>* <sup>¼</sup> *<sup>λ</sup>*<sup>0</sup> 2*π* 2

*a* � �

*b a* � �<sup>2</sup>

*ε<sup>r</sup>* ¼ 5*:*981 þ *j*0*:*0835 (10)

� 1 vuut (11)

*<sup>ω</sup>*<sup>0</sup> <sup>¼</sup> *<sup>k</sup>*0*<sup>c</sup>* <sup>¼</sup> <sup>2</sup>*:*<sup>405</sup> *<sup>c</sup>*

¼ 1*:*856 1ð Þ � *ε<sup>r</sup>*

If we use the last two formulas, then we can deduce the relative dielectric

2 *ε*0

s

The loss angle tangent is related to the attenuation coefficient of the field (*α*) and it represents the distance at which the electromagnetic field module decreases to

> *ac* 2*πf* � �<sup>2</sup>

where: *f* represents the frequency and *c* is the speed of light in a vacuum. Then

" #<sup>2</sup>

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

þ 1

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 *ε*<sup>0</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> tan <sup>2</sup>*<sup>δ</sup>* <sup>p</sup> � <sup>1</sup> � �

and *E*<sup>0</sup> ¼ *J*0ð Þ *k*0*r* is the energy in the empty cavity and *J0* represents the Bessel

*rdr* represents the energy found in the

(8)

(9)

(12)

$$I(\mathbf{z}) = I\_0 \mathbf{e}^{-\beta \mathbf{z}} \tag{16}$$

where: *I0* represents the intensity of the wave upon entering the environment (*z* = 0), *β* represents the absorption coefficient.

The salt from the mines of North America showed dielectric constants in the 5–7 range and the loss angle tangent between 0.015 and 0.030 at 300 MHz [40].

An important problem is to determine the penetration length of electromagnetic waves in saline environment (attenuation length.) Thus we will define the depth of penetration of the wave into the environment. We will note the distance d as representing this depth. This depth is the decrease of the intensity of the field e times from the initial one. Then the intensity of the wave at depth d becomes:

$$I(d) = I\_0 e^{-\beta d} \tag{17}$$

where:

$$d = \frac{1}{\beta} \tag{18}$$

We will consider the case of an almost dielectric environment (*σ* – small, *ε* – big). In this case the ratio (*σ*/*ε*) will be much smaller than the unit [37, 38]:

$$\frac{\sigma}{\varepsilon \rho} \ll 1, \frac{\alpha\_{\varepsilon}}{\omega} \ll 1 \text{ and } v \cong \frac{1}{\sqrt{\varepsilon \mu}} \tag{19}$$

which means that the electromagnetic wave has the same propagation speed for whatever its frequency is. This means that there is no dispersion (this is the case for salt).

Then the depth of penetration will be given by the relation:

$$d \cong \frac{1}{\sigma} \sqrt{\frac{\varepsilon}{\mu}} = \frac{1}{\sigma Z} \tag{20}$$

**3. Data collection in saline environment**

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

*Optimization of Cosmic Radiation Detection in Saline Environment*

Calculation of antennas [8]:

determined by the above formula.

dimensions (**Table 1**.) for salt work.

where: *μ<sup>0</sup>* = 4π10�<sup>7</sup> [N/m2

**Figure 4.** *Antenna dimensions.*

**Table 1.**

**117**

*environment.*

antennas will be calculated with the formula:

In order to be able to collect the data from the saline environment, we will use

the system presented in **Figure 1**. An important problem is the design of the antennas to work in the saline environment. The first problem, that arises, is the

*La*½ � *<sup>λ</sup>=*<sup>2</sup> <sup>¼</sup> *<sup>c</sup>*

And it represents the antenna length in *λ*/2 [m] and *c* = 3 ∙ 10<sup>8</sup> m/s and *f* = the resonance frequency of the antenna [Hz], *ε<sup>r</sup>* = 5.981 + j0.0835, taking into account the real part Rð Þffi *ε<sup>r</sup>* 6. **Figure 4** shows the shape and dimensions of the antenna

The antennas are made of Copper pipe with *Φ* = 6 mm and have the following

A second problem that arises is the determination of the radiation resistance of the antennas in saline environment. As shown in **Figure 4**, the antenna is a dipole antenna in *λ*/2 and then the formula for calculating the radiation resistance is:

> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi *μ*<sup>0</sup> *ε*<sup>0</sup> � *ε<sup>r</sup>*

> > *La λ* � �<sup>2</sup>

r

] and *<sup>ε</sup><sup>0</sup>* = 8.859 � <sup>10</sup>�<sup>12</sup> [F/m].

*Rrad* ¼ 0*:*19397

*Ra sare* <sup>¼</sup> <sup>2</sup>*<sup>π</sup>*

Then the radiation resistance is about 29.853 Ω. Following the analysis of **Table 1**, it is found that the antenna length is much smaller than λ and then we can say that the antennas are of Hertzian type and the radiation resistance of the

> 3 ffiffiffiffiffiffiffiffiffiffi *<sup>ε</sup>r sare* <sup>p</sup> *<sup>Z</sup>*<sup>0</sup>

Then, for salt work, a radiation resistance of about 13.5 Ω will be obtained. In these conditions, it is necessary to adapt the radiation resistance of the antennas to the characteristic impedance of the Anritsu MS2690A 50 Ω analyzer. For the

*f* [MHz] 300 400 500 600 700 800 900 1000 *La* [m] 0.204 0.153 0.122 0.102 0.087 0.077 0.068 0.061

*The dimensions of the transmitting and receiving antennas at different frequencies for working in saline*

2*f* ffiffiffiffi *εr*

p (22)

(23)

(24)

determination of the antenna length for working in saline environment.

where: *Z* is the impedance for the pulse of the wave.

In most practical cases tan *δ* ≪ 1, so for the calculation of the penetration depth the formula is used (**Figure 3**):

$$d = \frac{3 \bullet 10^8}{2\pi f (\varepsilon\_r)^{\frac{1}{2}} \tan \delta} \tag{21}$$

The 36.79% percentage represents a 1/e decrease of the electromagnetic field in the dielectric environment (the incident field from which the reflected field is subtracted is taken into account).

The two methods do not differ much from each other. The difference is that, in the indirect method, there will be two packages of measurements. Starting from the package of measurements in air, continuing with the measurements in saline environment and knowing the dielectric and attenuation parameters of the electromagnetic waves of the saline environment, the electrical parameters of the radiofrequency antennas in saline environment can be determined by calculations. Taking into account these considerations, the indirect method can generate errors, because the determination of the electrical parameters of the radio frequency antennas in saline environment is based on the measurements of these parameters in the air (where small errors can occur), then measurements of these parameters are made in saline environment (where there also can occur small errors) and following the calculations, the errors can be added, which means a greater error. Thus, the indirect method involves high degree errors in determining the electrical parameters of radio frequency antennas in saline environment.

For the direct method, a system for measuring the electrical parameters of radio frequency antennas in saline environment will be used. The measurements being direct, we deduce that the errors are given only by these measurements (by the measurement system, analyzer – the generator part and the analyzer part). No additional calculations are required. So, the direct method is a method with smaller errors, although a measurement system, adapted to the saline environment is needed, compared to the indirect method that uses the same system of measurement in the air and in the saline environment.

**Figure 3.** *Illustration of the penetration of electromagnetic waves in a dielectric environment [41].*

#### **3. Data collection in saline environment**

In order to be able to collect the data from the saline environment, we will use the system presented in **Figure 1**. An important problem is the design of the antennas to work in the saline environment. The first problem, that arises, is the determination of the antenna length for working in saline environment.

Calculation of antennas [8]:

Then the depth of penetration will be given by the relation:

where: *Z* is the impedance for the pulse of the wave.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

the formula is used (**Figure 3**):

subtracted is taken into account).

*d* ffi 1 *σ*

ffiffiffi *ε μ* r

In most practical cases tan *δ* ≪ 1, so for the calculation of the penetration depth

The 36.79% percentage represents a 1/e decrease of the electromagnetic field in

The two methods do not differ much from each other. The difference is that, in the indirect method, there will be two packages of measurements. Starting from the package of measurements in air, continuing with the measurements in saline environment and knowing the dielectric and attenuation parameters of the electromag-

radiofrequency antennas in saline environment can be determined by calculations. Taking into account these considerations, the indirect method can generate errors, because the determination of the electrical parameters of the radio frequency antennas in saline environment is based on the measurements of these parameters in the air (where small errors can occur), then measurements of these parameters are made in saline environment (where there also can occur small errors) and following the calculations, the errors can be added, which means a greater error. Thus, the indirect method involves high degree errors in determining the electrical

For the direct method, a system for measuring the electrical parameters of radio frequency antennas in saline environment will be used. The measurements being direct, we deduce that the errors are given only by these measurements (by the measurement system, analyzer – the generator part and the analyzer part). No additional calculations are required. So, the direct method is a method with smaller errors, although a measurement system, adapted to the saline environment is needed, compared to the indirect method that uses the same system of measure-

*<sup>d</sup>* <sup>¼</sup> <sup>3</sup> <sup>∙</sup> <sup>10</sup><sup>8</sup> 2*πf*ð Þ *ε<sup>r</sup>* 1 <sup>2</sup> tan *δ*

the dielectric environment (the incident field from which the reflected field is

netic waves of the saline environment, the electrical parameters of the

parameters of radio frequency antennas in saline environment.

*Illustration of the penetration of electromagnetic waves in a dielectric environment [41].*

ment in the air and in the saline environment.

**Figure 3.**

**116**

¼ 1

*<sup>σ</sup><sup>Z</sup>* (20)

(21)

$$L\_{a[\lambda/2]} = \frac{c}{\mathfrak{F}\sqrt{\varepsilon\_r}}\tag{22}$$

And it represents the antenna length in *λ*/2 [m] and *c* = 3 ∙ 10<sup>8</sup> m/s and *f* = the resonance frequency of the antenna [Hz], *ε<sup>r</sup>* = 5.981 + j0.0835, taking into account the real part Rð Þffi *ε<sup>r</sup>* 6. **Figure 4** shows the shape and dimensions of the antenna determined by the above formula.

The antennas are made of Copper pipe with *Φ* = 6 mm and have the following dimensions (**Table 1**.) for salt work.

A second problem that arises is the determination of the radiation resistance of the antennas in saline environment. As shown in **Figure 4**, the antenna is a dipole antenna in *λ*/2 and then the formula for calculating the radiation resistance is:

$$R\_{rad} = 0.19397 \sqrt{\frac{\mu\_0}{\varepsilon\_0 \times \varepsilon\_r}} \tag{23}$$

where: *μ<sup>0</sup>* = 4π10�<sup>7</sup> [N/m2 ] and *<sup>ε</sup><sup>0</sup>* = 8.859 � <sup>10</sup>�<sup>12</sup> [F/m].

Then the radiation resistance is about 29.853 Ω. Following the analysis of **Table 1**, it is found that the antenna length is much smaller than λ and then we can say that the antennas are of Hertzian type and the radiation resistance of the antennas will be calculated with the formula:

$$R\_{a\text{ }sare} = \frac{2\pi}{3\sqrt{\epsilon\_r \epsilon\_{sare}}} Z\_0 \left(\frac{L\_d}{\lambda}\right)^2 \tag{24}$$

Then, for salt work, a radiation resistance of about 13.5 Ω will be obtained. In these conditions, it is necessary to adapt the radiation resistance of the antennas to the characteristic impedance of the Anritsu MS2690A 50 Ω analyzer. For the

**Figure 4.** *Antenna dimensions.*


**Table 1.**

*The dimensions of the transmitting and receiving antennas at different frequencies for working in saline environment.*

frequencies *f*1 = 450 MHz and *f*2 = 750 MHz, *La*450MHz = 0.136 m and *La*750MHz = 0.082 m were obtained and for the radiation resistance the following values were obtained:

$$f\_1 = 450 \text{MHz} \Longrightarrow \mathbf{R\_{at}}\_{\text{sare 450MHz}} = \frac{1}{\sqrt{6}} \bullet \mathbf{789.586} \bullet \left(\frac{0,136}{0,667}\right)^2 = \mathbf{13.401} \Omega \tag{25}$$

There follows a local processing station *SR* with a Wireless transceiver and, at the other end, another transceiver with a processing system to connect with the computer system. The total amplification of 120 dB is required to bring a signal of 0.6 μV (20 m) at the level of 0.6 V that can be processed by *CADm* (analog-to digital

• *AH1n* and *AH2n* is the pair of antennas for horizontal polarization in the vertical

• *AV1n* and *AV2n* is the pair of antennas for vertical polarization in group n on the

• *CAH1n* and *CAH2n* are the circuits for adapting the impedance of the antennas with the horizontal polarization to the impedance of the 50 Ω cable;

• *CAV1n* and *CAV2n* are the circuits for adapting the impedance of the antennas

• P*Hn* and P*Vn* are the sums of the signals coming from the antennas *AH1n*, *AH2n*

• *FTB0m* is the first band pass filter to select the desired spectral components;

• *A1m*, *FTB1m* – *FTB4m*, *A5m* represents the 100 dB amplification chain together

• *CADm* is the converter from analog signal after amplification, to digital signal;

• *P* + *Tx*/*Rx Wireless* is the local information processing system that includes the hard and soft trigger circuit, the *Tx*/*Rx Wireless* transceiver and the receiving broadcast antenna, which is used to improve the noise signal ratio and to

*Block diagram of the system for receiving, local processing and wireless transmission of the measured data to the*

• *FIFOm* is the memory of the digital signal maintained as a buffer until the arrival of the trigger signal from the *P* + *Tx*/*Rx Wireless* (transceiver) system;

calibrate the system processing from *PC* computer.

with the vertical polarization to the impedance of the 50 Ω cable;

converter). It consists of the following blocks (**Figure 6**):

*Optimization of Cosmic Radiation Detection in Saline Environment*

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

group n;

vertical;

respectively *AV1n*, *AV2n*;

with *FTB0m* and *FAAm*;

**Figure 6.**

**119**

*computing system.*

$$f\_2 = 750 \text{MHz} \Longrightarrow \mathbf{R\_{at}}\_{\text{sare 750MHz}} = \frac{1}{\sqrt{6}} \bullet 789.586 \bullet \left(\frac{0,082}{0,400}\right)^2 = \mathbf{13.546} \Omega \tag{26}$$

The frequency, at which the best propagation of electromagnetic waves, was determined in saline environment (Cantacuzino Mine from Slănic Prahova), is 187.5 MHz. The noise level in saline environment (Mina Cantacuzino from Slănic Prahova) is �115 dBm and at an impedance of 13.5 Ω, a noise level of 0.20662 μV is obtained. **Figure 5** shows the graph determined theoretically according to the distance of the variation of the radio frequency voltage level at the receiving antenna level. An electromagnetic emission event of a neutrino with the energy of 10<sup>18</sup> eV that generated a Cherenkov cone in saline environment was taken into account in this graph.

Analyzing the graph in **Figure 5**, we determine that for a neutrino with the energy of 10<sup>18</sup> eV that generated a Cherenkov cone in saline environment, a radio frequency signal at the terminals of a receiving antenna comparable to the noise level measured in saline environment will be produced as an effect at a distance of 50 m. So, for longer distances it is necessary that the energy of the neutrino be greater than 10<sup>18</sup> eV (10<sup>23</sup> eV).

Thus, a "Hardware system for detecting cosmic radiation of electron neutron type in salt" was designed [9]. This system is used to measure the level of attenuation of the electromagnetic waves introduced by the saline environment. Also with this system, the dielectric parameters of the saline environment can be determined in order to create a map with the distribution of the attenuations introduced by the saline environment. This system is, in fact, a radio detection station [5], *SRmk* where m is equivalent to the Cartesian x coordinate, k is equivalent to the Cartesian y coordinate, and n is equivalent to the Cartesian z coordinate. Each radio station will include two antennas for horizontal polarization and two for vertical polarization, one impedance adjustment circuit for each antenna, one adder for each polarization, one band pass filter to select the desired spectral components, five amplifiers followed by one band pass filter (minus the last amplifier) with full chain amplification from the first band pass filter to the 120 dB anti-alloy filter, an anti-alloy filter, an analog-to-digital converter, a *FIFO* memory (first input – first output).

**Figure 5.** *The graph of the variation of the radio frequency voltage level at the receiving antenna level.*

#### *Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

frequencies *f*1 = 450 MHz and *f*2 = 750 MHz, *La*450MHz = 0.136 m and

values were obtained:

this graph.

**Figure 5.**

**118**

greater than 10<sup>18</sup> eV (10<sup>23</sup> eV).

*<sup>f</sup>* <sup>1</sup> <sup>¼</sup> <sup>450</sup>*MHz*¼)*Ra sare* <sup>450</sup>*MHz* <sup>¼</sup> <sup>1</sup>

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

*<sup>f</sup>* <sup>2</sup> <sup>¼</sup> <sup>750</sup>*MHz*¼)*Ra sare* <sup>750</sup>*MHz* <sup>¼</sup> <sup>1</sup>

*La*750MHz = 0.082 m were obtained and for the radiation resistance the following

ffiffiffi 6

ffiffiffi 6

The frequency, at which the best propagation of electromagnetic waves, was determined in saline environment (Cantacuzino Mine from Slănic Prahova), is 187.5 MHz. The noise level in saline environment (Mina Cantacuzino from Slănic Prahova) is �115 dBm and at an impedance of 13.5 Ω, a noise level of 0.20662 μV is obtained. **Figure 5** shows the graph determined theoretically according to the distance of the variation of the radio frequency voltage level at the receiving antenna level. An electromagnetic emission event of a neutrino with the energy of 10<sup>18</sup> eV that generated a Cherenkov cone in saline environment was taken into account in

Analyzing the graph in **Figure 5**, we determine that for a neutrino with the energy of 10<sup>18</sup> eV that generated a Cherenkov cone in saline environment, a radio frequency signal at the terminals of a receiving antenna comparable to the noise level measured in saline environment will be produced as an effect at a distance of 50 m. So, for longer distances it is necessary that the energy of the neutrino be

Thus, a "Hardware system for detecting cosmic radiation of electron neutron type in salt" was designed [9]. This system is used to measure the level of attenuation of the electromagnetic waves introduced by the saline environment. Also with this system, the dielectric parameters of the saline environment can be determined in order to create a map with the distribution of the attenuations introduced by the saline environment. This system is, in fact, a radio detection station [5], *SRmk* where m is equivalent to the Cartesian x coordinate, k is equivalent to the Cartesian y coordinate, and n is equivalent to the Cartesian z coordinate. Each radio station will include two antennas for horizontal polarization and two for vertical polarization, one impedance adjustment circuit for each antenna, one adder for each polarization, one band pass filter to select the desired spectral components, five amplifiers followed by one band pass filter (minus the last amplifier) with full chain amplification from the first band pass filter to the 120 dB anti-alloy filter, an anti-alloy filter, an analog-to-digital converter, a *FIFO* memory (first input – first output).

*The graph of the variation of the radio frequency voltage level at the receiving antenna level.*

<sup>p</sup> <sup>∙</sup> <sup>789</sup>*:*<sup>586</sup> <sup>∙</sup> 0, 136

<sup>p</sup> <sup>∙</sup> <sup>789</sup>*:*<sup>586</sup> <sup>∙</sup> 0, 082

0, 667 � �<sup>2</sup>

0, 400 � �<sup>2</sup> ¼ 13*:*401Ω (25)

¼ 13*:*546Ω (26)

There follows a local processing station *SR* with a Wireless transceiver and, at the other end, another transceiver with a processing system to connect with the computer system. The total amplification of 120 dB is required to bring a signal of 0.6 μV (20 m) at the level of 0.6 V that can be processed by *CADm* (analog-to digital converter). It consists of the following blocks (**Figure 6**):


#### **Figure 6.**

*Block diagram of the system for receiving, local processing and wireless transmission of the measured data to the computing system.*

For the correct analysis of the data it is necessary that the temporal relation and the absolute value of the electric field be known, that is to say, all the instrumental errors must be corrected before working with the involved physical quantities. This implies a correction of the delays, which occur in the system, and a calibration of the amplitude.

broadcast antenna placed at a depth of 1 m from level 0 and received with an identical antenna placed at the same depth, attenuations of about 50 m are obtained

direct communication with the PC made with CY7C6801BA.

*Optimization of Cosmic Radiation Detection in Saline Environment*

resolution of the analog-numerical circuit, in this case, is:

It also offers a bit error rate of the order of 10�18.

processed by RD143 is on a frequency of 187.5 MHz.

*The signal at the input of the RD143 digital processing system.*

signal processed by CAN increases.

**Figure 8.**

**121**

*Rez* <sup>¼</sup> <sup>1</sup>*LSB* <sup>¼</sup> *Vmax*

At the output of the system, the signal is processed by *CADm*, which is made with the RD-143 development board. It consists of an ADC083000 analog-to-digital converter (CAN), an amplifier for improving the signal/noise ratio achieved with the LMH6555 low-distortion differential amplifier, a tact signal generator, a Field Programmable Gate Array (FPGA) block, a local processor, a PLL loop frequency synthesizer, VCO oscillator made with LMX2531 LQ1500E, and a USB interface for

The analog-numeric converter ADC083000 produced by National Semiconductor is an 8-bit converter that has a working power consumption of 1.9 W at a supply voltage of *Vcc* = 2.2 V, the maximum input signal on the Wine + and Wine� inputs is 2.5 V and the maximum conversion rate is 3GSPS (3 gigabytes per second). The

<sup>2</sup>*<sup>n</sup>* <sup>¼</sup> <sup>2</sup>*:*<sup>5</sup>

Following the laboratory tests, it was found that the actual number of bits used by RD143 for quantization, around 187.5 MHz (the signal value from the CAN input – analog-to-digital converter) is 7.3 bits, which means that the noise introduced by the CAN is very small. In fact, this noise increases as the frequency of the

Another important feature, determined by laboratory measurements, of this CAN is the low power consumption, reaching a consumption of 1.9 W at the maximum sampling frequency (3 GHz). Moreover, a linear characteristic of the power consumption, characteristic between 1.4 and 1.9 W. is observed. The signal

The dipole antenna of the system was found to pick up the radio signal generated by the USRP (Universal Software Radio Peripheral). The signal reached in the signal processing unit (e.g. laptop) is a distorted sinusoidal signal with the fundamental on 187.49 MHz and the amplitude 66.23db (the input signal was �50 dB), which means an amplification of 116.23 dB (a close amplification of the theoretical one) (**Figure 8**).

<sup>28</sup> <sup>¼</sup> <sup>9</sup>*:*8*mV* (27)

for the frequency of 187.5 MHz.

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

For the correction of these events it is necessary that a well-known signal be present in all data and that it will provide us the necessary temporal information. There is no need for an absolute time scale, as the measurements are not compared to external events. For this reason, only the relative temporal delays between the antennas should be known.

It is necessary to determine the attenuations introduced by the connection cables.

We used two types of cables:


The measured attenuations are presented in **Table 2**.

Following the measurements, the graph of variation of the power of a signal with a constant level measured at a fixed point at a distance of 20 m from the emission antenna was determined (**Figure 7**). The transmitting and receiving antennas were introduced in saline at a depth of 1 m from level 0.

Following the analysis of this graph, it is deduced that the attenuation of the electromagnetic waves is great for frequencies greater than 500 MHz, but it has a variation of about 20 dBm for a spectrum of 600 MHz. These attenuations fall for lengths of approximately 20 m. For the same signal levels introduced in the


**Table 2.**

*The attenuations measured on the connection cables used in the measurements in saline environment.*

**Figure 7.** *The power received at a fixed point 20 m from the transmitting antenna for various frequencies emitted.*

*Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

For the correct analysis of the data it is necessary that the temporal relation and the absolute value of the electric field be known, that is to say, all the instrumental errors must be corrected before working with the involved physical quantities. This implies a correction of the delays, which occur in the system, and a calibration of

For the correction of these events it is necessary that a well-known signal be present in all data and that it will provide us the necessary temporal information. There is no need for an absolute time scale, as the measurements are not compared to external events. For this reason, only the relative temporal delays between the

It is necessary to determine the attenuations introduced by the connection

Following the measurements, the graph of variation of the power of a signal with a constant level measured at a fixed point at a distance of 20 m from the emission antenna was determined (**Figure 7**). The transmitting and receiving antennas were

Following the analysis of this graph, it is deduced that the attenuation of the electromagnetic waves is great for frequencies greater than 500 MHz, but it has a variation of about 20 dBm for a spectrum of 600 MHz. These attenuations fall for lengths of approximately 20 m. For the same signal levels introduced in the

*f* **Cable CFD400-E Cable R-6763, O400** 450 MHz 0.31 dBm 3.05 dBm 750 MHz 0.6 dBm 4.22 dBm

*The attenuations measured on the connection cables used in the measurements in saline environment.*

*The power received at a fixed point 20 m from the transmitting antenna for various frequencies emitted.*

the amplitude.

cables.

**Table 2.**

**Figure 7.**

**120**

antennas should be known.

We used two types of cables:

• type CFD400-E (blue) with a length of 5 m.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

introduced in saline at a depth of 1 m from level 0.

• type R-6763, O400 (black) with a length of 21 m.

The measured attenuations are presented in **Table 2**.

broadcast antenna placed at a depth of 1 m from level 0 and received with an identical antenna placed at the same depth, attenuations of about 50 m are obtained for the frequency of 187.5 MHz.

At the output of the system, the signal is processed by *CADm*, which is made with the RD-143 development board. It consists of an ADC083000 analog-to-digital converter (CAN), an amplifier for improving the signal/noise ratio achieved with the LMH6555 low-distortion differential amplifier, a tact signal generator, a Field Programmable Gate Array (FPGA) block, a local processor, a PLL loop frequency synthesizer, VCO oscillator made with LMX2531 LQ1500E, and a USB interface for direct communication with the PC made with CY7C6801BA.

The analog-numeric converter ADC083000 produced by National Semiconductor is an 8-bit converter that has a working power consumption of 1.9 W at a supply voltage of *Vcc* = 2.2 V, the maximum input signal on the Wine + and Wine� inputs is 2.5 V and the maximum conversion rate is 3GSPS (3 gigabytes per second). The resolution of the analog-numerical circuit, in this case, is:

$$\text{Rez} = \text{1LSB} = \frac{V\_{\text{max}}}{2^{\text{n}}} = \frac{2.5}{2^{8}} = 9.8 mV \tag{27}$$

It also offers a bit error rate of the order of 10�18.

Following the laboratory tests, it was found that the actual number of bits used by RD143 for quantization, around 187.5 MHz (the signal value from the CAN input – analog-to-digital converter) is 7.3 bits, which means that the noise introduced by the CAN is very small. In fact, this noise increases as the frequency of the signal processed by CAN increases.

Another important feature, determined by laboratory measurements, of this CAN is the low power consumption, reaching a consumption of 1.9 W at the maximum sampling frequency (3 GHz). Moreover, a linear characteristic of the power consumption, characteristic between 1.4 and 1.9 W. is observed. The signal processed by RD143 is on a frequency of 187.5 MHz.

The dipole antenna of the system was found to pick up the radio signal generated by the USRP (Universal Software Radio Peripheral). The signal reached in the signal processing unit (e.g. laptop) is a distorted sinusoidal signal with the fundamental on 187.49 MHz and the amplitude 66.23db (the input signal was �50 dB), which means an amplification of 116.23 dB (a close amplification of the theoretical one) (**Figure 8**).

**Figure 8.** *The signal at the input of the RD143 digital processing system.*

**4.1 Inside the volume of the Cherenkov detector**

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

*Optimization of Cosmic Radiation Detection in Saline Environment*

and simplify the measurement chain.

environment through iterations.

kov detector placed in saline environment:

where *α*, *i*∈ *N* , *p ϵ R* and *p*, *α*, *i >* 0; *Lc*<sup>3</sup>

step and it is between 20 m ÷ 500 m.

**Figure 10.**

**123**

Determination of the Cherenkov cone inside the volume of the Cherenkov detector involves the design of a method to optimize the Cherenkov detector of electromagnetic radiation in the saline environment by determining the optimal points of placement of the detection elements and the Cherenkov detector in the saline environment, in order to minimize the number of measurement points and number of electromagnetic radiation sensing elements generated to reduce costs

The first problem that occurs is the creation of a map with the distribution of the dielectric parameters of the saline environment. For this, a sufficiently large number of measurements of the dielectric parameters of the saline environment will be

The problem solved by the optimization method of the Cherenkov detector of electromagnetic radiation in the saline environment removes the disadvantages of the Cherenkov detectors in the saline environment that have been proposed so far. Thus the method minimizes the number of detection elements and implicitly of the measurement chain, being also an economical and much faster method, characterized in the fact that it determines the optimal points of placement of the detection elements for the determined volume of the Cherenkov detector in saline

An iteration formula is used to obtain the optimal volume of the future Cheren-

*<sup>i</sup>* ¼ *p i*½ � þ *α*ð Þ *i* � 1 (28)

*<sup>i</sup>* represents the length of the side of the

executed in order to interpolate and extrapolate the measurement results.

*Lc*<sup>3</sup>

cube with iteration *i*; *i* represents the number of the iteration; *α* represents a coefficient that is dependent on the attenuation length of the electromagnetic waves through saline environment and adjusts to whole values; *p* represents the iteration

*An example of optimal placement of the detection elements of a Cherenkov detector for two iterations.*

This results in a Cherenkov detector consisting of at least two or more cubeshaped detectors in the cube and it also determines the optimal position of the future Cherenkov electromagnetic radiation detector in saline environment (**Figure 10**).

**Figure 9.** *The system shown in Figure 6 at the laboratory level.*

Distortions due to the existence of 3rd and 4th harmonics offer a distortion factor of 10%. The receiver design was performed for saline environment, medium with relative permeability different from that of the air. This could be one of the causes of a fairly large distortion factor. **Figure 9** shows the spectrum of the radio signal generated by the USRP and processed with the proposed experimental model.

#### **4. Methods for determination and detection of Cherenkov cone in saline environment**

Following the studies and articles published so far, it can be deduced that in order to make a Cherenkov detector in saline environment, many detecting elements and correspondingly many holes in saline environment, many chains of amplifiers (to bring the level detected by the workable TTL level detection (transistor-transistor logic), to compensate for losses on connection cables, etc.), many radio stations (*SRmk*) etc. Under these conditions, an optimization of the number of detection elements of a Cherenkov detector in saline environment and implicitly of all corresponding component elements is required.

To optimize a Cherenkov detector, it is necessary to carry out a study in order to achieve the objective. Following the study it was concluded that the optimization of a Cherenkov detector in saline environment is necessary in order to determine the optimal positions by placing the detection elements for to obtain the maximum information. Thus, it is necessary to know the attenuation of electromagnetic waves in saline environment. This aspect involves a large number of measurements in the volume of the entire salt block in which the future Cherenkov detector will be placed. Because of the attenuation of the electromagnetic waves (the product of the interaction of a neutron with sufficiently high energy with a saline environment that generates the Cherenkov cone) is given by the dielectric permittivity of the saline environment, it is necessary to create a map with the distribution of the dielectric parameters of the saline environment. Knowing this map will determine the optimal positions of the detection elements and their number as well.

In these conditions, two patents have been proposed, which deal with the methods of determining the Cherenkov detector inside and outside the volume of the Cherenkov detector [10, 11].

#### **4.1 Inside the volume of the Cherenkov detector**

Determination of the Cherenkov cone inside the volume of the Cherenkov detector involves the design of a method to optimize the Cherenkov detector of electromagnetic radiation in the saline environment by determining the optimal points of placement of the detection elements and the Cherenkov detector in the saline environment, in order to minimize the number of measurement points and number of electromagnetic radiation sensing elements generated to reduce costs and simplify the measurement chain.

The first problem that occurs is the creation of a map with the distribution of the dielectric parameters of the saline environment. For this, a sufficiently large number of measurements of the dielectric parameters of the saline environment will be executed in order to interpolate and extrapolate the measurement results.

The problem solved by the optimization method of the Cherenkov detector of electromagnetic radiation in the saline environment removes the disadvantages of the Cherenkov detectors in the saline environment that have been proposed so far.

Thus the method minimizes the number of detection elements and implicitly of the measurement chain, being also an economical and much faster method, characterized in the fact that it determines the optimal points of placement of the detection elements for the determined volume of the Cherenkov detector in saline environment through iterations.

An iteration formula is used to obtain the optimal volume of the future Cherenkov detector placed in saline environment:

$$L\mathbf{c}\_i^3 = p[i + a(i-1)]\tag{28}$$

where *α*, *i*∈ *N* , *p ϵ R* and *p*, *α*, *i >* 0; *Lc*<sup>3</sup> *<sup>i</sup>* represents the length of the side of the cube with iteration *i*; *i* represents the number of the iteration; *α* represents a coefficient that is dependent on the attenuation length of the electromagnetic waves through saline environment and adjusts to whole values; *p* represents the iteration step and it is between 20 m ÷ 500 m.

This results in a Cherenkov detector consisting of at least two or more cubeshaped detectors in the cube and it also determines the optimal position of the future Cherenkov electromagnetic radiation detector in saline environment (**Figure 10**).

*An example of optimal placement of the detection elements of a Cherenkov detector for two iterations.*

Distortions due to the existence of 3rd and 4th harmonics offer a distortion factor of 10%. The receiver design was performed for saline environment, medium with relative permeability different from that of the air. This could be one of the causes of a fairly large distortion factor. **Figure 9** shows the spectrum of the radio signal generated by the USRP and processed with the proposed experimental model.

**4. Methods for determination and detection of Cherenkov cone in saline**

To optimize a Cherenkov detector, it is necessary to carry out a study in order to achieve the objective. Following the study it was concluded that the optimization of a Cherenkov detector in saline environment is necessary in order to determine the optimal positions by placing the detection elements for to obtain the maximum information. Thus, it is necessary to know the attenuation of electromagnetic waves in saline environment. This aspect involves a large number of measurements in the volume of the entire salt block in which the future Cherenkov detector will be placed. Because of the attenuation of the electromagnetic waves (the product of the interaction of a neutron with sufficiently high energy with a saline environment that generates the Cherenkov cone) is given by the dielectric permittivity of the saline environment, it is necessary to create a map with the distribution of the dielectric parameters of the saline environment. Knowing this map will determine

Following the studies and articles published so far, it can be deduced that in order to make a Cherenkov detector in saline environment, many detecting elements and correspondingly many holes in saline environment, many chains of amplifiers (to bring the level detected by the workable TTL level detection (transistor-transistor logic), to compensate for losses on connection cables, etc.), many radio stations (*SRmk*) etc. Under these conditions, an optimization of the number of detection elements of a Cherenkov detector in saline environment and

implicitly of all corresponding component elements is required.

the optimal positions of the detection elements and their number as well. In these conditions, two patents have been proposed, which deal with the methods of determining the Cherenkov detector inside and outside the volume of

**environment**

*The system shown in Figure 6 at the laboratory level.*

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**Figure 9.**

the Cherenkov detector [10, 11].

**122**

The method of optimization of the Cherenkov detector of electromagnetic radiation in the saline environment has, as first stage, the determination of the imprint of the saline environment, in which the future Cherenkov detector is placed, which is realized by measurements in order to determine the dielectric parameters of the environment and its attenuation length at the frequency of work set (187.5 MHz). In order to reach the first stage, measurements will be made to determine the propagation of the electromagnetic waves at different points of the volume of the environment in a vertical and horizontal plane [8, 31] and function of the measurement results, the measurements can be resumed or multiplied for to determine entirely the real distribution of the environmental attenuation for the propagation of the electromagnetic waves. These measurements will be performed using antennas whose electrical parameters (directivity characteristic, radiation resistance, loss resistance, antenna efficiency, front-to-rear ratio) are very well known to work in saline environment. These measurements will be performed horizontally and vertically, storing the data in a database, which from their processing they will lead to drawing a map with the distribution of the attenuation lengths of the electromagnetic waves. The second step consists in configuring the electrical parameters of the detection elements at this frequency (187.5 MHz), by determining the directivity characteristics, radiation resistance, loss resistance, efficiency and front-to-back ratio, for the horizontal and vertical plane. This data will be stored in another database, which represents the information regarding the detection elements of the Cherenkov detector. The determination of the electrical parameters of the detection elements of the Cherenkov detector will be carried out by resuming or multiplying the measurements so that the actual values of the electrical parameters for the detection elements can be determined as accurately as possible. The two databases (the environmental footprint and the electrical parameters of the detection elements) and the use of a dedicated software will determine the optimal placement points of the detection elements for the volume determined by each iteration. Thus, the minimum number of iterations can be determined to optimize the Cherenkov detector.

**4.2 Outside the volume of the Cherenkov detector**

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

*Optimization of Cosmic Radiation Detection in Saline Environment*

reaches the detector elements of the detector.

(planes) and obtained by using the formula:

where: *α*, *i*∈ *N* <sup>∗</sup> , *p ϵ R şi p*, *α*, *i >* 0; *Lcex*<sup>3</sup>

**Figure 11.**

**125**

*detector in saline environment.*

*Lcex*<sup>3</sup>

cube delimited by the planes outside the volume of the Cherenkov detector; *i* represents the number of the iteration; *α* represents a coefficient that is dependent on the attenuation length of the electromagnetic waves through saline environment and it adjusts to whole values; *p* represents the iteration step and it is between 20 ÷ 500 m and it is chosen larger than the iteration step of the Cherenkov cone determination resulted inside the Cherenkov detector volume (**Figure 11**).

*An example of determination of the spatial positions of the placement plans of the detection elements external to the volume of the Cherenkov detector for a higher iteration of the determination of the volume of the Cherenkov*

The determination of the Cherenkov cone of electromagnetic radiation in the saline environment outside the volume of the Cherenkov detector is determined by placing at optimum points some detection elements outside its volume in all the x, y, z and positive and negative directions knowing the attenuation fingerprint in the electromagnetic wave field of the saline environment in order to determine the possible Cherenkov Cones that could form outside the detector volume depending on the energy determined by the detection elements in the vicinity of the detector. So far, no method for the determination of a Cherenkov Cone outside the detector volume is known, even though some of the energy emitted by the cone

This method determines the Cherenkov cone regardless of the position in which it is generated outside the detector volume, being an economical and predictable method, because outside the detector there are a minimum number of detection elements placed in optimal positions determined by their placement surfaces

*<sup>i</sup>* ¼ *p*½ � 1 þ *i*ð Þ *α* þ 1 (29)

*<sup>i</sup>* represents the length of the side of the

This method has the following advantages:


This method determines the positions of the optimum measurement points, which lead to the minimization of the number of measurements, the number of electromagnetic radiation detection elements and implicitly of the measurement chain and it also determines the optimal position of the future Cherenkov detector in the total volume of the saline environment. All these aspects lead to cost reduction. In order to determine the Cherenkov cone in saline environment, the method requires the use of a dedicated software that uses a database containing the footprint of the saline environment for which a cosmic radiation detector is desired.

#### **4.2 Outside the volume of the Cherenkov detector**

The method of optimization of the Cherenkov detector of electromagnetic radiation in the saline environment has, as first stage, the determination of the imprint of the saline environment, in which the future Cherenkov detector is placed, which is realized by measurements in order to determine the dielectric parameters of the environment and its attenuation length at the frequency of work set (187.5 MHz). In order to reach the first stage, measurements will be made to determine the propagation of the electromagnetic waves at different points of the volume of the environment in a vertical and horizontal plane [8, 31] and function of the measurement results, the measurements can be resumed or multiplied for to determine entirely the real distribution of the environmental attenuation for the propagation of the electromagnetic waves. These measurements will be performed using antennas whose electrical parameters (directivity characteristic, radiation resistance, loss resistance, antenna efficiency, front-to-rear ratio) are very well known to work in saline environment. These measurements will be performed horizontally and vertically, storing the data in a database, which from their processing they will lead to drawing a map with the distribution of the attenuation lengths of the electromagnetic waves. The second step consists in configuring the electrical parameters of the detection elements at this frequency (187.5 MHz), by determining the directivity characteristics, radiation resistance, loss resistance, efficiency and front-to-back ratio, for the horizontal and vertical plane. This data will be stored in another database, which represents the information regarding the detection elements of the Cherenkov detector. The determination of the electrical parameters of the detection elements of the Cherenkov detector will be carried out by resuming or multiplying the measurements so that the actual values of the electrical parameters for the detection elements can be determined as accurately as possible. The two databases (the environmental footprint and the electrical parameters of the detection elements) and the use of a dedicated software will determine the optimal placement points of the detection elements for the volume determined by each iteration. Thus, the minimum number of iterations

• Determination of the optimal positioning of the Cherenkov detector in the total

• Determination of the optimal placement points of the detection elements for

• Minimization of the number of detection elements and the measuring chain, which implies very low labor and material prices compared to the known methods and minimization of the number of wells necessary for the detector;

This method determines the positions of the optimum measurement points, which lead to the minimization of the number of measurements, the number of electromagnetic radiation detection elements and implicitly of the measurement chain and it also determines the optimal position of the future Cherenkov detector in the total volume of the saline environment. All these aspects lead to cost reduction. In order to determine the Cherenkov cone in saline environment, the method requires the use of a dedicated software that uses a database containing the footprint of the saline environment for which a cosmic radiation detector is desired.

• Software processing time is short compared to other methods;

• Determination of Cherenkov Cone under real conditions.

can be determined to optimize the Cherenkov detector. This method has the following advantages:

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

volume of the saline environment;

**124**

the volume determined by each iteration;

The determination of the Cherenkov cone of electromagnetic radiation in the saline environment outside the volume of the Cherenkov detector is determined by placing at optimum points some detection elements outside its volume in all the x, y, z and positive and negative directions knowing the attenuation fingerprint in the electromagnetic wave field of the saline environment in order to determine the possible Cherenkov Cones that could form outside the detector volume depending on the energy determined by the detection elements in the vicinity of the detector.

So far, no method for the determination of a Cherenkov Cone outside the detector volume is known, even though some of the energy emitted by the cone reaches the detector elements of the detector.

This method determines the Cherenkov cone regardless of the position in which it is generated outside the detector volume, being an economical and predictable method, because outside the detector there are a minimum number of detection elements placed in optimal positions determined by their placement surfaces (planes) and obtained by using the formula:

$$L\mathfrak{c}\_{\mathfrak{c}\chi}{}^{3} = p[\mathbf{1} + i(a+\mathbf{1})] \tag{29}$$

where: *α*, *i*∈ *N* <sup>∗</sup> , *p ϵ R şi p*, *α*, *i >* 0; *Lcex*<sup>3</sup> *<sup>i</sup>* represents the length of the side of the cube delimited by the planes outside the volume of the Cherenkov detector; *i* represents the number of the iteration; *α* represents a coefficient that is dependent on the attenuation length of the electromagnetic waves through saline environment and it adjusts to whole values; *p* represents the iteration step and it is between 20 ÷ 500 m and it is chosen larger than the iteration step of the Cherenkov cone determination resulted inside the Cherenkov detector volume (**Figure 11**).

#### **Figure 11.**

*An example of determination of the spatial positions of the placement plans of the detection elements external to the volume of the Cherenkov detector for a higher iteration of the determination of the volume of the Cherenkov detector in saline environment.*

The method is based on the determination of the attenuation fingerprint of the saline environment (the map of the spatial distribution of the electromagnetic waves attenuation in the saline environment) in the field of the electromagnetic waves and it leads to the increased probability to determine the generation of the Cherenkov Cone from outside the detector volume by determining the energy levels measured by the external detection elements providing that they are higher than the energy levels measured by the detection elements inside the Cherenkov detector.

The first step consists in determining the dielectric parameters of the saline environment in which the detection elements from outside the volume of the Cherenkov detector are to be located and it represents precisely the footprint of the

*Optimization of Cosmic Radiation Detection in Saline Environment*

In the second stage, for the working frequency of the detection elements in the saline environment (187.5 MHz), the directivity characteristics, the radiation resistance, the loss resistance, the efficiency, and the front-to-back ratio are determined. The third stage consists in processing the real data obtained when a Cherenkov cone is generated as a result of an interaction of cosmic radiation of the neutron nature with the saline environment in which the whole system (the Cherenkov detector and its external sensing elements) is located together with the two databases from the previous stages and depending on the energy levels measured by the external and internal elements the spatial position, in which the Cherenkov Cone was generated, is deduced. If the energy measured by the external sensing elements is greater than the energy measured by the internal elements then the Cherenkov

The information, "decoded" from the analysis of the electromagnetic energy generated by the Cherenkov cone (which is in a directly determined relation by the energy of the neutrino, which produced the Cherenkov phenomenon), are transmitted by the nuclear phenomena (fusion, fission, nuclear diffusion), which took place in the Universe at astronomic distanced (much larger than the detection possibilities known so far). This information brings an important contribution to

The determination of the Cherenkov cone in salt spray (in salt spray the neutri-

The maximum distance between the detection elements placed in salt spray at Slănic Prahova is given by the noise level, which was measured here (115 dBm) and it is of 50 m (0.2 μV, the graph from **Figure 5**). The detection of this level

processing level with a DAC system (digital-analog converter). Thus we deduce that the attenuation length of the saline spray determines the placement points of the

In order to minimize the costs of implementation of a Cherenkov detector for the determination and detection of the Cherenkov cone in saline spray (and in other environments where a map of the distribution of the spatial density of the dielectric permittivity in the volume of the entire environment, can be carried out), we need two stages: - the implementation of the map of the spatial density distribution of the dielectric permittivity in the volume of the entire salt spray and the determination of the optimum number of detection elements of the future Cherenkov detector and their optimum spatial placement position. In this regards, two methods for the

) in order to bring the signal at digital

requires amplifications of about 129.5 dB on the frequency 187.5 Mhz

nos with energies of the order 10<sup>12</sup> ÷ 10<sup>23</sup> eV are determined, which represent phenomena in the Universe that are generated by solar, galaxies, quasars, pulsars etc. systems), implies the implementation of a system, which measures the distribution of the density of the environment dielectric permittivity, which occurs in order to reduce the electromagnetic waves generated following the interaction between the environment with a neutrino. Thus a map, of the distribution of the "attenuation lengths" of the electromagnetic waves in the environment in which the

respective saline environment.

*DOI: http://dx.doi.org/10.5772/intechopen.91156*

**5. Conclusions**

the knowledge of the Universe.

measurement were done, is carried out.

(120 dB + 9.5 dB or an amplification of 3 <sup>10</sup><sup>6</sup>

detection elements of a Cherenkov detector.

**127**

Cone was generated outside the detector volume.

The determination of the Cherenkov cone in saline environment outside the volume of the Cherenkov detector consists in determining the optimal position of placement of the external detection elements, using a dedicated software.

For this, a minimum number of detection elements are placed outside the detector volume, which have very well established positions on the external surfaces of the detector, calculated by a higher iteration ratio than the detector volume calculation in all positive, negative *x*, *y*, *z* directions (Eq. (29)).

Then the attenuation of the saline environment (the map/fingerprint of the attenuation of the electromagnetic waves in the saline environment) will be calculated in the field of the electromagnetic waves [5, 8, 10, 31] as a result of measurements made outside the Cherenkov detector volume. In order to determine the Cherenkov cone outside the Cherenkov detector volume, the energy levels given by the sensing elements located outside the detector volume will be measured and if the energy measured by the external sensing elements is greater than the energy measured by the internal elements of the Cherenkov detector, then it is decided that a real Cherenkov cone outside the volume of the Cherenkov detector was generated. Thus we obtain the position in space of the Cherenkov Cone generated outside the detector in real situations using the dedicated software.

The method has the following advantages:


The application of the method for the determination of the Cherenkov cone in saline environment outside the volume of the Cherenkov detector requires three steps prior to the method.

The first step consists in determining the dielectric parameters of the saline environment in which the detection elements from outside the volume of the Cherenkov detector are to be located and it represents precisely the footprint of the respective saline environment.

In the second stage, for the working frequency of the detection elements in the saline environment (187.5 MHz), the directivity characteristics, the radiation resistance, the loss resistance, the efficiency, and the front-to-back ratio are determined.

The third stage consists in processing the real data obtained when a Cherenkov cone is generated as a result of an interaction of cosmic radiation of the neutron nature with the saline environment in which the whole system (the Cherenkov detector and its external sensing elements) is located together with the two databases from the previous stages and depending on the energy levels measured by the external and internal elements the spatial position, in which the Cherenkov Cone was generated, is deduced. If the energy measured by the external sensing elements is greater than the energy measured by the internal elements then the Cherenkov Cone was generated outside the detector volume.

#### **5. Conclusions**

The method is based on the determination of the attenuation fingerprint of the saline environment (the map of the spatial distribution of the electromagnetic waves attenuation in the saline environment) in the field of the electromagnetic waves and it leads to the increased probability to determine the generation of the Cherenkov Cone from outside the detector volume by determining the energy levels measured by the external detection elements providing that they are higher than the energy

The determination of the Cherenkov cone in saline environment outside the volume of the Cherenkov detector consists in determining the optimal position of

Then the attenuation of the saline environment (the map/fingerprint of the attenuation of the electromagnetic waves in the saline environment) will be calculated in the field of the electromagnetic waves [5, 8, 10, 31] as a result of measurements made outside the Cherenkov detector volume. In order to determine the Cherenkov cone outside the Cherenkov detector volume, the energy levels given by the sensing elements located outside the detector volume will be measured and if the energy measured by the external sensing elements is greater than the energy measured by the internal elements of the Cherenkov detector, then it is decided that a real Cherenkov cone outside the volume of the Cherenkov detector was generated. Thus we obtain the position in space of the Cherenkov Cone generated outside the

• determination of the Cherenkov cone generated outside the Cherenkov

• determination of the optimal positioning of the detection elements outside the volume of the Cherenkov detector in the saline environment by using a

• it establishes the plans (surfaces) for placing the detection elements outside the Cherenkov detector volume obtained by an iteration higher than the detector

• it minimizes the number of external detection elements and it optimizes the measurement chain, which implies very low labour and material prices and it

• it minimizes the data processing time with the help of the dedicated software;

• this method can be used for any type of environment as long as the environmental mitigation footprint in the field in which the Cherenkov detector works in the respective environment does not change during the determination period.

The application of the method for the determination of the Cherenkov cone in saline environment outside the volume of the Cherenkov detector requires three

• it determines the Cherenkov cone generated outside the detector under real

minimizes the number of wells required outside the detector;

levels measured by the detection elements inside the Cherenkov detector.

placement of the external detection elements, using a dedicated software. For this, a minimum number of detection elements are placed outside the detector volume, which have very well established positions on the external surfaces of the detector, calculated by a higher iteration ratio than the detector volume

calculation in all positive, negative *x*, *y*, *z* directions (Eq. (29)).

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

detector in real situations using the dedicated software. The method has the following advantages:

detector volume;

dedicated software;

volume determination;

conditions;

steps prior to the method.

**126**

The information, "decoded" from the analysis of the electromagnetic energy generated by the Cherenkov cone (which is in a directly determined relation by the energy of the neutrino, which produced the Cherenkov phenomenon), are transmitted by the nuclear phenomena (fusion, fission, nuclear diffusion), which took place in the Universe at astronomic distanced (much larger than the detection possibilities known so far). This information brings an important contribution to the knowledge of the Universe.

The determination of the Cherenkov cone in salt spray (in salt spray the neutrinos with energies of the order 10<sup>12</sup> ÷ 10<sup>23</sup> eV are determined, which represent phenomena in the Universe that are generated by solar, galaxies, quasars, pulsars etc. systems), implies the implementation of a system, which measures the distribution of the density of the environment dielectric permittivity, which occurs in order to reduce the electromagnetic waves generated following the interaction between the environment with a neutrino. Thus a map, of the distribution of the "attenuation lengths" of the electromagnetic waves in the environment in which the measurement were done, is carried out.

The maximum distance between the detection elements placed in salt spray at Slănic Prahova is given by the noise level, which was measured here (115 dBm) and it is of 50 m (0.2 μV, the graph from **Figure 5**). The detection of this level requires amplifications of about 129.5 dB on the frequency 187.5 Mhz (120 dB + 9.5 dB or an amplification of 3 <sup>10</sup><sup>6</sup> ) in order to bring the signal at digital processing level with a DAC system (digital-analog converter). Thus we deduce that the attenuation length of the saline spray determines the placement points of the detection elements of a Cherenkov detector.

In order to minimize the costs of implementation of a Cherenkov detector for the determination and detection of the Cherenkov cone in saline spray (and in other environments where a map of the distribution of the spatial density of the dielectric permittivity in the volume of the entire environment, can be carried out), we need two stages: - the implementation of the map of the spatial density distribution of the dielectric permittivity in the volume of the entire salt spray and the determination of the optimum number of detection elements of the future Cherenkov detector and their optimum spatial placement position. In this regards, two methods for the

determination and detection of the Cherenkov cone in salt spray are noticed: inside and outside the volume of the detector.

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The Cherenkov cone in salt spray is generated following the interaction of a UHE neutrino (Ultra High Energy, 10<sup>12</sup> ÷ 10<sup>23</sup> eV) with the saline environment. The detection of the information generated by the Cherenkov cone in salt spray implies knowing the energy, the direction, and the direction of travel of the neutrino, which interacted with this environment. The generation of UHE neutrinos may be due to some nuclear-related phenomena, which have a very high energy and give these neutrinos energies equivalent to the phenomena and provide information about these violent phenomena in the Universe. Thus, we can determine the nuclear phenomena in the Universe.

#### **Acknowledgements**

This work has been carried out on the Core Programme of the Romanian Ministry of Education and Research, National Authority for Scientific Research, PN-19-18 (18N/08. 02. 2019).

#### **Notes/thanks/other declarations**

We thank the Professors from the Faculty of Electronics, Telecommunications, and Information Technology at the Polytechnic University of Bucharest, Romania: Octavian Fratu, Alina Mihaela Bădescu, Alexandru Vulpe, and Răzvan Crăciunescu for the support and the materials made available.

#### **Author details**

Valeriu Savu, Mădălin Ion Rusu\* and Dan Savastru National Institute of Research and Development for Optoelectronics INOE 2000, Magurele, Romania

\*Address all correspondence to: madalin@inoe.ro

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Optimization of Cosmic Radiation Detection in Saline Environment DOI: http://dx.doi.org/10.5772/intechopen.91156*

#### **References**

determination and detection of the Cherenkov cone in salt spray are noticed: -

The Cherenkov cone in salt spray is generated following the interaction of a UHE neutrino (Ultra High Energy, 10<sup>12</sup> ÷ 10<sup>23</sup> eV) with the saline environment. The detection of the information generated by the Cherenkov cone in salt spray implies knowing the energy, the direction, and the direction of travel of the neutrino, which interacted with this environment. The generation of UHE neutrinos may be due to some nuclear-related phenomena, which have a very high energy and give these neutrinos energies equivalent to the phenomena and provide information about these violent phenomena in the Universe. Thus, we can determine the nuclear

This work has been carried out on the Core Programme of the Romanian Ministry of Education and Research, National Authority for Scientific Research, PN-19-18

We thank the Professors from the Faculty of Electronics, Telecommunications, and Information Technology at the Polytechnic University of Bucharest, Romania: Octavian Fratu, Alina Mihaela Bădescu, Alexandru Vulpe, and Răzvan Crăciunescu

National Institute of Research and Development for Optoelectronics INOE 2000,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

inside and outside the volume of the detector.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

phenomena in the Universe.

**Notes/thanks/other declarations**

for the support and the materials made available.

Valeriu Savu, Mădălin Ion Rusu\* and Dan Savastru

\*Address all correspondence to: madalin@inoe.ro

provided the original work is properly cited.

**Acknowledgements**

(18N/08. 02. 2019).

**Author details**

Magurele, Romania

**128**

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[39] Crețu TI. Fizică - Curs Universitar. București: Editura Tehnică; 1996

[20] Hill DA. Fields of horizontal currents located above the earth. IEEE Transactions on Geoscience and Remote

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

nonlinear quantum theory. Physics Letters A. 2010;**375**:2305-2308

[31] Savu V, Fratu O, Rusu MI, Savastru D, Tenciu D, Vulpe A, et al. Determination of the electromagnetic wave propagation for the detection of the Cherenkov radiation cone in salt environment. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics. 2018;**80**(1):251-260

2012;**64**(1):281-293

[30] Badescu AM et al. Radio technique for investigating high energy cosmic neutrinos. Romanian Reports in Physics.

[32] IEEE Standard Definitions of Terms for Antennas, IEEE Std 145-1993 (Revision of IEEE Std 145-1983)

[33] Available from: http://www.scritube.

LUI-MAXWELL-PROPAGAR24262.php

Northern Ohio Geological Society; 1978

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nr. 82-104/2008

U.T. Press; 2011

electromagn42125.php

[34] Unterberger R. Radar and sonar probing of salt. In: International Symposium on Salts. Hamburg:

com/stiinta/fizica/ECUATIILE-

[21] Saltzberg D, Gorham P, Walz D, et al. Observation of the Askaryan effect: Coherent microwave emission from change asymmetry in high energy particle cascades. Physical Review Letters. 2001;**86**:2802-2803

[22] Dagkesamanskii RD, Matveev VA, Zheleznykh IM. Prospects of radio detection of extremely high energy neutrinos bombarding the Moon. Nuclear Instruments and Methods in Physics Research A. 2010. In press

[23] Gorham PW et al. Experimental limit on the cosmic diffuse ultrahighenergy neutrino flux. Physical Review

[24] Gorham PW et al. Accelerator measurements of the Askaryan effect in rock salt: A roadmap toward Teraton underground neutrino detectors. Physiological Reviews. 2005;**D72**:

[25] Gorham PW et al. Observations of the Askaryan effect in ice. Physical Review Letters. 2007;**99**:171101

[26] Askaryan GA. Radiation of volume and surface compression waves during impingement of a nonrelativistic

electron stream at the surface of a dense medium. Soviet physics - Technical

[27] Luo C, Ibanescu M, Johnson SG, Joannopoulos JD. Cerenkov radiation in photonic crystals. Science. 2003;**299**:

[28] Coleman SR, Glashow SL. Cosmic ray and neutrino tests of special relativity. Physics Letters B. 1997;**405**:249

[29] Zloshchastiev KG. Vacuum Cherenkov effect in logarithmic

physics. 1959;**4**(2):234-235

Letters. 2004;**93**:041101

023002

368-371

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Sensing. 1989;**GE-26**(6)

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[41] Available from: http://media0.wgz. ro/files/media0:4b51f7d6af096.pdf.upl/ ET5b-%20Incalzirea%

**Chapter 8**

**Abstract**

Sensitivity and Uncertainty

Quantification of Neutronic

and JENDL-4.0 Evaluations

*M. Kaddour and S. Elouahdani*

Integral Data Using ENDF/B-VII.1

*Mustapha Makhloul, H. Boukhal,T. El Bardouni, E. Chakir,*

Many integral neutronic parameters such as the effective multiplication factors (keff) are based on neutron reactions with matter through cross sections. However, these cross sections present uncertainties, of origin multiple, which reduce the safety margin of nuclear installations. In order to minimize these risks, a sensitivity

analysis is necessary to indicate the rate of change of a reactor performance parameter compared to variations in cross sections. Thus, several critical benchmarks were taken from the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE), and their sensitivities and covariance matrix of the desired cross section were processed by MCNP6 and NJOY codes, respectively, in ENDF/B-VII.1 and JENDL-4.0 evaluations. The results obtained show that the 44 energy groups give the most varied sensitivity profiles than those given by others (15 and 33). In addition, we observed large uncertainties on the keff due to the H-1 and O-16 cross-sectional uncertainties (200–1000 pcm) in ENDF/B -VII.1 and the U-235 cross section in JENDL-4.0; however, keff's uncertainties due to the

**Keywords:** keff, sensitivity, covariance matrix, uncertainty, MCNP6.1, NJOY,

Prediction of integral nuclear parameters requires a reliable nuclear database such as microscopic nuclear parameters, cross sections, covariance matrices, etc. Many previous works [1, 2] have proved that the capture cross section of the uranium 235 has an important effect on the criticality calculations [3, 4]. For example, the relative uncertainty of keff in BFS core due to the 235U capture cross-

In present study, the uncertainty prediction in the multiplication factors is based on the ENDF/B-VII.1 and JENDL-4.0 evaluations where MCNP6 [6] Monte Carlo code is used for the sensitivity and keff calculations and the NJOY99 [7] is applied to calculate the covariances in three energy group structures (15, 33 and 44) for the

cross-sectional uncertainties of the U-238 are very small.

multigroup cross section

sectional uncertainty is near 202 pcm [5].

**1. Introduction**

**133**

#### **Chapter 8**

## Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1 and JENDL-4.0 Evaluations

*Mustapha Makhloul, H. Boukhal,T. El Bardouni, E. Chakir, M. Kaddour and S. Elouahdani*

#### **Abstract**

Many integral neutronic parameters such as the effective multiplication factors (keff) are based on neutron reactions with matter through cross sections. However, these cross sections present uncertainties, of origin multiple, which reduce the safety margin of nuclear installations. In order to minimize these risks, a sensitivity analysis is necessary to indicate the rate of change of a reactor performance parameter compared to variations in cross sections. Thus, several critical benchmarks were taken from the International Handbook of Evaluated Criticality Safety Benchmark Experiments (IHECSBE), and their sensitivities and covariance matrix of the desired cross section were processed by MCNP6 and NJOY codes, respectively, in ENDF/B-VII.1 and JENDL-4.0 evaluations. The results obtained show that the 44 energy groups give the most varied sensitivity profiles than those given by others (15 and 33). In addition, we observed large uncertainties on the keff due to the H-1 and O-16 cross-sectional uncertainties (200–1000 pcm) in ENDF/B -VII.1 and the U-235 cross section in JENDL-4.0; however, keff's uncertainties due to the cross-sectional uncertainties of the U-238 are very small.

**Keywords:** keff, sensitivity, covariance matrix, uncertainty, MCNP6.1, NJOY, multigroup cross section

#### **1. Introduction**

Prediction of integral nuclear parameters requires a reliable nuclear database such as microscopic nuclear parameters, cross sections, covariance matrices, etc. Many previous works [1, 2] have proved that the capture cross section of the uranium 235 has an important effect on the criticality calculations [3, 4]. For example, the relative uncertainty of keff in BFS core due to the 235U capture crosssectional uncertainty is near 202 pcm [5].

In present study, the uncertainty prediction in the multiplication factors is based on the ENDF/B-VII.1 and JENDL-4.0 evaluations where MCNP6 [6] Monte Carlo code is used for the sensitivity and keff calculations and the NJOY99 [7] is applied to calculate the covariances in three energy group structures (15, 33 and 44) for the

most abundant isotopes in the studied benchmarks (235U, 238U, <sup>1</sup> H, and 16O). All benchmarks were taken from IHECSBE [8].

#### **2. Study approach**

#### **2.1 Multigroup structure**

In this article, the effect of the multigroup energy of neutrons on the sensitivity of multiplication factors was studied for three cases (15, 33, and 44 groups). The covariances for many cross sections are often presented in the evaluated data libraries (ENDF/B-VII.1 and JENDL-4.0). All files were processed by the NJOY99 code to calculate the multigroup of interest cross sections in the ENDF-6 format. The modules RECONR and BROADR were used before to reconstruct the cross sections (MF = 3) at room temperature 300°K. The GROUPR module was used to generate the desired data in the grouped-wise format gendf for the three presentations (15, 33, and 44 groups) to retain the characteristic structure in the cross sections between 10<sup>5</sup> eV and 20 MeV. The energetic structures were generated from the fine-group library for resonance nuclides, with different weight flux functions: fission Maxwellian (10 MeV–70 keV), 1/E (70 keV–0.125 eV), and thermal Maxwellian (0.125–10<sup>5</sup> eV). **Tables 1**–**3** below present the three energy group structures.

Figures below illustrate the comparison of the pointwise and multigroup representations for the 235.238U cross sections (**Figures 1** and **2**).

Figures above present that the pointwise and multigroup cross sections are very close in the two evaluations ENDF/B-VII.1 and JENDL-4.0.

#### **2.2 Covariance data of cross sections**

It is necessary to process the multigroup covariance matrices for each energy group structure (15, 33, and 44). Thus, an appropriate input file for nuclear code NJOY was prepared using several modules as ERROR, GROUPER, and COVR [11–13] to process the ENDF file (MF = 33) and generate the multigroup covariance matrices for the desired cross sections. The following figures show a comparison of these covariance matrices in the two evaluations studied using the structures of 15, 33, and 44 energy groups.

**Figure 3** shows the uncertainty and covariance for the 235U elastic cross section in the energy region from 10<sup>5</sup> eV to 20 MeV. In this figure, we can see that the


lowest uncertainty is given by the 44-group structure where around the energy 10 keV, the uncertainty is 4% in the ENDF/B-VII.1 and 9.5% in JENDL-4.0. In

of the 235U in the energy less than 10 eV are, respectively, 7.5% and 1% in JENDL-4.0 and ENDF/B-VII.1 for 15 and 33 groups; however, in the 44-group structure, one can see that this maximum is 15% around the energy 3 eV. In the energy interval [10 eV; 20 MeV], these uncertainties are very close to 1% for the two evaluations in 33- and 44-group structures, while for the 15-group structure,

According to **Figure 4**, the maximum uncertainties in the fission cross sections

addition, negative correlations are observed in JENDL-4.0.

**Group number**

**Table 2.**

**Table 3.**

**135**

*44 Neutron energy group structure [10].*

**Group number**

*33 Neutron energy group structure [10].*

**Upper energy (eV)**

**Upper energy (eV)**

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Group number**

**Group number**

 1.0000E-05 16 3.2500E-01 31 3.0000E+03 3.0000E-03 17 3.5000E-01 32 1.7000E+04 7.5000E-03 18 3.7500E-01 33 2.5000E+04 1.0000E-02 19 4.0000E-01 34 1.0000E+05 2.5300E-02 20 6.2500E-01 35 4.0000E+05 3.0000E-02 21 1.0000E+00 36 9.0000E+05 4.0000E-02 22 1.7700E+00 37 1.4000E+06 5.0000E-02 23 3.0000E+00 38 1.8500E+06 7.0000E-02 24 4.7500E+00 39 2.3540E+06 1.0000E-01 25 6.0000E+00 40 2.4790E+06 1.5000E-01 26 8.1000E+00 41 3.0000E+06 2.0000E-01 27 1.0000E+01 42 4.8000E+06 2.2500E-01 28 3.0000E+01 43 6.4340E+06 2.5000E-01 29 1.0000E+02 44 8.1873E+06 2.7500E-01 30 5.5000E+02 45 2.0000E+07

 1.0000E-01 12 4.5400E+02 23 1.1100E+05 5.4000E-01 13 7.4900E+02 24 1.8300E+05 4.0000E+00 14 1.2300E+03 25 3.0200E+05 8.3200E+00 15 2.0300E+03 26 4.9800E+05 1.3700E+01 16 3.3500E+03 27 8.2100E+05 2.2600E+01 17 5.5300E+03 28 1.3500E+06 4.0200E+01 18 9.1200E+03 29 2.2300E+06 6.7900E+01 19 1.5000E+04 30 3.6800E+06 9.1700E+01 20 2.4800E+04 31 6.0700E+06 1.4900E+02 21 4.0900E+04 32 1.0000E+07

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

**Upper energy (eV)**

**Upper energy (eV)**

**Group number**

**Group number** **Upper energy (eV)**

**Upper energy (eV)**

#### **Table 1.**

*15 Neutron energy group structure [9].*

**Group number Upper energy (eV) Group number Upper energy (eV) Group number Upper energy (eV)** 1 1.0000E-01 12 4.5400E+02 23 1.1100E+05 2 5.4000E-01 13 7.4900E+02 24 1.8300E+05 3 4.0000E+00 14 1.2300E+03 25 3.0200E+05 4 8.3200E+00 15 2.0300E+03 26 4.9800E+05 5 1.3700E+01 16 3.3500E+03 27 8.2100E+05 6 2.2600E+01 17 5.5300E+03 28 1.3500E+06 7 4.0200E+01 18 9.1200E+03 29 2.2300E+06 8 6.7900E+01 19 1.5000E+04 30 3.6800E+06 9 9.1700E+01 20 2.4800E+04 31 6.0700E+06 10 1.4900E+02 21 4.0900E+04 32 1.0000E+07

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

#### **Table 2.**

most abundant isotopes in the studied benchmarks (235U, 238U, <sup>1</sup>

In this article, the effect of the multigroup energy of neutrons on the sensitivity of multiplication factors was studied for three cases (15, 33, and 44 groups). The covariances for many cross sections are often presented in the evaluated data libraries (ENDF/B-VII.1 and JENDL-4.0). All files were processed by the NJOY99 code to calculate the multigroup of interest cross sections in the ENDF-6 format. The modules RECONR and BROADR were used before to reconstruct the cross sections (MF = 3) at room temperature 300°K. The GROUPR module was used to generate the desired data in the grouped-wise format gendf for the three presentations (15, 33, and 44 groups) to retain the characteristic structure in the cross sections between 10<sup>5</sup> eV and 20 MeV. The energetic structures were generated from the fine-group library for resonance nuclides, with different weight flux functions: fission Maxwellian (10 MeV–70 keV), 1/E (70 keV–0.125 eV), and thermal Maxwellian (0.125–10<sup>5</sup> eV). **Tables 1**–**3** below present the three energy group

Figures below illustrate the comparison of the pointwise and multigroup

Figures above present that the pointwise and multigroup cross sections are very

It is necessary to process the multigroup covariance matrices for each energy group structure (15, 33, and 44). Thus, an appropriate input file for nuclear code NJOY was prepared using several modules as ERROR, GROUPER, and COVR [11–13] to process the ENDF file (MF = 33) and generate the multigroup covariance matrices for the desired cross sections. The following figures show a comparison of these covariance matrices in the two evaluations studied using the structures of 15,

**Figure 3** shows the uncertainty and covariance for the 235U elastic cross section in the energy region from 10<sup>5</sup> eV to 20 MeV. In this figure, we can see that the

**Group number Energy range (eV) Group number Energy range (eV)** 1.0000E-05 9 2.4800E+04 1.1000E-01 10 6.7400E+04 5.4000E-01 11 1.8300E+05 4.0000E+00 12 4.9800E+05 2.2600E+01 13 1.3500E+06 4.5400E+02 14 2.2300E+06 2.0400E+03 15 6.0700E+06 9.1200E+03 16 1.9600E+07

representations for the 235.238U cross sections (**Figures 1** and **2**).

close in the two evaluations ENDF/B-VII.1 and JENDL-4.0.

**2.2 Covariance data of cross sections**

33, and 44 energy groups.

*15 Neutron energy group structure [9].*

**Table 1.**

**134**

benchmarks were taken from IHECSBE [8].

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**2. Study approach**

structures.

**2.1 Multigroup structure**

H, and 16O). All

*33 Neutron energy group structure [10].*


#### **Table 3.**

*44 Neutron energy group structure [10].*

lowest uncertainty is given by the 44-group structure where around the energy 10 keV, the uncertainty is 4% in the ENDF/B-VII.1 and 9.5% in JENDL-4.0. In addition, negative correlations are observed in JENDL-4.0.

According to **Figure 4**, the maximum uncertainties in the fission cross sections of the 235U in the energy less than 10 eV are, respectively, 7.5% and 1% in JENDL-4.0 and ENDF/B-VII.1 for 15 and 33 groups; however, in the 44-group structure, one can see that this maximum is 15% around the energy 3 eV. In the energy interval [10 eV; 20 MeV], these uncertainties are very close to 1% for the two evaluations in 33- and 44-group structures, while for the 15-group structure,

**Figure 1.** *The pointwise and multigroup (15, 33, and 44) capture cross section for the 235U.*

the uncertainties in JENDL-4.0 are higher than those in ENDF/B-VII.1. Also, negative correlations appeared in JENDL-4.0.

#### **2.3 Sensitivity-uncertainty theory**

Sensitivity coefficients represent the percentage effect on some nuclear system response (e.g., multiplication factor keff) due to a percentage change in an input parameter such as cross section (capture, fission, elastic, inelastic, etc.). The sensitivity of keff (noted simply k) to a multigroup cross section *σ<sup>x</sup>:<sup>g</sup>*, for an energy group g, is defined according to [14] by Eq. (1), where the first order of the perturbation theory is used [15–17]:

$$S\_{\mathbf{x},\mathbf{g}} = \frac{\sigma\_{\mathbf{x},\mathbf{g}}}{k} \frac{\partial k}{\partial \sigma\_{\mathbf{x},\mathbf{g}}} \tag{1}$$

These coefficients are supposed to be constant in the first order of perturbation

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

where *m* is the number of critical systems considered and n is the number of

The sensitivity matrix coefficients have been calculated using MCNP6.1 code

The integral quantities calculated with a reference cross section set σ are denoted

*<sup>i</sup>* <sup>¼</sup> <sup>1</sup>*:*2*:* … *:n and j* <sup>¼</sup> <sup>1</sup>*:*2*:* … *:<sup>m</sup>* (2)

*k*<sup>0</sup> ¼ *k*ð Þ 1 þ *S:δσ* (3)

, which deviates

theory, so the sensitivity matrix S (Eq. (2)) is also constant [18–20]:

*The pointwise and multigroup (15, 33, and 44) elastic cross section for the 238U.*

by k. The integral quantities k' calculated with a cross section set σ<sup>0</sup>

*Sk* <sup>¼</sup> <sup>σ</sup><sup>i</sup> *k j ∂k <sup>j</sup> ∂*σj

by *δ*σ from σ, have the following relation with *k*:

energy groups (n = 15, 33, and 44).

using KSEN card.

**137**

**Figure 2.**

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Figure 2.** *The pointwise and multigroup (15, 33, and 44) elastic cross section for the 238U.*

These coefficients are supposed to be constant in the first order of perturbation theory, so the sensitivity matrix S (Eq. (2)) is also constant [18–20]:

$$\mathbf{S}\_{k} = \left[\frac{\sigma\_{\mathbf{i}}}{k\_{\rangle}} \frac{\partial k\_{\rangle}}{\partial \sigma\_{\mathbf{j}}}\right] i = \mathbf{1}.2...n \; and \; j = \mathbf{1}.2...m \tag{2}$$

where *m* is the number of critical systems considered and n is the number of energy groups (n = 15, 33, and 44).

The sensitivity matrix coefficients have been calculated using MCNP6.1 code using KSEN card.

The integral quantities calculated with a reference cross section set σ are denoted by k. The integral quantities k' calculated with a cross section set σ<sup>0</sup> , which deviates by *δ*σ from σ, have the following relation with *k*:

$$k'=k(\mathbf{1}+\mathbf{S}.\delta\sigma)\tag{3}$$

the uncertainties in JENDL-4.0 are higher than those in ENDF/B-VII.1. Also,

*The pointwise and multigroup (15, 33, and 44) capture cross section for the 235U.*

Sensitivity coefficients represent the percentage effect on some nuclear system response (e.g., multiplication factor keff) due to a percentage change in an input parameter such as cross section (capture, fission, elastic, inelastic, etc.). The sensitivity of keff (noted simply k) to a multigroup cross section *σ<sup>x</sup>:<sup>g</sup>*, for an energy group g, is defined according to [14] by Eq. (1), where the first order of the perturbation

> *∂k ∂*σx*:*<sup>g</sup>

(1)

*Sx:<sup>g</sup>* <sup>¼</sup> <sup>σ</sup>x*:*<sup>g</sup> *k*

negative correlations appeared in JENDL-4.0.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**2.3 Sensitivity-uncertainty theory**

theory is used [15–17]:

**136**

**Figure 1.**

**Figure 3.**

*Uncertainty and covariance for the 235 U elastic cross section using 15, 33, and 44 structure energy groups in ENDF/B-VII.1 and JENDL-4.0 evaluations.*

The covariance of k'/k is given by

$$V\_k = (\mathbf{S}\sigma' - \mathbf{S}\sigma)(\mathbf{S}\sigma' - \mathbf{S}\sigma)^t$$

$$V\_k = \mathbf{S}(T - T\_0)(T - T\_0)^t\mathbf{S}^t$$

$$V\_k = \mathbf{S}\mathbf{M}\mathbf{S}^t\tag{4}$$

A common practice in uncertainty calculations is the relative sensitivity coefficients

where G is the relative sensitivity matrix and P is the relative covariance matrix

Eq. (7) mathematically links the uncertainty of the integral data and the uncertainties of the cross sections through the associated sensitivity coefficients. Thus, a high sensitivity and an uncertain cross section generate a large uncertainty in k.

In this work, 25 HEU-SOL-THERM thermal experiments, 4 HEU-MET-INTER intermediate experiments, and 21 HEU-MET-FAST fast experiments are studied. The calculated, experimental *keff* and their uncertainties for each benchmark are

ð Þ <sup>Δ</sup>*k=<sup>k</sup>* <sup>2</sup> <sup>¼</sup> *GPG<sup>t</sup>* (7)

provided from the sensitivity analysis. Therefore, the relative matrices are used as

*Uncertainty and covariance for the 235U fission cross section using 15, 33, and 44 energy group structures in*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

of the interest cross section.

*ENDF/B-VII.1 and JENDL-4.0 evaluations.*

**Figure 4.**

**139**

**3. Results and discussion**

**3.1 Description of benchmark systems**

where t stands for the transpose of the matrix S.

The square root of the diagonal term Vii of *Vk* is the standard deviation in the integral quantity ki. Thus, the prior nuclear data uncertainty of k can be obtained in matrix expression form by the so-called sandwich rule [20, 21]:

$$\left(\Delta k\right)^{2} = \text{SMS}^{t} \tag{5}$$

The non-diagonal term *Vij*ð Þ *i* 6¼ *j* gives the degree of correlation between the errors of *ki* and *k <sup>j</sup>*. The element *rij* of the correlation matrix is obtained by dividing the element *Vij* by the products of standard deviation *Vii* and *Vjj*:

$$r\_{\vec{ij}} = \frac{V\_{\vec{ij}}}{\sqrt{V\_{\vec{ii}}V\_{\vec{jj}}}} \tag{6}$$

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Figure 4.**

The covariance of k'/k is given by

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

*ENDF/B-VII.1 and JENDL-4.0 evaluations.*

**Figure 3.**

**138**

where t stands for the transpose of the matrix S.

matrix expression form by the so-called sandwich rule [20, 21]:

the element *Vij* by the products of standard deviation *Vii* and *Vjj*:

*Vk* <sup>¼</sup> *<sup>S</sup>*σ<sup>0</sup> ð Þ � *<sup>S</sup>*<sup>σ</sup> *<sup>S</sup>*σ<sup>0</sup> ð Þ � *<sup>S</sup>*<sup>σ</sup> *<sup>t</sup> Vk* <sup>¼</sup> *S T*ð Þ � *<sup>T</sup>*<sup>0</sup> ð Þ *<sup>T</sup>* � *<sup>T</sup>*<sup>0</sup> *<sup>t</sup>*

*Uncertainty and covariance for the 235 U elastic cross section using 15, 33, and 44 structure energy groups in*

The square root of the diagonal term Vii of *Vk* is the standard deviation in the integral quantity ki. Thus, the prior nuclear data uncertainty of k can be obtained in

The non-diagonal term *Vij*ð Þ *i* 6¼ *j* gives the degree of correlation between the errors of *ki* and *k <sup>j</sup>*. The element *rij* of the correlation matrix is obtained by dividing

> *rij* <sup>¼</sup> *Vij* ffiffiffiffiffiffiffiffiffiffiffiffi *ViiVjj*

*St Vk* <sup>¼</sup> *SMSt* (4)

ð Þ <sup>Δ</sup>*<sup>k</sup>* <sup>2</sup> <sup>¼</sup> *SMSt* (5)

<sup>p</sup> (6)

*Uncertainty and covariance for the 235U fission cross section using 15, 33, and 44 energy group structures in ENDF/B-VII.1 and JENDL-4.0 evaluations.*

A common practice in uncertainty calculations is the relative sensitivity coefficients provided from the sensitivity analysis. Therefore, the relative matrices are used as

$$(\Delta k/k)^2 = \text{GPG}^t\tag{7}$$

where G is the relative sensitivity matrix and P is the relative covariance matrix of the interest cross section.

Eq. (7) mathematically links the uncertainty of the integral data and the uncertainties of the cross sections through the associated sensitivity coefficients. Thus, a high sensitivity and an uncertain cross section generate a large uncertainty in k.

#### **3. Results and discussion**

#### **3.1 Description of benchmark systems**

In this work, 25 HEU-SOL-THERM thermal experiments, 4 HEU-MET-INTER intermediate experiments, and 21 HEU-MET-FAST fast experiments are studied. The calculated, experimental *keff* and their uncertainties for each benchmark are


summarized in **Table 4**. All calculations were performed using 100,000 neutrons per cycle, 150 inactive cycles, and 4000 active cycles to minimize statistical uncer-

**Isotope ENDF/B-VII.1 JENDL-4.0 ENDF/B-VII.1 JENDL-4.0** U-234 5.1587E-03 7.4997E-03 1.4957E-03 1.9720E-03 U-235 8.0536E-01 8.0423E-01 1.4577E-01 1.5009E-01 U-238 1.7438E-02 1.7762E-02 4.2719E-02 4.1731E-02

**Benchmarks k.exp std.exp k.cal (ENDF/B-VII.1) std.cal k.cal (JENDL-4.0) std.cal** Hmf011.001 0.9989 0.0015 0.99887 0.00004 0.99265 0.00003 Hmf012.001 0.9992 0.0018 0.99810 0.00003 0.99236 0.00003 Hmf014.001 0.9989 0.0017 0.99774 0.00003 0.99684 0.00003 Hmf015.001 0.9996 0.0017 0.99447 0.00003 0.99774 0.00003 Hmf018.002 1.0000 0.0014 0.99946 0.00003 0.99337 0.00003 Hmf020.002 1.0000 0.0028 1.00057 0.00003 0.99416 0.00003 Hmf021.002 1.0000 0.0024 0.99750 0.00003 1.00132 0.00004 Hmf022.002 1.0000 0.0021 0.99746 0.0003 0.99782 0.00003 Hmf026.011 0.9982 0.0042 1.00312 0.00004 1.00647 0.00005 Hmf028.001 1.0000 0.0030 1.00286 0.00003 1.00745 0.00005

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

**Hst001.001 Hst001.006 Hst035.007**

**Hmf001.001 Hmf003.001**

**Isotope ENDF/B-VII.1 JENDL-4.0 ENDF/B-VII.1 JENDL-4.0 ENDF/B-VII.1 JENDL-4.0** U-234 -2.7926E-03 -2.6083E-03 -2.0123E-03 -1.8550E-03 -2.3645E-03 -2.4621E-03 U-235 1.0503E-01 1.1931E-01 2.2592E-01 2.2535E-01 1.3115E-01 1.3959E-01 U-236 -2.9683E-04 -4.2700E-04 -5.0385E-05 -1.6201E-04 -2.3107E-04 -2.4627E-04 U-238 -2.7572E-03 -3.3237E-03 -1.1858E-03 -1.3662E-03 -6.4877E-03 -5.4229E-03 H-1 5.5723E-01 5.4111E-01 3.4059E-01 3.4260E-01 3.9636E-01 4.0646E-01 O-16 1.3385E-01 1.3190E-01 1.1264E-01 1.1672E-01 9.0869E-02 9.3703E-02 N-14 -2.8936E-03 -6.3375E-04 -2.9080E-03 -5.5300E-03 -3.6365E-03 -5.4211E-03

The total sensitivity calculations were performed in order to identify the most important cross sections for neutron-induced reactions in critical experiments summarized in **Table 4**. The total integrated sensitivities obtained using the ENDF/B-VII.1 and JENDL-4.0 evaluations are presented in **Tables 5** and **6**. We can see from

tainty (5 pcm).

**Table 4.**

**Table 5.**

**Table 6.**

**141**

Keff *benchmark cases and their statistical uncertainties (1σ).*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

*Total integrated sensitivity for thermal benchmark (%%).*

*Total integrated sensitivity for fast benchmark (%%).*

**3.2 Total sensitivity evaluation**

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*


#### **Table 4.**

**Benchmarks k.exp std.exp k.cal (ENDF/B-VII.1) std.cal k.cal (JENDL-4.0) std.cal** Hst001.001 1.0004 0.0060 0.99815 0.00005 0.99952 0.00005 Hst001.002 1.0021 0.0072 0.99722 0.00006 0.99927 0.00006 Hst001.003 1.0003 0.0035 1.00155 0.00005 1.00296 0.00005 Hst001.004 1.0008 0.0053 0.99815 0.00005 1.00048 0.00005 Hst001.005 1.0001 0.0049 0.99874 0.00005 0.99949 0.00005 Hst001.006 1.0002 0.0046 1.00196 0.00005 1.00283 0.00005 Hst001.007 1.0008 0.0040 0.99781 0.00005 0.99910 0.00005 Hst001.008 0.9998 0.0038 0.99797 0.00005 0.99930 0.00005 Hst001.009 1.0008 0.0054 0.99412 0.00006 0.99633 0.00006 Hst001.010 0.9993 0.0054 0.99241 0.00005 0.99338 0.00005 Hst009.001 0.9990 0.0043 0.99695 0.00005 1.00096 0.00005 Hst009.002 1.0000 0.0039 0.99686 0.00005 1.00034 0.00005 Hst009.003 1.0000 0.0036 0.99556 0.00005 0.99830 0.00005 Hst009.004 0.9986 0.0035 0.98894 0.00005 0.99112 0.00005 Hst009.010 1.0000 0.0057 0.99745 0.00005 1.00153 0.00005 Hst010.001 1.0000 0.0029 0.99453 0.00005 0.99633 0.00005 Hst010.002 1.0000 0.0018 0.99496 0.00005 0.99678 0.00005 Hst010.003 1.0000 0.0029 0.99247 0.00005 0.99237 0.00005 Hst010.004 0.9992 0.0029 0.99052 0.00005 0.99994 0.00004 Hst011.001 1.0000 0.0023 0.99859 0.00004 0.99773 0.00003 Hst011.002 1.0000 0.0023 0.99866 0.00004 0.99602 0.00004 Hst012.001 0.9999 0.0058 0.99723 0.00003 0.99745 0.00004 Hst013.001 1.0012 0.0026 0.99868 0.00003 1.00569 0.00005 Hst028.001 1.0000 0.0023 0.99642 0.00005 0.99580 0.00004 Hst035.007 1.0000 0.0035 1.00467 0.00005 0.99938 0.00004 Hmi006.001 0.9977 0.0008 0.99297 0.00004 1.00151 0.00004 Hmi006.002 1.0001 0.0008 0.99682 0.00004 1.00315 0.00004 Hmi006.003 1.0015 0.0009 1.00082 0.00004 0.99751 0.00003 Hmi006.004 1.0016 0.0008 1.00732 0.00004 0.99025 0.00003 Hmf001.001 1.0004 0.0024 0.99976 0.00003 0.98929 0.00003 Hmf003.001 1.0000 0.0050 0.99501 0.00003 0.99386 0.00003 Hmf003.002 1.0000 0.0050 0.99436 0.00003 0.99208 0.00003 Hmf003.003 1.0000 0.0050 0.99918 0.00003 0.99638 0.00003 Hmf003.004 1.0000 0.0050 0.99721 0.00003 1.00187 0.00003 Hmf003.005 1.0000 0.0030 1.00146 0.00003 1.00190 0.00003 Hmf003.008 1.0000 0.0030 1.00214 0.00003 1.00515 0.00003 Hmf003.009 1.0000 0.0050 1.00244 0.00003 1.00960 0.00003 hmf003.010 1.0000 0.0050 1.00505 0.00003 0.99315 0.00003 Hmf003.011 1.0000 0.0030 1.00886 0.00003 0.99656 0.00004 Hmf008.001 0.9989 0.0016 0.99577 0.00003 0.99518 0.00003

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**140**

Keff *benchmark cases and their statistical uncertainties (1σ).*


#### **Table 5.**

*Total integrated sensitivity for thermal benchmark (%%).*


#### **Table 6.**

*Total integrated sensitivity for fast benchmark (%%).*

summarized in **Table 4**. All calculations were performed using 100,000 neutrons per cycle, 150 inactive cycles, and 4000 active cycles to minimize statistical uncertainty (5 pcm).

#### **3.2 Total sensitivity evaluation**

The total sensitivity calculations were performed in order to identify the most important cross sections for neutron-induced reactions in critical experiments summarized in **Table 4**. The total integrated sensitivities obtained using the ENDF/B-VII.1 and JENDL-4.0 evaluations are presented in **Tables 5** and **6**. We can see from

**Figure 5.**

*Sensitivity profiles of 235U capture cross section for thermal benchmarks with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 6.**

*Sensitivity profiles of 235U capture cross section for thermal benchmarks with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 7.**

*Sensitivity profiles of 235U capture cross section for thermal benchmarks with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

these tables that the total integrated sensitivity obtained with the two nuclear evaluations is almost the same; in addition, the sensitivities of U-234, U-236, and N-14 are very low compared to the others. Thus, for the quantification of sensitivity and uncertainty, only U-235, U-238, H-1, and O-16 are taken into account.

**3.3 Sensitivities of keff with respect to multigroup cross section**

**Figure 8.**

**Figure 9.**

**Figure 10.**

**143**

*and JENDL-4.0.*

*and JENDL-4.0.*

*and JENDL-4.0.*

In this study, the sensitivity coefficients obtained with the two libraries ENDF/B-VII.1 and JENDL-4.0 are evaluated using MCNP6.1 code in three

*Sensitivity profiles of 235U fission cross section for thermal benchmarks with 44 energy groups—ENDF/B-VII.1*

*Sensitivity profiles of 235U fission cross section for thermal benchmarks with 15 energy groups—ENDF/B-VII.1*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

*Sensitivity profiles of 235U fission cross section for thermal benchmarks with 33 energy groups—ENDF/B-VII.1*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Figure 8.**

*Sensitivity profiles of 235U fission cross section for thermal benchmarks with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 9.**

*Sensitivity profiles of 235U fission cross section for thermal benchmarks with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 10.**

*Sensitivity profiles of 235U fission cross section for thermal benchmarks with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

#### **3.3 Sensitivities of keff with respect to multigroup cross section**

In this study, the sensitivity coefficients obtained with the two libraries ENDF/B-VII.1 and JENDL-4.0 are evaluated using MCNP6.1 code in three

these tables that the total integrated sensitivity obtained with the two nuclear evaluations is almost the same; in addition, the sensitivities of U-234, U-236, and N-14 are very low compared to the others. Thus, for the quantification of sensitivity and

*Sensitivity profiles of 235U capture cross section for thermal benchmarks with 44 energy groups—ENDF/B-*

*Sensitivity profiles of 235U capture cross section for thermal benchmarks with 33 energy groups—ENDF/B-*

*Sensitivity profiles of 235U capture cross section for thermal benchmarks with 15 energy groups—ENDF/B-*

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

uncertainty, only U-235, U-238, H-1, and O-16 are taken into account.

**Figure 6.**

**Figure 5.**

*VII.1 and JENDL-4.0.*

**Figure 7.**

**142**

*VII.1 and JENDL-4.0.*

*VII.1 and JENDL-4.0.*

**Figure 11.** *Sensitivity profiles of the 238U capture cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 12.** *Sensitivity profiles of the 238U capture cross section with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 13.** *Sensitivity profiles of the 238U capture cross section with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

multigroup structures (15, 33, and 44). Given the large number of cross sections for each energy group, the sensitivities of certain cross sections are only presented.

From these figures, it can be seen that the 44-group structure of energy gives very varied sensitivity profiles depending on the neutron energy; moreover, this group structure gives sensitivities slightly lower than those given by the structures of 15 and 33 groups. Consequently, it can be said that the precision of the sensitivity increases for the structure containing the largest number of energy groups. Thus, low uncertainties on nuclear data are expected with this structure (44 groups) in

*Sensitivity profiles of the 238U elastic cross section with 44 energy groups—ENDF and JENDL-4.0.*

*Sensitivity profiles of the 238U elastic cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

*Sensitivity profiles of the 238U elastic cross section with 33 energy groups—ENDF and JENDL-4.0.*

the two evaluations (ENDF/B-VII.1 and JENDL-4.0).

**Figure 14.**

**Figure 15.**

**Figure 16.**

**145**

#### *3.3.1 Sensitivity for the 235U cross section*

The results obtained are presented in the figures below for the 235U cross sections (**Figures 5**–**10**).

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Figure 14.**

*Sensitivity profiles of the 238U elastic cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 15.** *Sensitivity profiles of the 238U elastic cross section with 33 energy groups—ENDF and JENDL-4.0.*

**Figure 16.** *Sensitivity profiles of the 238U elastic cross section with 44 energy groups—ENDF and JENDL-4.0.*

From these figures, it can be seen that the 44-group structure of energy gives very varied sensitivity profiles depending on the neutron energy; moreover, this group structure gives sensitivities slightly lower than those given by the structures of 15 and 33 groups. Consequently, it can be said that the precision of the sensitivity increases for the structure containing the largest number of energy groups. Thus, low uncertainties on nuclear data are expected with this structure (44 groups) in the two evaluations (ENDF/B-VII.1 and JENDL-4.0).

multigroup structures (15, 33, and 44). Given the large number of cross sections for each energy group, the sensitivities of certain cross sections are only presented.

*Sensitivity profiles of the 238U capture cross section with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*Sensitivity profiles of the 238U capture cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

*Sensitivity profiles of the 238U capture cross section with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

The results obtained are presented in the figures below for the 235U cross sec-

*3.3.1 Sensitivity for the 235U cross section*

tions (**Figures 5**–**10**).

**Figure 11.**

**Figure 12.**

**Figure 13.**

**144**

**Figure 17.**

*Sensitivity profiles of the <sup>1</sup> H elastic cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 18.** *Sensitivity profiles of the <sup>1</sup> H elastic cross section with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 19.** *Sensitivity profiles of the <sup>1</sup> H elastic cross section with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

#### *3.3.2 Sensitivity for the 238U cross section*

The sensitivities of the multiplication factors for the 238U cross sections are shown in the figures below (**Figures 11**–**16**).

These figures show that thermal and intermediate critical experiment designs demonstrate low sensitivity to the capture and elastic cross sections of the 238U at high energies and a significant sensitivity at thermal and resonance energies. However, the fast critical experiments demonstrate, at high energies, high levels of sensitivity to the capture and elastic cross sections of the 238U. Also, the structure of the 44 energy groups gives very varied sensitivity profiles compared to those given

*Sensitivity profiles of the 16O elastic cross section with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*Sensitivity profiles of the 16O elastic cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

*Sensitivity profiles of the 16O elastic cross section with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

by structures 15 and 33.

**Figure 20.**

**Figure 21.**

**Figure 22.**

**147**

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Figure 20.**

*Sensitivity profiles of the 16O elastic cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 21.** *Sensitivity profiles of the 16O elastic cross section with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 22.** *Sensitivity profiles of the 16O elastic cross section with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

high energies and a significant sensitivity at thermal and resonance energies. However, the fast critical experiments demonstrate, at high energies, high levels of sensitivity to the capture and elastic cross sections of the 238U. Also, the structure of the 44 energy groups gives very varied sensitivity profiles compared to those given by structures 15 and 33.

*3.3.2 Sensitivity for the 238U cross section*

**Figure 18.**

**Figure 17.**

*Sensitivity profiles of the <sup>1</sup>*

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**Figure 19.**

**146**

*Sensitivity profiles of the <sup>1</sup>*

*Sensitivity profiles of the <sup>1</sup>*

shown in the figures below (**Figures 11**–**16**).

The sensitivities of the multiplication factors for the 238U cross sections are

These figures show that thermal and intermediate critical experiment designs demonstrate low sensitivity to the capture and elastic cross sections of the 238U at

*H elastic cross section with 33 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*H elastic cross section with 15 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

*H elastic cross section with 44 energy groups—ENDF/B-VII.1 and JENDL-4.0.*

#### *3.3.3 Sensitivity for <sup>1</sup> H and 16O cross sections*

The sensitivities of the keff's with respect to the cross sections of <sup>1</sup> H and 16O are presented in the figures below (**Figures 17**–**22**).

In the following, all the results concerning only the structure of the group of 44

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

The nuclear data uncertainties of keff are calculated using Eq. (7), and the predictions of *Δk=k* due to the uncertainty of the 235U cross sections are presented in

*Δk/k (pcm) prediction due to the uncertainties in 235U elastic cross sections with 44 energy groups for thermal*

*Δk/k (pcm) prediction due to the uncertainties in 235U elastic cross sections with 44 energy groups for fast*

neutrons and presented for both ENDF/B-VII.1 and JENDL-4.0.

**3.4 Nuclear data uncertainty prediction of keff**

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

the figures below (**Figures 23**–**26**).

*benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

*benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 25.**

**Figure 26.**

**149**

The figures above show that all thermal critical benchmarks demonstrate low sensitivity to the <sup>1</sup> H and 16O elastic cross sections for low resonance energies and significant sensitivity for high energies. In addition, the structure of the 44 energy groups gives very varied sensitivity profiles compared to those given by the 15- and 33-group structures. Also, the sensitivities given by ENDF/B-VII.1 are slightly lower than those given by JENDL-4.0.

#### **Figure 23.**

*Δk/k (pcm) prediction due to the uncertainties in 235U capture cross sections with 44 energy groups for thermal benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 24.**

*Δk/k (pcm) prediction due to the uncertainties in 235U capture cross sections with 44 energy groups for fast benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

In the following, all the results concerning only the structure of the group of 44 neutrons and presented for both ENDF/B-VII.1 and JENDL-4.0.

#### **3.4 Nuclear data uncertainty prediction of keff**

The nuclear data uncertainties of keff are calculated using Eq. (7), and the predictions of *Δk=k* due to the uncertainty of the 235U cross sections are presented in the figures below (**Figures 23**–**26**).

**Figure 25.**

*3.3.3 Sensitivity for <sup>1</sup>*

sensitivity to the <sup>1</sup>

**Figure 23.**

**Figure 24.**

**148**

than those given by JENDL-4.0.

*benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

*benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

*H and 16O cross sections*

presented in the figures below (**Figures 17**–**22**).

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

The sensitivities of the keff's with respect to the cross sections of <sup>1</sup>

The figures above show that all thermal critical benchmarks demonstrate low

significant sensitivity for high energies. In addition, the structure of the 44 energy groups gives very varied sensitivity profiles compared to those given by the 15- and 33-group structures. Also, the sensitivities given by ENDF/B-VII.1 are slightly lower

*Δk/k (pcm) prediction due to the uncertainties in 235U capture cross sections with 44 energy groups for thermal*

*Δk/k (pcm) prediction due to the uncertainties in 235U capture cross sections with 44 energy groups for fast*

H and 16O elastic cross sections for low resonance energies and

H and 16O are

*Δk/k (pcm) prediction due to the uncertainties in 235U elastic cross sections with 44 energy groups for thermal benchmarks—ENDF/B-VII.1 and JENDL-4.0.*

**Figure 26.**

*Δk/k (pcm) prediction due to the uncertainties in 235U elastic cross sections with 44 energy groups for fast benchmarks—ENDF/B-VII.1 and JENDL-4.0.*


We can see from these figures that, in general, the relative uncertainties of keff

*H and 16O capture and elastic cross sections.*

using ENDF/B-VII.1 are less than those using JENDL-4.0. For example, these uncertainties due to the 235U capture cross section are 250 pcm, and in the elastic cross section case, they are 15 pcm for thermal benchmarks and 100–400 pcm for fast benchmarks. Concerning the predictions *Δk=k* due to the uncertainty of the 238U cross sections, they are all very small except for the elastic and inelastic cross

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

The total uncertainties of the effective multiplication factors due to U-235,

**Table 7** shows that for thermal benchmarks, the relative uncertainties of keff with the ENDF/B-VII.1 are lower than those with JENDL-4.0. However, for fast benchmarks, these uncertainties are greater with the JENDL-4.0 evaluation.

The degree of correlation between benchmarks errors is calculated using Eq. (6);

**Figures 27** and **28** show that the correlations between the benchmarks using ENDFB-VII.1 are lower than those using JENDL-4.0. Thus, a close similarity

The multigroup effect on the sensitivities of keff with respect to cross sections U-235, U-238, H-1, and O-16 is studied using 15, 33, and 44 energy groups. We found that the structure of the 44 groups gives the most varied sensitivity profiles in the two evaluations ENDF/B-VII.1 and JENDL-4.0, allowing a better investigation

The results obtained show that the keff sensitivity profiles are approximately the same for the two nuclear evaluations ENDF/B-VII.1 and JENDL-4.0. However, the covariances of the cross sections are different between the two evaluations, which is why differences between the uncertainties of the nuclear data are observed between these evaluations. For example, the total uncertainties in the thermal benchmark Hst001.001 are, respectively, 0.962 and 1.564% with ENDF/B-VII.1 and JENDL-4.0, and for the fast benchmark Hmf.001.001, these uncertainties are 0.439 and

U-238, H-1, and O-16 are summarized in **Table 7**.

*Correlation between fast benchmarks due to the uncertainties in <sup>1</sup>*

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

**3.5 Correlation between benchmark errors**

between several experiences is noted.

of the uncertainties of the nuclear data.

**4. Conclusions**

**151**

the results obtained are presented in the figures below.

sections.

**Figure 28.**

*(a) ENDF/B-VII.1 (b) JENDL-4.0.*

#### **Table 7.**

*Total uncertainty of keff (%).*

#### **Figure 27.**

*Correlation between thermal benchmarks due to the uncertainties in 235U capture cross sections. (a) ENDF/B-VII.1 (b) JENDL-4.0.*

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

**Figure 28.**

**Thermal benchmarks**

**Table 7.**

**Figure 27.**

**150**

*(b) JENDL-4.0.*

*Total uncertainty of keff (%).*

**Δkeff/keff-(%) ENDF/B-VII.1**

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

**Δkeff/keff-(%) JENDL-4.0**

Hst001.001 0.962 1.564 Hmi006.001 0.617 0.389 Hst001.002 0.931 1.214 Hmi006.002 0.800 0.274 Hst001.003 0.963 1.566 Hmi006.003 0.628 0.143 Hst001.004 0.934 1.200 Hmi006.004 0.827 0.159 Hst001.005 1.021 2.219 Hmf001.001 0.439 0.063 Hst001.006 1.011 2.160 Hmf003.001 0.442 0.057 Hst001.007 0.965 1.609 Hmf003.002 0.490 0.075 Hst001.008 0.963 1.587 Hmf003.003 0.492 0.083 Hst001.009 0.940 1.227 Hmf003.004 0.598 0.129 Hst001.010 0.995 2.104 Hmf003.005 0.446 0.053 Hst009.001 0.918 1.051 Hmf003.008 0.702 0.189 Hst009.002 0.929 1.122 Hmf003.009 0.667 0.159 Hst009.003 0.947 1.281 hmf003.010 0.603 0.141 Hst009.004 0.980 1.471 Hmf003.011 0.543 0.096 Hst009.010 0.917 1.065 Hmf008.001 0.648 0.221 Hst010.001 1.004 1.785 Hmf011.001 0.505 0.999 Hst010.002 1.009 1.820 Hmf012.001 0.458 0.086 Hst010.003 1.004 1.800 Hmf014.001 0.462 0.070 Hst010.004 1.010 1.747 Hmf015.001 0.463 0.084 Hst011.001 1.069 2.295 Hmf018.002 0.437 0.057 Hst011.002 1.074 2.306 Hmf020.002 0.447 0.244 Hst012.001 1.274 3.150 Hmf021.002 0.423 0.035 Hst013.001 1.281 3.237 Hmf022.002 0.421 0.035 Hst028.001 1.007 2.066 Hmf026.011 0.505 1.326 Hst035.007 0.880 1.682 Hmf028.001 0.489 0.075

*Correlation between thermal benchmarks due to the uncertainties in 235U capture cross sections. (a) ENDF/B-VII.1*

**Fast benchmarks** **Δkeff/keff-(%) ENDF/B-VII.1** **Δkeff/keff-(%) JENDL-4.0**

*Correlation between fast benchmarks due to the uncertainties in <sup>1</sup> H and 16O capture and elastic cross sections. (a) ENDF/B-VII.1 (b) JENDL-4.0.*

We can see from these figures that, in general, the relative uncertainties of keff using ENDF/B-VII.1 are less than those using JENDL-4.0. For example, these uncertainties due to the 235U capture cross section are 250 pcm, and in the elastic cross section case, they are 15 pcm for thermal benchmarks and 100–400 pcm for fast benchmarks. Concerning the predictions *Δk=k* due to the uncertainty of the 238U cross sections, they are all very small except for the elastic and inelastic cross sections.

The total uncertainties of the effective multiplication factors due to U-235, U-238, H-1, and O-16 are summarized in **Table 7**.

**Table 7** shows that for thermal benchmarks, the relative uncertainties of keff with the ENDF/B-VII.1 are lower than those with JENDL-4.0. However, for fast benchmarks, these uncertainties are greater with the JENDL-4.0 evaluation.

#### **3.5 Correlation between benchmark errors**

The degree of correlation between benchmarks errors is calculated using Eq. (6); the results obtained are presented in the figures below.

**Figures 27** and **28** show that the correlations between the benchmarks using ENDFB-VII.1 are lower than those using JENDL-4.0. Thus, a close similarity between several experiences is noted.

#### **4. Conclusions**

The multigroup effect on the sensitivities of keff with respect to cross sections U-235, U-238, H-1, and O-16 is studied using 15, 33, and 44 energy groups. We found that the structure of the 44 groups gives the most varied sensitivity profiles in the two evaluations ENDF/B-VII.1 and JENDL-4.0, allowing a better investigation of the uncertainties of the nuclear data.

The results obtained show that the keff sensitivity profiles are approximately the same for the two nuclear evaluations ENDF/B-VII.1 and JENDL-4.0. However, the covariances of the cross sections are different between the two evaluations, which is why differences between the uncertainties of the nuclear data are observed between these evaluations. For example, the total uncertainties in the thermal benchmark Hst001.001 are, respectively, 0.962 and 1.564% with ENDF/B-VII.1 and JENDL-4.0, and for the fast benchmark Hmf.001.001, these uncertainties are 0.439 and

0.063% with ENDF/B -VII.1 and JENDL-4.0, respectively. These differences are mainly due to the high covariances in JENDL-4.0 compared to those in ENDF/B-VII.1, in particular for the elastic cross section of the U-235 and of the fission for the U-238.

**References**

[1] Cabellos O. Presentation and discussion of the UAM/exercise I-1b: "Pin-cell burn-up benchmark" with the hybrid method. Science and Technology of Nuclear Installations. 2013;**2013**:1-12.

*DOI: http://dx.doi.org/10.5772/intechopen.92779*

des évaluations des sections efficaces et application à une maquette critique: le réacteur expérimentale EOLE; 2015

[10] Bowman SM. Experience with the SCALE Criticality Safety Cross-Section Libraries. Washington, DC: The Office: For sale by the U.S. G.P.O., Supt. of

[11] Broadhead BL, Rearden BT, Hopper CM, Wagschal JJ, Parks CV. Sensitivity and uncertainty based criticality safety validation techniques. Nuclear Science and Engineering. 2004;

[12] Rochman D, Vasiliev A,

[13] Sobes V, Leal L, Arbanas G, Forget B. Resonance parameter adjustment based on integral experiments. Nuclear Science and Engineering. 2016;**183**(3). DOI:

[14] Kiedrowski BC. 'MCNP6. 1 k-Eigenvalue sensitivity capability: a user's guide', Los Alamos National Laboratory (LANL), MCNP Documentation & Website; 2013. DOI: 10.13182/NSE10-22

[15] Chow ETY. An investigation of methods for neutron cross section error identification utilizing integral data [PhD thesis]. Georgia Institute of

[16] Reupke WA. The consistency of differential and integral thermonuclear neutronics data [PhD thesis]. Georgia

[17] Williams ML, Wiarda D, Ilas G, Marshall WJ, Rearden BT. Covariance

Institute of Technology; 1977

anucene.2016.01.042

10.13182/NSE15-50

Technology; 1974

Ferroukhi H, Zhu T, van der Marck SC, Koning AJ. Nuclear data uncertainty for criticality-safety: Monte Carlo vs. linear perturbation. Annals of Nuclear Energy. 2016;**92**:150-160. DOI: 10.1016/j.

Docs.; 2000

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1…*

**146**(3):340-366

DOI: 10.1155/2013/790206

Parashari S, Makwana R,

Cross-Section at the Neutron Energy 8.96 MeV; 2017

MeV Energy Region; 2011

[2] Vibha V, Mukherjee S, Naik H,

[3] Iwamoto O et al. Uranium-235 Capture Cross-Section in the keV to

[4] Palmiotti G et al. Combined use of integral experiments and covariance data. Nuclear Data Sheets. 2014;**118**: 596-636. DOI: 10.1016/j.nds.2014.04.145

[5] Otuka N, Nakagawa T, Shibata K. Uranium-235 neutron capture cross section at keV energies. Journal of Nuclear Science and Technology. 2007;

[6] Pelowitz DB et al. MCNP6 User's Manual. Los Alamos National

[8] Briggs JB. International handbook of evaluated criticality safety benchmark experiments. Nuclear Energy Agency, NEA/NSC/DOC (95). Exp. Needs Crit. Saf., vol. 3, Sep. 2004 [Online]. Available: https://www.oecd-nea.org/ science/wpncs/icsbep/handbook.html

[9] Kaddour M. Analyse de sensibilité des problèmes de criticité et du

coefficient de température aux données nucléaires: Contribution à l'amélioration

**44**(6):815-818. DOI: 10.1080/ 18811248.2007.9711318

[7] Macfarlane RE, Muir DW, Boicourt RM, Kahler AC. The NJOY Nuclear Data Processing System, Version 2012. Los Alamos National

Laboratory (LANL); 2012

Laboratory; 2013

**153**

Suryanarayana SV. 238U(n,γ) Reaction

These results demonstrated that the covariances of most neutron reactions with the nuclei studied in this work require more investigation and re-estimation.

### **Acknowledgements**

The work leading to this publication has been supported by the Radiations and Nuclear Systems Laboratory at Abdelmalek Essaadi University of Tetuan. Thank you to all the contributors of our laboratory team.

### **Author details**

Mustapha Makhloul<sup>1</sup> \*, H. Boukhal<sup>1</sup> , T. El Bardouni<sup>1</sup> , E. Chakir<sup>2</sup> , M. Kaddour<sup>1</sup> and S. Elouahdani<sup>1</sup>

1 Radiations and Nuclear Systems Laboratory, Faculty of Sciences of Tetuan, University Abdelmalek Essaadi, Morocco

2 SIMO Lab, Faculty of Sciences of Kenitra, Morocco

\*Address all correspondence to: mustapha342011@hotmail.fr

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Sensitivity and Uncertainty Quantification of Neutronic Integral Data Using ENDF/B-VII.1… DOI: http://dx.doi.org/10.5772/intechopen.92779*

#### **References**

0.063% with ENDF/B -VII.1 and JENDL-4.0, respectively. These differences are mainly due to the high covariances in JENDL-4.0 compared to those in ENDF/B-VII.1, in particular for the elastic cross section of the U-235 and of the fission for the

the nuclei studied in this work require more investigation and re-estimation.

These results demonstrated that the covariances of most neutron reactions with

The work leading to this publication has been supported by the Radiations and Nuclear Systems Laboratory at Abdelmalek Essaadi University of Tetuan. Thank

U-238.

**Acknowledgements**

**Author details**

Mustapha Makhloul<sup>1</sup>

and S. Elouahdani<sup>1</sup>

**152**

you to all the contributors of our laboratory team.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

\*, H. Boukhal<sup>1</sup>

2 SIMO Lab, Faculty of Sciences of Kenitra, Morocco

\*Address all correspondence to: mustapha342011@hotmail.fr

University Abdelmalek Essaadi, Morocco

provided the original work is properly cited.

, T. El Bardouni<sup>1</sup>

1 Radiations and Nuclear Systems Laboratory, Faculty of Sciences of Tetuan,

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, E. Chakir<sup>2</sup>

, M. Kaddour<sup>1</sup>

[1] Cabellos O. Presentation and discussion of the UAM/exercise I-1b: "Pin-cell burn-up benchmark" with the hybrid method. Science and Technology of Nuclear Installations. 2013;**2013**:1-12. DOI: 10.1155/2013/790206

[2] Vibha V, Mukherjee S, Naik H, Parashari S, Makwana R, Suryanarayana SV. 238U(n,γ) Reaction Cross-Section at the Neutron Energy 8.96 MeV; 2017

[3] Iwamoto O et al. Uranium-235 Capture Cross-Section in the keV to MeV Energy Region; 2011

[4] Palmiotti G et al. Combined use of integral experiments and covariance data. Nuclear Data Sheets. 2014;**118**: 596-636. DOI: 10.1016/j.nds.2014.04.145

[5] Otuka N, Nakagawa T, Shibata K. Uranium-235 neutron capture cross section at keV energies. Journal of Nuclear Science and Technology. 2007; **44**(6):815-818. DOI: 10.1080/ 18811248.2007.9711318

[6] Pelowitz DB et al. MCNP6 User's Manual. Los Alamos National Laboratory; 2013

[7] Macfarlane RE, Muir DW, Boicourt RM, Kahler AC. The NJOY Nuclear Data Processing System, Version 2012. Los Alamos National Laboratory (LANL); 2012

[8] Briggs JB. International handbook of evaluated criticality safety benchmark experiments. Nuclear Energy Agency, NEA/NSC/DOC (95). Exp. Needs Crit. Saf., vol. 3, Sep. 2004 [Online]. Available: https://www.oecd-nea.org/ science/wpncs/icsbep/handbook.html

[9] Kaddour M. Analyse de sensibilité des problèmes de criticité et du coefficient de température aux données nucléaires: Contribution à l'amélioration des évaluations des sections efficaces et application à une maquette critique: le réacteur expérimentale EOLE; 2015

[10] Bowman SM. Experience with the SCALE Criticality Safety Cross-Section Libraries. Washington, DC: The Office: For sale by the U.S. G.P.O., Supt. of Docs.; 2000

[11] Broadhead BL, Rearden BT, Hopper CM, Wagschal JJ, Parks CV. Sensitivity and uncertainty based criticality safety validation techniques. Nuclear Science and Engineering. 2004; **146**(3):340-366

[12] Rochman D, Vasiliev A, Ferroukhi H, Zhu T, van der Marck SC, Koning AJ. Nuclear data uncertainty for criticality-safety: Monte Carlo vs. linear perturbation. Annals of Nuclear Energy. 2016;**92**:150-160. DOI: 10.1016/j. anucene.2016.01.042

[13] Sobes V, Leal L, Arbanas G, Forget B. Resonance parameter adjustment based on integral experiments. Nuclear Science and Engineering. 2016;**183**(3). DOI: 10.13182/NSE15-50

[14] Kiedrowski BC. 'MCNP6. 1 k-Eigenvalue sensitivity capability: a user's guide', Los Alamos National Laboratory (LANL), MCNP Documentation & Website; 2013. DOI: 10.13182/NSE10-22

[15] Chow ETY. An investigation of methods for neutron cross section error identification utilizing integral data [PhD thesis]. Georgia Institute of Technology; 1974

[16] Reupke WA. The consistency of differential and integral thermonuclear neutronics data [PhD thesis]. Georgia Institute of Technology; 1977

[17] Williams ML, Wiarda D, Ilas G, Marshall WJ, Rearden BT. Covariance applications in criticality safety, light water reactor analysis, and spent fuel characterization. Nuclear Data Sheets. 2015;**123**:92-96

[18] Broadhead B, Hopper CM, Parks CV, Childs RL. Sensitivity and Uncertainty Analyses Applied to Criticality Safety Validation, methods development. United States: Oak Ridge National Lab; ORNL/TM–13692/V1. 1999

[19] Kuroi H, Mitani H. Adjustment to cross section data to fit integral experiments by least squares method. Journal of Nuclear Science and Technology. 1975;**12**(11):663-680

[20] Makhloul M, Boukhal H, El Bardouni T, Kaddour M, Chakir E, El Ouahdani S. 235U elastic cross-section adjustment in criticality benchmarks – Comparison between JENDL-4.0 and ENDF/-VII.1. Annals of Nuclear Energy. 2018;**114**:541-550. DOI: 10.1016/j. anucene.2017.12.018

[21] Salvatores M et al. Methods and issues for the combined use of integral experiments and covariance data: Results of a NEA international collaborative study. Nuclear Data Sheets. 2014;**118**:38-71

applications in criticality safety, light water reactor analysis, and spent fuel characterization. Nuclear Data Sheets.

*Nuclear Power Plants - Processes in the Nuclear Fuel Cycle*

[19] Kuroi H, Mitani H. Adjustment to cross section data to fit integral experiments by least squares method. Journal of Nuclear Science and Technology. 1975;**12**(11):663-680

[20] Makhloul M, Boukhal H, El Bardouni T, Kaddour M, Chakir E, El Ouahdani S. 235U elastic cross-section adjustment in criticality benchmarks – Comparison between JENDL-4.0 and ENDF/-VII.1. Annals of Nuclear Energy. 2018;**114**:541-550. DOI: 10.1016/j.

[21] Salvatores M et al. Methods and issues for the combined use of integral experiments and covariance data: Results of a NEA international collaborative study. Nuclear Data

anucene.2017.12.018

Sheets. 2014;**118**:38-71

**154**

[18] Broadhead B, Hopper CM, Parks CV, Childs RL. Sensitivity and Uncertainty Analyses Applied to Criticality Safety Validation, methods development. United States: Oak Ridge National Lab; ORNL/TM–13692/V1.

2015;**123**:92-96

1999

### *Edited by Nasser Awwad*

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Published in London, UK © 2021 IntechOpen © vlastas / iStock

Nuclear Power Plants - Processes in the Nuclear Fuel Cycle

Nuclear Power Plants

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*Edited by Nasser Awwad*