**7.2 Bounding neutrino effective dose – circular muon collider**

The bounding neutrino effective dose for a circular muon collider could be obtained using the methodology of the previous section. However, a number of operational assumptions including the ring circumference and average magnetic induction would be required. Instead, we use an alternative approach to illustrate the various methods than can be utilized to determine the neutrino effective dose as a function of distance. To accomplish this, consider the energy distribution or differential fluence *dN E dE ii i* / where Ni is the number of neutrinos of generation i per unit area, Ei is the neutrino energy, and i = 1, 2, and 3 for the three neutrino generations. The neutrino effective dose H can be determined once the neutrino fluence to effective dose conversion factor C(Ei) is known.

Cossairt et al. (1997) provide an approach for treating the neutrinos and their antiparticles in the first two generations. In view of the limited data, Cossairt et al. (1997) did not consider the generation 3 neutrinos, but these neutrinos become more important as the accelerator energy increases.

One of the initial goals of a muon accelerator will be the development of a pure muon neutrino beam to investigate the magnitude of the neutrino mass. Focusing on the muon neutrino is also warranted because Cossairt et al. (1997) provides a muon neutrino fluence to effective dose conversion factor. Following Cossairt et al. (1997) and Silari & Vincke (2002), we limit the subsequent discussion to muon neutrinos that result from muon decays (Eq. 1) in a circular muon collider and drop the subscript i:

$$H = \int\_0^E \frac{dN(E)}{dE} \mathbf{C}(E) dE \tag{15}$$

where Eo is the energy of the primary muons before decay.

Silari & Vincke (2002) provide a differential fluence value in the laboratory system that is averaged over all neutrino production angles. They also assume the accelerator's shielding is thick enough to attenuate the primary muon beam, and that it is thicker than the range of 102 Particle Physics

The values of Table 3 suggest that the annual effective dose limit for occupational exposures of 20 mSv/y and the annual effective dose limit to the public (1 mSv/y) can be exceeded by TeV energy muon accelerators (ICRP 103, 2007). The values in Table 3 also exceed the emergency effective dose limit of 250 mSv set for the Fukushima Daiichi accident that is

A TeV - PeV scale muon collider will also challenge the acute lethal radiation dose (LD50, 30) of about 4 Gy (Bevelacqua 2010a). Although the feasibility of TeV - PeV scale machines remains to be determined, the significant radiation hazards associated with their operation

Selecting an accelerator location will be an issue for TeV energy muon linear colliders due to public radiation concerns arising from neutrino interactions. Given these radiation concerns, a muon collider location may be restricted to low population or geographically isolated

The bounding neutrino effective dose for a circular muon collider could be obtained using the methodology of the previous section. However, a number of operational assumptions including the ring circumference and average magnetic induction would be required. Instead, we use an alternative approach to illustrate the various methods than can be utilized to determine the neutrino effective dose as a function of distance. To accomplish this, consider the energy distribution or differential fluence *dN E dE ii i* / where Ni is the number of neutrinos of generation i per unit area, Ei is the neutrino energy, and i = 1, 2, and 3 for the three neutrino generations. The neutrino effective dose H can be determined once

Cossairt et al. (1997) provide an approach for treating the neutrinos and their antiparticles in the first two generations. In view of the limited data, Cossairt et al. (1997) did not consider the generation 3 neutrinos, but these neutrinos become more important as the accelerator

One of the initial goals of a muon accelerator will be the development of a pure muon neutrino beam to investigate the magnitude of the neutrino mass. Focusing on the muon neutrino is also warranted because Cossairt et al. (1997) provides a muon neutrino fluence to effective dose conversion factor. Following Cossairt et al. (1997) and Silari & Vincke (2002), we limit the subsequent discussion to muon neutrinos that result from muon decays (Eq. 1)

> ( ) ( ) *Eo dN E H C E dE*

Silari & Vincke (2002) provide a differential fluence value in the laboratory system that is averaged over all neutrino production angles. They also assume the accelerator's shielding is thick enough to attenuate the primary muon beam, and that it is thicker than the range of

*dE* (15)

0

merits careful attention to the effects of neutrino effective doses at offsite locations.

areas to minimize the public neutrino effective dose.

in a circular muon collider and drop the subscript i:

where Eo is the energy of the primary muons before decay.

**7.2 Bounding neutrino effective dose – circular muon collider** 

the neutrino fluence to effective dose conversion factor C(Ei) is known.

based on ICRP 60 (1991).

energy increases.

all secondary radiation. Accordingly, the neutrino radiation is in equilibrium with its secondary radiation.

Using the equilibrium condition and averaging over all production angles, provides the following differential fluence relationship for the neutrino radiation from a circular muon collider (Silari & Vincke, 2002):

$$\frac{dN(E)}{dE} = \frac{2}{E\_o} \left( 1 - \frac{E}{E\_o} \right) \Phi \tag{16}$$

where N(E) is the number of neutrinos per unit area, E is the neutrino energy, Eo is the energy of the primary muons before decay, and Φ is the integral neutrino fluence (total number of neutrinos per unit area) following the muon decays.

For secondary particle equilibrium, the fluence to effective dose conversion factor relationship of Cossairt et al. (1997) is used:

$$\text{C}(E) = KE^2 \tag{17}$$

Eq. 17 was derived for the neutrino energy range of 0.5 GeV to 10 TeV. In deriving the muon neutrino effective dose to fluence conversion factor of Eq. 17, Cossairt et al. (1997) did not consider the effects of the third lepton generation.

In Eq. 17, K = 10-15 μSv-cm2/GeV2. In view of the trend in the neutrino data (Particle Data Group, 2010; Quigg, 1997), Eq. 17 is used at energies beyond those considered by Cossairt et al. (1997). This is reasonable because increasing energy and increasing number of secondary shower particles (hadrons) is the main reason for the rising fluence to effective dose conversion factor with increasing neutrino energy for the equilibrium (shielded neutrino) case or process D described earlier. It is also reasonable because the neutrino attenuation length (λ) decreases with increasing energy of the primary neutrinos. Although TeV energy units are used in the final result, GeV units are used in the derivation of the neutrino effective dose to facilitate comparison with Silari & Vincke (2002) and Johnson et al. (1998). Prior to developing the neutrino effective dose relationship for a circular muon collider, the neutrino attenuation length is briefly examined.

The neutrino attenuation length is written in terms of the neutrino interaction cross section σν:

$$\mathcal{A} = \frac{A}{\rho N\_A \sigma\_\nu} = \frac{1}{N \sigma\_\nu} \tag{18}$$

where A and ρ are the atomic number and density of the shielding medium, NA is Avogadro's number, N is the number density of atoms of the shielding medium per unit volume, and σν is on the order of 10-35 cm2 (E / 1 TeV ) (Johnson et al. ,1998) where the neutrino energy is expressed in TeV.

These results permit the neutrino attenuation length to be written as (Johnson et al. ,1998):

$$\mathcal{A} = 0.5 \text{x} 10^6 km \left(\frac{1 \text{TeV}}{E}\right) \left(\frac{3 \text{ g} / \text{cm}^3}{\rho}\right) \tag{19}$$

facility). Recognizing that the muons may decay at any location along the return arm,

*<sup>E</sup> N dr E N Sv cm <sup>H</sup>*

 

Silari & Vincke (2002) provides parameters for the planned muon facility at CERN. For a 50 GeV muon energy in the storage ring, N = 1021 muons per year decaying in the ring, a return arm length pointing toward the surface (l = 6.0x104 cm), and a 100 m thickness of material (d) traversed by the neutrino beam between the end of the return arm and the surface, a surface neutrino effective dose of 47 mSv/yr is predicted. Since the planned CERN design has 3 return arms, the effective dose rate at the end of one of the arms would be about 16 mSv/y (47 mSv/3). Increasing muon energy will lead to higher muon effective dose rates, additional muon shielding requirements, and will force the collider deeper underground

Muon Energy (TeV) d (m) L (km) φ (mrad) θ (μrad)

These results suggest that the circular muon collider be installed underground to shield the muon beam in the event the beam becomes misdirected. This required shielding is

> <sup>3</sup> 0.6 3 /

 

(25)

100

*<sup>m</sup>* (26)

*dx km g cm*

<sup>2</sup> 2 2 36

horizontal accelerator beam with respect to the earth's center before it exits the earth:

*<sup>d</sup> L d R d d R km*

where R = 6400 km is the earth's radius. Table 4 provides representative values of d and L. In addition to d and L, a number of other relevant parameters associated with the circular collider of Eq. 26 are summarized in Table 4. In Table 4, φ is the half-angle subtended by the

When compared to muons, neutrinos have a much smaller interaction cross section. The earth shielding that completely attenuates the muons will have a negligible effect on the neutrinos. Accordingly, the neutrinos will produce a nontrivial annual effective dose at the earth's surface where the beam emerges. In order to evaluate the magnitude of this neutrino effective dose, assume the earth is a sphere, and a horizontal, circular muon collider is situated a depth d below the earth's surface. The neutrino beam exit point from the earth

Table 4. Geometrical Parameters for Representative Cases of Circular Muon Colliders

*dE TeV*

1 100 36 5.6 106 2 100 36 5.6 53 5 200 51 8 21 10 500 80.5 12.5 11

10 10 1 1

*o o*

6 6

*d l*

*d*

(See Table 4, derived from Silari & Vincke, (2002).

determined by the muon energy loss (Silari & Vincke, 2002):

will be at a horizontal distance L given by Silari & Vincke (2002):

13 4 13 4 2

2 4

(24)

*l l d dl r GeV*

leads to the neutrino effective dose:

Since the neutrino attenuation length is very long, the neutrino fluence is very weakly attenuated while traversing a shield. Therefore, shielding is not an effective dose reduction tool for neutrinos.

The effective dose arising from an energy independent neutrino fluence spectrum is accomplished by performing the integration of Eq. 15 using Eqs. 16 and 17:

$$H = \int\_{0}^{E\_{\text{p}}} \frac{2}{E\_{o}} \left(1 - \frac{E}{E\_{o}}\right) \Phi\left(KE^{2}\right) dE = \frac{K}{6} E\_{o}^{2} \,\Phi\tag{20}$$

where H is the annual neutrino effective dose in μSv and Φ is the total number of neutrinos per unit area that is assumed to be independent of energy (Johnson et al. ,1998).

The neutrino fluence Φ is the total number of neutrinos traversing a surface behind the shielding. The surface is governed by the divergence of the neutrino beam and the distance r from the neutrino source. The neutrino's half-divergence angle (θ) is:

$$\theta = \frac{mc^2}{E} = \frac{1}{\gamma} \approx \frac{1}{10\,E\_o} \tag{21}$$

where mc2 is the muon rest mass in MeV, E is the muon energy, θ is the opening half-angle or characteristic angle of the decay cone expressed in radians, and Eo is the energy of the primary muon beam in GeV.

The neutrino fluence Φ at a given distance r from the muon decay point is just the number of neutrinos N per unit area:

$$\Phi = \frac{N}{\pi \left(\theta r\right)^2} \tag{22}$$

Combining Eqs. 20 - 22 and using the numerical value for K yields a compact form for the annual neutrino effective dose from a circular muon collider:

$$H = \frac{10^{-15}}{6} \frac{E\_o}{\pi \left(\theta r\right)^2} = \frac{10^{-15}}{6} \frac{E\_o}{\pi} \frac{N}{r} \frac{\left(10E\_o\right)^2}{r^2} = \frac{10^{-13}}{6\pi r^2} \frac{E\_o}{G\epsilon} \frac{\mu Sv - cm^2}{G\epsilon V^4} \tag{23}$$

The circular muon collider neutrino effective dose of Eq. 23 has a very strong dependence on the neutrino energy.

Eq. 23 provides the neutrino effective dose assuming all muons decay at the same point. Recognizing that the muons can decay at all storage ring locations with equal probability provides a more physical description of the effective dose. For facilities such as the European Laboratory for Particle Physics (CERN), the neutrino effective dose may to be calculated as an integral over the length of the return arm (l) (Silari & Vincke, 2002) of the storage ring pointing toward the surface from d to d + l, where d is the thickness of material traversed by the neutrino beam between the end of the return arm and the surface of the earth along the direction of the return arm. The quantity d may also be described as the approximate minimum thickness of earth needed to absorb the circulating muons if beam misdirection or total beam loss occurs (i.e., the beam exits the 104 Particle Physics

Since the neutrino attenuation length is very long, the neutrino fluence is very weakly attenuated while traversing a shield. Therefore, shielding is not an effective dose reduction

The effective dose arising from an energy independent neutrino fluence spectrum is

*E K <sup>H</sup> K E dE E*

where H is the annual neutrino effective dose in μSv and Φ is the total number of neutrinos

The neutrino fluence Φ is the total number of neutrinos traversing a surface behind the shielding. The surface is governed by the divergence of the neutrino beam and the distance r

<sup>2</sup> 1 1

*E E*

where mc2 is the muon rest mass in MeV, E is the muon energy, θ is the opening half-angle or characteristic angle of the decay cone expressed in radians, and Eo is the energy of the

The neutrino fluence Φ at a given distance r from the muon decay point is just the number of

Combining Eqs. 20 - 22 and using the numerical value for K yields a compact form for the

The circular muon collider neutrino effective dose of Eq. 23 has a very strong dependence on

Eq. 23 provides the neutrino effective dose assuming all muons decay at the same point. Recognizing that the muons can decay at all storage ring locations with equal probability provides a more physical description of the effective dose. For facilities such as the European Laboratory for Particle Physics (CERN), the neutrino effective dose may to be calculated as an integral over the length of the return arm (l) (Silari & Vincke, 2002) of the storage ring pointing toward the surface from d to d + l, where d is the thickness of material traversed by the neutrino beam between the end of the return arm and the surface of the earth along the direction of the return arm. The quantity d may also be described as the approximate minimum thickness of earth needed to absorb the circulating muons if beam misdirection or total beam loss occurs (i.e., the beam exits the

10 10 (10 ) 10 6 6 ( ) 6 *Eo N N E E E N Sv cm oo o <sup>H</sup>*

<sup>2</sup> ( ) *N r*

15 2 15 2 2 13 4 2

2 2 24

(23)

*r r r GeV*

10 *<sup>o</sup>*

2 2

6

*o*

(20)

(21)

(22)

accomplished by performing the integration of Eq. 15 using Eqs. 16 and 17:

<sup>2</sup> <sup>1</sup>

*o o*

per unit area that is assumed to be independent of energy (Johnson et al. ,1998).

*mc*

*E E*

0

from the neutrino source. The neutrino's half-divergence angle (θ) is:

annual neutrino effective dose from a circular muon collider:

  *Eo*

tool for neutrinos.

primary muon beam in GeV.

neutrinos N per unit area:

the neutrino energy.

facility). Recognizing that the muons may decay at any location along the return arm, leads to the neutrino effective dose:

$$H = \frac{10^{-13}}{6\pi} \frac{E\_o^{-4}}{d} \int\_d^{d+l} \frac{N}{l} \frac{dr}{r^2} = \frac{10^{-13}}{6\pi l} \frac{E\_o^{-4}}{d} N \left(\frac{1}{d} - \frac{1}{d+l}\right) \frac{\mu Sv - cm^2}{GcV^4} \tag{24}$$

Silari & Vincke (2002) provides parameters for the planned muon facility at CERN. For a 50 GeV muon energy in the storage ring, N = 1021 muons per year decaying in the ring, a return arm length pointing toward the surface (l = 6.0x104 cm), and a 100 m thickness of material (d) traversed by the neutrino beam between the end of the return arm and the surface, a surface neutrino effective dose of 47 mSv/yr is predicted. Since the planned CERN design has 3 return arms, the effective dose rate at the end of one of the arms would be about 16 mSv/y (47 mSv/3). Increasing muon energy will lead to higher muon effective dose rates, additional muon shielding requirements, and will force the collider deeper underground (See Table 4, derived from Silari & Vincke, (2002).


Table 4. Geometrical Parameters for Representative Cases of Circular Muon Colliders

These results suggest that the circular muon collider be installed underground to shield the muon beam in the event the beam becomes misdirected. This required shielding is determined by the muon energy loss (Silari & Vincke, 2002):

$$\frac{dE}{d\mathbf{x}} = 0.6 \frac{\text{TeV}}{km} \left(\frac{\rho}{\text{\AA} \,\text{g} \,/\,\text{cm}^3}\right) \tag{25}$$

When compared to muons, neutrinos have a much smaller interaction cross section. The earth shielding that completely attenuates the muons will have a negligible effect on the neutrinos. Accordingly, the neutrinos will produce a nontrivial annual effective dose at the earth's surface where the beam emerges. In order to evaluate the magnitude of this neutrino effective dose, assume the earth is a sphere, and a horizontal, circular muon collider is situated a depth d below the earth's surface. The neutrino beam exit point from the earth will be at a horizontal distance L given by Silari & Vincke (2002):

$$L = \sqrt{2 \, dR - d^2} \approx \sqrt{2 \, dR} \approx 36 \, km \sqrt{\frac{d}{100 \, m}}\tag{26}$$

where R = 6400 km is the earth's radius. Table 4 provides representative values of d and L.

In addition to d and L, a number of other relevant parameters associated with the circular collider of Eq. 26 are summarized in Table 4. In Table 4, φ is the half-angle subtended by the horizontal accelerator beam with respect to the earth's center before it exits the earth:

Physics and cost parameters associated with 0.1, 3, 10, and 100 TeV circular muon colliders (King 1999a) are summarized in Table 6. Given current levels of technology, the collider cost will present a funding challenge as TeV muon energies are reached. In addition to funding issues, the control of radiation from the muon beams and neutrino plumes must be addressed. The feasibility of higher energy colliders will necessarily depend on

Accelerator Energy (TeV) 0.1 3 10 100 Circumference (km) 0.35 6 15 100 Average Magnetic Field (T) 3.0 5.2 7.0 10.5

As the collider energy increases, muon shielding requirements dictate a subsurface facility. The impact of locating the muon collider deeper underground with increasing accelerator energy can also be investigated. Using Eq. 28 and the data summarized in Table 4, permit the calculation of the neutrino effective dose upon its exit from the earth's surface. If the same beam properties are assumed as for the linear muon collider (i.e., N = 6.4x1018 muon decays per year) and r = L (Table 4), then the magnitude and size of the resultant radiation

1 100 36 3.6 2.6 2 100 36 1.8 42 5 200 51 1.0 820 10 500 80.5 0.8 5.2x103 50 500 80.5 0.16 3.3x106 100 500 80.5 0.081 5.2x107 500 500 80.5 0.016 3.3x1010 1000 500 80.5 0.0081 5.2x1011

Cost Feasible Challenging Challenging Problematic

Beam Radius at the Earth's Surface (m) d H at the Earth's Surface (mSv/y)

0.1 8.5x10-4 3.4x10-5 2.1x10-6 9.4x10-9 3.4x10-9 2 140 5.4 0.34 1.5x10-3 5.4x10-4 25 3.3x106 1.3x105 8.3x103 37 13 100 8.5x108 3.4x107 2.1x106 9.4x103 3.4x103 500 5.3x1011 2.1x1010 1.3x109 5.9x106 2.1x106 1000 8.5x1012 3.4x1011 2.1x1010 9.4x107 3.4x107

H (mSv/y) at the Specified Distance (r) from the Accelerator 5 km 25 km 100 km 1500 km 2500 km

Accelerator Energy (TeV)a

a The muon beam energy is half the accelerator energy.

Table 5. Annual Neutrino Effective Doses for a Circular Muon Collider.

technological development as well as financial support of scientific agencies.

Table 6. Circular Muon Collider Physics and Cost Parameters.

plumes derived from Eq. 28 are summarized in Table 7.

L (Horizontal Distance at the Earth's Surface) (km) c

Table 7. Neutrino Effective Dose Characteristics for a Circular Muon Collider.

Muon Energy (TeV) a d

(m)b

a The accelerator energy is twice the muon energy. b Accelerator depth below the surface of the earth.

c Horizontal exit point distance from the surface of the earth. d The half-divergence angle is determined from Eq. 5.

$$\text{Sim}\,\mathfrak{q} = \text{L} \,\, / \,\, \mathbb{R} \tag{27}$$

The functional form of Eq. 24 suggests that the calculation of neutrino effective dose from a circular muon collider is dependent of the assumed physical configuration and beam characteristics. An estimate of the neutrino effective dose for a circular muon collider can be made using Eq. 23. For comparison with Eq. 14, Eq. 23 is rewritten in terms of TeV and mSv units:

$$H = \frac{10^{-4}}{6\pi r^2} \frac{E\_o^4 N}{T e V^4} \tag{28}$$

where N is the number of muon decays per year, Eo is the muon energy in TeV, r is the distance from the point of muon decay in cm, and H is the annual neutrino effective dose in mSv. For consistency with the linear muon collider assumptions, 6.4x1018 muon decays per year are assumed in subsequent calculations. Given the TeV muon energies and the earth shielding present, charged particle equilibrium is assumed to exist. Moreover, the neutrino beam is limited to muon neutrinos only.

The muon neutrino effective dose to fluence conversion factor is assumed to be valid at energies beyond those utilized in Cossairt et al. (1997). Given the TeV muon energies, Process D of Cossairt et al. (1997) will dominate the neutrino effective dose.

In deriving the circular muon collider effective dose relationship, a number of assumptions were made. First, the neutrino effective dose calculation assumes a 100% occupancy factor, and is an annual average based on the number of muon decays in a year. Second, the muon beam is well-collimated. In addition, the irradiated individual is (1) assumed to be within the footprint of the neutrino beam and the hadronic particle shower that results from the neutrino interactions, (2) irradiated by only one of the muon beam's decay neutrinos whose energy is one-half the total circular muon collider energy, and (3) uniformly irradiated by the neutrino and hadronic radiation types.

Table 5 summarizes the results of neutrino effective dose values as a function of distance from the muon decay location (r) for a circular muon collider. Since the facility energy is the sum of the muon and antimuon energies, a 100 TeV accelerator consists of a 50 TeV muon beam and a 50 TeV antimuon beam.

The long, thin conical radiation plumes present a radiation challenge well beyond the facility boundary. For example, a 25 TeV circular muon collider produces a neutrino effective dose of 37 mSv/y at a distance of 1500 km from the facility. Although the neutrino effective dose plume will only have a radius of 12 m at 1500 km, it presents a radiation challenge for muon collider health physicists and management. The effective dose values summarized in Table 5 have the potential to impart lethal doses to small areas. The large effective dose values and their control must be addressed in facility design and licensing.

The importance of properly characterizing offsite public effective doses is illustrated by the Fukushima Daiichi Nuclear Power Station (FDNPS) accident in Japan (Butler; 2011a, 2011b). These doses focused attention on inadequacies in the FDNPS design and licensing bases. Offsite effective doses and their profile must be carefully and credibly addressed in muon collider design and licensing evaluations.

106 Particle Physics

 Sin φ = L / R (27) The functional form of Eq. 24 suggests that the calculation of neutrino effective dose from a circular muon collider is dependent of the assumed physical configuration and beam characteristics. An estimate of the neutrino effective dose for a circular muon collider can be made using Eq. 23. For comparison with Eq. 14, Eq. 23 is rewritten in terms of TeV and mSv

> 4 4 2 2 4

(28)

*r TeV*

*E No mSv cm <sup>H</sup>* 

where N is the number of muon decays per year, Eo is the muon energy in TeV, r is the distance from the point of muon decay in cm, and H is the annual neutrino effective dose in mSv. For consistency with the linear muon collider assumptions, 6.4x1018 muon decays per year are assumed in subsequent calculations. Given the TeV muon energies and the earth shielding present, charged particle equilibrium is assumed to exist. Moreover, the neutrino

The muon neutrino effective dose to fluence conversion factor is assumed to be valid at energies beyond those utilized in Cossairt et al. (1997). Given the TeV muon energies,

In deriving the circular muon collider effective dose relationship, a number of assumptions were made. First, the neutrino effective dose calculation assumes a 100% occupancy factor, and is an annual average based on the number of muon decays in a year. Second, the muon beam is well-collimated. In addition, the irradiated individual is (1) assumed to be within the footprint of the neutrino beam and the hadronic particle shower that results from the neutrino interactions, (2) irradiated by only one of the muon beam's decay neutrinos whose energy is one-half the total circular muon collider energy, and (3) uniformly irradiated by

Table 5 summarizes the results of neutrino effective dose values as a function of distance from the muon decay location (r) for a circular muon collider. Since the facility energy is the sum of the muon and antimuon energies, a 100 TeV accelerator consists of a 50 TeV muon

The long, thin conical radiation plumes present a radiation challenge well beyond the facility boundary. For example, a 25 TeV circular muon collider produces a neutrino effective dose of 37 mSv/y at a distance of 1500 km from the facility. Although the neutrino effective dose plume will only have a radius of 12 m at 1500 km, it presents a radiation challenge for muon collider health physicists and management. The effective dose values summarized in Table 5 have the potential to impart lethal doses to small areas. The large effective dose values and their control must be addressed in facility design and licensing.

The importance of properly characterizing offsite public effective doses is illustrated by the Fukushima Daiichi Nuclear Power Station (FDNPS) accident in Japan (Butler; 2011a, 2011b). These doses focused attention on inadequacies in the FDNPS design and licensing bases. Offsite effective doses and their profile must be carefully and credibly addressed in muon

10 6

Process D of Cossairt et al. (1997) will dominate the neutrino effective dose.

units:

beam is limited to muon neutrinos only.

the neutrino and hadronic radiation types.

beam and a 50 TeV antimuon beam.

collider design and licensing evaluations.


a The muon beam energy is half the accelerator energy.

Table 5. Annual Neutrino Effective Doses for a Circular Muon Collider.

Physics and cost parameters associated with 0.1, 3, 10, and 100 TeV circular muon colliders (King 1999a) are summarized in Table 6. Given current levels of technology, the collider cost will present a funding challenge as TeV muon energies are reached. In addition to funding issues, the control of radiation from the muon beams and neutrino plumes must be addressed. The feasibility of higher energy colliders will necessarily depend on technological development as well as financial support of scientific agencies.


Table 6. Circular Muon Collider Physics and Cost Parameters.

As the collider energy increases, muon shielding requirements dictate a subsurface facility. The impact of locating the muon collider deeper underground with increasing accelerator energy can also be investigated. Using Eq. 28 and the data summarized in Table 4, permit the calculation of the neutrino effective dose upon its exit from the earth's surface. If the same beam properties are assumed as for the linear muon collider (i.e., N = 6.4x1018 muon decays per year) and r = L (Table 4), then the magnitude and size of the resultant radiation plumes derived from Eq. 28 are summarized in Table 7.


a The accelerator energy is twice the muon energy.

b Accelerator depth below the surface of the earth.

c Horizontal exit point distance from the surface of the earth.

d The half-divergence angle is determined from Eq. 5.

Table 7. Neutrino Effective Dose Characteristics for a Circular Muon Collider.

beams that can be oriented to minimize the interaction of the neutrinos. A simple dose reduction technique orients the linear accelerators at an angle such that the neutrino beams exit the accelerator above the ground. This configuration minimizes the residual neutrino interactions with the earth and man-made structures. Secondly, the spent muons can be removed from the beam following collisions or interactions before they decay into high-

A number of radiation protection issues associated with TeV energy muon colliders will challenge accelerator health physicists. The issues related to large neutrino effective dose values and effective neutrino dosimetry were previously noted. Before construction of a muon collider, thorough studies will be performed to define the accelerator's radiation footprint. These studies will: (1) define muon collider shielding requirements; (2) assess induced activity within the facility and the environment (e.g., air, water, and soil), including the extent of groundwater activation; (3) assess radiation streaming through facility penetrations (e.g., ventilation ducts and access points); (4) assess various accident scenarios such as loss of power or beam misdirection; and (5) assess the various pathways for liquid and airborne releases of radioactive material. Facility waste generation and

In addition to the aforementioned radiation protection issues, the TeV energy neutrino beam will create new issues. Radiation protection concerns unique to muon colliders have been reported by Autin et al. (1999), Bevelacqua (2004), Johnson et al. (1998), Mokhov & Cossairt (1998), and Mokhov et al. (2000). These authors suggest that above about 1.5 TeV, the neutrino induced secondary radiation will pose a significant hazard even at distances on the order of tens to hundreds of kilometers. The neutrino radiation hazard presents both a

These issues also complicate the process for locating a suitable site for a TeV energy muon collider. There are a number of potential solutions to reduce the neutrino effective dose associated with a muon collider. These include using radiation boundaries or fenced-off areas to denote areas with elevated effective dose values. Building the collider on elevated ground or at an isolated area would also minimize human exposure. Effective dose

In a linear muon collider operating at the higher TeV energies, dose reduction is achieved by locating the interaction region above the earth's surface. In a circular muon collider, dose reduction is achieved by minimizing the straight sections in the ring, burying the collider deep underground to increase the distance before the neutrino beam exits the ground, and

Orders of magnitude reductions in the neutrino effective dose are required for the muon colliders noted in this chapter (See Tables 3, 5, and 7) to meet current regulations for public exposures (ICRP, 2007). Some of the possible effective dose reduction solutions may be difficult to implement for the TeV energy muon colliders. The most feasible options for locating and operating the highest TeV energy muon collider are to either use (1) an isolated location where no one is exposed to the neutrino radiation before it exits into the atmosphere as a result of the earth's curvature, or (2) a linear muon collider

reduction measures are also available for specific muon collider configurations.

orienting the collider ring to take advantage of natural topographical features.

energy neutrinos.

**9. Other radiation protection issues** 

decommissioning are other areas that will require evaluation.

physical as well as political challenge (King, 1999a).

Although the effective dose results at the earth's surface are significant, they occur over a relatively small area. The results also assume a 100% occupancy factor for this small area, which is not likely. The magnitude of the neutrino effective dose merits significant attention and emphasis on radiation monitoring and control. For example, a 500 TeV muon beam would deliver an acute absorbed dose rate of about 1 Gy/s to a 3.2 cm diameter circle. This absorbed dose rate is sufficient to deliver a biological detriment to the body within seconds (Bevelacqua, 2010a).

Dose management controls will be similar to those enacted for direct beam exposures at conventional accelerators. Interlocks associated with beam misalignment are effective in limiting the probability that the beam is directed toward an unanticipated direction. However, additional methods to control the offsite neutrino dose must be developed because lethal exposures can occur in a very short time even though the areas involved are small. Subjecting the public to potentially lethal effective doses represents unique facility licensing challenges that must be addressed in facility safety analyses. Public perception and stakeholder involvement will be key elements in licensing TeV-PeV scale muon colliders. The need for public involvement in licensing and regulatory discussions becomes particularly important when high effective doses could result from facility operations.
