**2. Computer modeling of the electrodynamic systems**

As mentioned above, the energy of the microwave electromagnetic field is used to excite and heat the plasma. Various designs of oscillatory structures (resonators) are used as electrodynamic structures that form fields with the required distribution of power lines, the type and shape of which depend on the frequency of the electromagnetic field used. For example, for the excitation (pumping) of the active medium in helium-neon lasers, electromagnetic oscillations are used, the frequency of which lies in the range of 200 … 400 MHz with an average microwave power level of 2 … 5 W. In this case, a classical oscillatory circuit in the form of a flat capacitor is used as an oscillatory electrodynamic system. **Figure 2** shows the design of such a capacitor, the results of simulation and experiment [4]. An analysis of the

significant difference in the frequencies of the exciting microwave field, the designs of electrodynamic systems, in the volume of which a regular electromagnetic field is formed, have significant differences. These features of the excitation elements must be taken into account when designing devices, the operation of which is based on

*Examples of structural elements of sources of electromagnetic radiation with microwave excitation. A ring laser*

*gyroscope [2] (a) and an optical radiation source based on an electrodeless sulfur lamp (b) [2].*

*Microwave Heating - Electromagnetic Fields Causing Thermal and Non-Thermal Effects*

The analysis shows that the main structural elements of these devices are the active medium and the electrodynamic system for the formation of a regular electromagnetic field. A gas or a gas mixture (sometimes with the addition of an impurity, for example, sulfur S8, as in the case of a sulfur lamp) is considered as an active medium with nonlinear properties. Under the action of an external microwave electromagnetic field, the gas mixture is ionized and plasma is formed. At this stage, it is important to understand the ongoing physical processes that underlie the

the use of gas-discharge media (plasma).

**Figure 1.**

**124**

*Microwave Heating - Electromagnetic Fields Causing Thermal and Non-Thermal Effects*

**Figure 2.** *Capacitor design for exciting a helium-neon laser mixture.*

results obtained showed that the pump parameters of the active medium (heliumneon mixture) depend on the dimensions of the flask (its inner diameter and length) containing the active medium and are selected taking into account the maximum efficiency of the pump energy transfer process (see **Figure 1a**).

example of the waveguide with a cross-section (72x34) mm. This approach may be realized using the waveguide structure that is schematically shown in **Figures 4** and **5**. An electromagnetic wave *E* from the output of the magnetron originates to the input of the waveguide structure at *x* ¼ *L*<sup>0</sup> (see **Figure 5**). Next at *x* ¼ 0 and *z* ¼ 0, the wave is divided into two waves and that enters the inputs 1 and 2 of a waveguide and propagates towards each other (see **Figures 4** and **5**). As a result of the interference of the two coherent waves in the waveguide, the standing wave is formed as it may be

For increasing the intensity of the electric component of a total electromagnetic field and enhancing the efficiency of exciting plasma are of interest to view a case of contraction of the narrow size *b*. The main results of computer modeling the propagation of the waves in the space of the waveguide *L*<sup>0</sup> � *L*<sup>4</sup> taking into account a change of the size of the narrow wall in the waveguide are shown in **Figure 7**. As indicated in **Figure 7**, the general regularity of changing the intensity of the total electromagnetic field in the waveguide *E* ¼ *E*<sup>1</sup> þ *E*<sup>2</sup> is nonlinear and satisfies the condition *E* � 1*=b*, where *b* – the size of the narrow wall of the waveguide. By varying the high of the narrow wall of the waveguide we may choose a necessary value of the intensity of electric components and thus increasing the efficiency of controlling by a process of plasma heating. Such an approach of increasing the efficiency of the excitation process of the plasma mixture can be used for the choice of an optimum design of the electrodynamic structure. Among possible electrodynamic structures having an enhanced concentration of the electric component of electromagnetic field one can select both the resonant species of such structures and non-resonant. To the first group, we can relate toroid and coaxial resonators. The

seen from **Figure 6**.

**127**

*Results of computer modeling the cylindrical resonator.*

*Microwave Heating of Low-Temperature Plasma and Its Application*

*DOI: http://dx.doi.org/10.5772/intechopen.97167*

**Figure 3.**

With the increasing frequency, an electrodynamic system usually modified its shape and dimensions. For frequencies in the range of more than 1000 MHz, cavity resonators are usually used (see **Figure 1b**). In our case, we used a cylindrical resonator having the following geometrical dimensions: a diameter 172 mm and a height 120 mm. As a source of electromagnetic oscillation, there was used a magnetron generator, possessing a frequency of generation 2.45 GHz and the output power 800 W.

**Figure 3** illustrates the results of a computer modeling of the two modes of oscillations excited into the cylindrical resonator, namely, the *H*<sup>111</sup> and *H*<sup>011</sup> modes, correspondingly. The dependences of the reflection coefficient modulus from frequency and the spatial distributions of components of an electric field of the given oscillation modes have been shown.

As is seen, the different modes of oscillations are excited in the cylindrical resonators. As a rule, the given modes have distinct frequencies and possessing different distributions of the electric component of an electromagnetic field. The interest is the oscillations with the frequencies close to the frequency of the magnetron, i.e., to the frequency of 2.45 GHz. On the other hand, it is significant that the selected mode of oscillation had a maximum of the electric field in the area corresponding to the location where must be the bulb with the gaseous mixture. This permits to make an excitation process more effective.

In addition to the resonance excitation method of the plasma for forming a standing wave, we may use the interference of two coherent waves propagating towards each other in a waveguide [3]. Let us consider this approach using an

#### *Microwave Heating of Low-Temperature Plasma and Its Application DOI: http://dx.doi.org/10.5772/intechopen.97167*

**Figure 3.** *Results of computer modeling the cylindrical resonator.*

example of the waveguide with a cross-section (72x34) mm. This approach may be realized using the waveguide structure that is schematically shown in **Figures 4** and **5**. An electromagnetic wave *E* from the output of the magnetron originates to the input of the waveguide structure at *x* ¼ *L*<sup>0</sup> (see **Figure 5**). Next at *x* ¼ 0 and *z* ¼ 0, the wave is divided into two waves and that enters the inputs 1 and 2 of a waveguide and propagates towards each other (see **Figures 4** and **5**). As a result of the interference of the two coherent waves in the waveguide, the standing wave is formed as it may be seen from **Figure 6**.

For increasing the intensity of the electric component of a total electromagnetic field and enhancing the efficiency of exciting plasma are of interest to view a case of contraction of the narrow size *b*. The main results of computer modeling the propagation of the waves in the space of the waveguide *L*<sup>0</sup> � *L*<sup>4</sup> taking into account a change of the size of the narrow wall in the waveguide are shown in **Figure 7**.

As indicated in **Figure 7**, the general regularity of changing the intensity of the total electromagnetic field in the waveguide *E* ¼ *E*<sup>1</sup> þ *E*<sup>2</sup> is nonlinear and satisfies the condition *E* � 1*=b*, where *b* – the size of the narrow wall of the waveguide. By varying the high of the narrow wall of the waveguide we may choose a necessary value of the intensity of electric components and thus increasing the efficiency of controlling by a process of plasma heating. Such an approach of increasing the efficiency of the excitation process of the plasma mixture can be used for the choice of an optimum design of the electrodynamic structure. Among possible electrodynamic structures having an enhanced concentration of the electric component of electromagnetic field one can select both the resonant species of such structures and non-resonant. To the first group, we can relate toroid and coaxial resonators. The

results obtained showed that the pump parameters of the active medium (heliumneon mixture) depend on the dimensions of the flask (its inner diameter and length) containing the active medium and are selected taking into account the maximum efficiency of the pump energy transfer process (see **Figure 1a**).

*Microwave Heating - Electromagnetic Fields Causing Thermal and Non-Thermal Effects*

With the increasing frequency, an electrodynamic system usually modified its shape and dimensions. For frequencies in the range of more than 1000 MHz, cavity resonators are usually used (see **Figure 1b**). In our case, we used a cylindrical resonator having the following geometrical dimensions: a diameter 172 mm and a height 120 mm. As a source of electromagnetic oscillation, there was used a magnetron generator, possessing a frequency of generation 2.45 GHz and the

**Figure 3** illustrates the results of a computer modeling of the two modes of oscillations excited into the cylindrical resonator, namely, the *H*<sup>111</sup> and *H*<sup>011</sup> modes, correspondingly. The dependences of the reflection coefficient modulus from frequency and the spatial distributions of components of an electric field of the given

As is seen, the different modes of oscillations are excited in the cylindrical resonators. As a rule, the given modes have distinct frequencies and possessing different distributions of the electric component of an electromagnetic field. The interest is the oscillations with the frequencies close to the frequency of the magnetron, i.e., to the frequency of 2.45 GHz. On the other hand, it is significant that the

In addition to the resonance excitation method of the plasma for forming a standing wave, we may use the interference of two coherent waves propagating towards each other in a waveguide [3]. Let us consider this approach using an

selected mode of oscillation had a maximum of the electric field in the area corresponding to the location where must be the bulb with the gaseous mixture.

This permits to make an excitation process more effective.

output power 800 W.

**Figure 2.**

**126**

oscillation modes have been shown.

*Capacitor design for exciting a helium-neon laser mixture.*

**Figure 4.** *Schematic image of the waveguide structure with a metal insert having a height h.*

**Figure 5.** *Image of the curve L*<sup>0</sup> *L*<sup>4</sup> *along which the electric field value is calculated.*

second group of such structures can be presented by the single- and double-ridged waveguides. Thus, an application of the above-mentioned electrodynamic structures enables improving the process of exciting plasma and enhancing the efficiency of transformation of energy.

**3. Mathematical models and modeling of stochastic processes in plasma**

*Dependence the intensity of the electric component from a value of b*<sup>0</sup> *at the point z = 2127 (see Figures 4 and 6).*

*Distributions of the electric component of the total electromagnetic wave for different values of the height b*<sup>0</sup> *of*

*Microwave Heating of Low-Temperature Plasma and Its Application*

*DOI: http://dx.doi.org/10.5772/intechopen.97167*

Due to the variety of processes taking place in a spatially inhomogeneous plasma, an analytical description of a real plasma in the general case is very difficult. Therefore, simplified plasma models are usually considered, stipulating the condi-

The state of a real plasma at an arbitrary pressure is determined by a) the concentration of particles of all kinds *N* (the number of particles per unit volume);

**3.1 Mathematical description of the state of the plasma and its model**

tions under which a real plasma can be close to its accepted model.

**Figure 6.**

**Figure 7.**

**129**

*the waveguide.*
