A Preliminary Assessment of the Usability of Magnetoplasma Compressors in Scientific and Technical Applications

Abstract

This paper presents a preliminary analysis of the plasma dynamic modes of operation of end-type magnetoplasma compressor (MPC) discharges. The characteristic methods used to organize the optical pumping of a photodissociation gas laser using an MPC discharge are briefly described. The kinetic and energy characteristics of photodissociation gas optical quantum generators (OQGs) with optical pumping by an MPC discharge were evaluated. Based on the numerical calculations, an analysis of the radiation–plasma dynamic structures and the spectral brightness characteristics of the MPC discharge in the ohmic mode of plasma heating was carried out.

1. Introduction

Among the existing powerful high-brightness sources of UV radiation, i.e., sources generating fluxes with a power density of >1–10 MW/cm², a group of thermal (plasma) sources with a number of technical and physical advantages is widely used in scientific and practical applications. The creation of plasma with a temperature of 20–100 kK or higher, a concentration of heavy particles of 10¹⁷–10²⁰ cm⁻³, and a volume of plasma formation of 10–100 cm³ can generate thermal UV radiation fluxes with a specified intensity, which is made possible through the use of open (non-lamp) pulse discharges to carry the high (10⁷–10¹¹ W), pulsed (1–100 microseconds), and high-current (10²–10³ kA) discharge of an energy storage device to an interelectrode node with various configurations in a vacuum and or in a gas atmosphere. Increasing attention is being paid to the processes occurring in electric discharge sources and their effects on substances with different physicochemical properties; this attention has mainly arisen because of the following two circumstances:

Firstly, the study of the presence of a variety of physical processes and phenomena occurring in these electric discharge sources, such as the generation and propagation of supersonic pulsed emitting plasma jets, strong shock waves, and thermal broadband radiation, is of great interest.

Secondly, the possibility of creating radiation–plasma dynamic systems based on the electric discharge sources of UV radiation and shock waves can solve various problems in engineering, technology, and scientific research, including the optical pumping of powerful optical quantum generators (OQGs) operating in the visible and UV spectral ranges. It should also be noted that the possibility of using plasma sources of this type can be used for initiating the volumetric and rapid ignition of a fuel–air mixture owing to their effective generation of radicals.

One of the promising technical devices used for this purpose is an erosion-type pulsed plasma accelerator—a magnetoplasma compressor (MPC) [1,2,3,4,5,6,7,8,9,10]. In this case, the main configuration of the electrode assembly consists of a coaxial electrode system with a short (0.5–1 cm) channel length (end-type MPC discharge), with the diameter of a central electrode being D₁ = 0.8–1.5 cm, and that of an outer electrode with a diameter being D₂ = 3–10 cm, being selected as the main configuration of the electrode assembly. The energy is stored in low-inductive (less than 100 nH) capacitor banks with a capacity (C) ranging from 30 to 900 µF, and the stored energy is in the range of W₀ = 0.3–500 kJ. Variations in the duration of the discharge current pulse can be 5–100 microseconds with a range of current amplitude J_m = 100–2000 kA. It should be noted that the effect of pulsed UV radiation fluxes from MPC discharges on gas mixtures can be investigated using a scheme in which the MPC sources are placed outside the treated gas volume and separated by quartz glass that transmits radiation in the required spectral range. According to this scheme, photodissociation gas lasers with active media containing metal dihalides MeG₂ (Me is for metal) can be constructed (for example, mercury dihalides are HgG₂, where G ≡ Cl, Br, I, etc.).

Theoretical and numerical studies of the kinetic and spatiotemporal processes in photodissociation lasers, as well as of the modeling of the plasma dynamic characteristics of MPC discharges, are a necessary stage of research to quantitatively detail the parameters and internal structure of the discharge plasma; to obtain a correct interpretation of the available experimental data; to optimize such multiparametric systems; and to establish the peculiarity of plasma modes and parameters in the terms of the energy power and design characteristics of different systems that have not yet been studied by existing experiments [11,12,13,14,15,16,17].

In this paper (based on a numerical experiment), an attempt was made to initially assess the possibility of intensifying (based on MPC-type discharges) the combustion of a fuel mixture in a supersonic flow, as well as to search for sources of exposure to an active laser medium. To solve such problems, a photo-plasma dynamic method was proposed in this work, in which powerful electrical discharges (MPC, capillary discharge, etc.) create an optical effect through a transparent barrier (or directly in a combustible medium). During the implementation of the second treatment scheme, the gas was exposed to purely photochemical actions during the duration when the sources outside the area were disturbed by the discharge, the boundary of which is a shock wave (SW or system of SWs) that propagates through the gas and is a mobile effective surface of discharge radiation, i.e., in the latter case, the combustible mixture is exposed to combined (and volumetric) UV radiation fluxes (plasma and SW) initiating a complex of photochemical, plasma chemical, and thermo-baric reactions in the medium.

2. Plasma Dynamic Modes during the Functioning of End-Type MPC Discharges

The physical processes in MPC discharges proceed in time as follows: the main high-current stage of the MPC discharge occurs after the capacitive energy storage begins to discharge into the interelectrode gap. From this moment on, the composition of the electric discharge plasma is determined by the products of erosion of the interelectrode dielectric insert (IDI) and the electrodes of the MPC discharge, which are formed mainly under the influence of the streams of broadband intrinsic radiation from the plasma. At the same time, the light-erosion plasma accelerated by magneto-gasodynamic forces is inhibited by the gas surrounding the MPC discharge. As a result, a complex flow with a system of shock-wave discontinuities and contact boundaries occurs in the radially inhomogeneous plasma flow running into the gas barrier.

In the case of qualitative one-dimensional approximation of the braking zone of an MPC discharge [8,9], its gas-dynamic structure (the configuration of the rupture decay) consists of two shock waves in the plasma flow SWP and undisturbed gas SWG, and a contact boundary (CB) separating the regions of shock-compressed gas and plasma.

We consider the contact boundary to be a “piston” that moves (at a speed $\mathrm{u}={\mathrm{u}}_2-{\mathrm{u}}_{\mathrm{k}\mathrm{g}}$) into a “stationary” (relative to the piston) plasma with a density of ${\mathsf{\rho }}_2$. In this case, the speed of the contact boundary ${\mathrm{u}}_{\mathrm{k}\mathrm{g}}={\mathrm{u}}_2{\mathsf{\alpha }}^{-1}$, with $\mathsf{\alpha }=1+\sqrt{{\mathsf{\rho }}_1/{\mathsf{\rho }}_2}$, is determined by the velocity of the plasma flow ${\mathrm{u}}_2$ and the ratio of the initial densities of the plasma ${\mathsf{\rho }}_2$ and the undisturbed gas medium ${\mathsf{\rho }}_1$. The density ${\mathsf{\rho }}_2$, pressure ${\mathrm{P}}_2$, and temperature ${\mathrm{T}}_2$ of the shock-compressed plasma behind the SWP front are determined by the following relations:

$${\mathrm{P}}_2\approx {\mathsf{\rho }}_2{\mathrm{u}}_2^2\left({\displaystyle \frac{\mathsf{\alpha }-1}{\mathsf{\alpha }}}\right), {\mathrm{T}}_2\approx {\displaystyle \frac{\left({\gamma }_2-1\right)}{2}}{\displaystyle \frac{{\mathsf{\mu }}_2}{\mathrm{R}}}{\displaystyle \frac{{\mathrm{u}}^2}{1+{\mathrm{Z}}_2}},$$

(1)

where ${\gamma }_2, {\mathsf{\mu }}_2, {\mathrm{Z}}_2$ are the adiabatic index, the average molecular weight, and the average ion charge of the shock-compressed plasma, respectively.

It follows from these relations that, depending on the initial parameters (${\mathsf{\rho }}_1$, ${\mathrm{u}}_1$, ${\mathsf{\mu }}_1$ and ${\mathsf{\rho }}_2$, ${\mathrm{u}}_2$, and ${\mathsf{\mu }}_2$), two characteristic modes of operation of the MPC discharge can be distinguished: the shock-wave acceleration mode and the flow deceleration mode on a gas barrier [8].

The shock-wave acceleration mode is realized when the density of the pushing plasma flow is in the order of ${\mathsf{\rho }}_{\mathrm{I}\mathrm{I}}$ or exceeds the initial density of the gas medium ${\mathsf{\rho }}_{\mathrm{I}}$ and is most effective when ${\mathsf{\rho }}_{\mathrm{I}\mathrm{I}}\approx {\mathsf{\rho }}_1$. In this case, the efficiency of transferring the kinetic energy of the high-speed flow into the energy of the shock-compressed gas is maximum and is approximately 50%.

The flow deceleration mode on a gas barrier is realized when the density of the plasma flow ${\mathsf{\rho }}_{\mathrm{I}\mathrm{I}}$ is significantly greater than the density of the undisturbed gas ${\mathsf{\rho }}_{\mathrm{I}}$. In this case, about 70–90% of the kinetic energy of the plasma flow passes into the internal energy of the shock-compressed plasma.

This qualitative analysis of plasma dynamic processes in erosive MPCs with a coaxial electrode channel shows that the most optimal effect is obtained (from the point of view of creating a high-brightness UV emitter) when using the end structure (with a minimum length of the channel (L)).

A more detailed analysis of the numerical calculations performed in the work shows that classifying an MPC’s modes of existence can be carried out as follows:

$${\mathsf{\lambda }}_{\mathrm{R}}={\stackrel{-}{\mathrm{R}}}_{\mathrm{o}\mathrm{m}}/{\stackrel{-}{\mathrm{R}}}_{\mathrm{pl}}={\displaystyle \underset{0}{\overset{{\mathrm{t}}_1}{\int }}\left(\frac{1}{{\mathrm{J}}^2\left(\mathrm{t}\right)}{\displaystyle \underset{\mathrm{V}}{\int }\frac{{\left(\overrightarrow{\mathrm{j}}\right)}^2}{\sigma }\mathrm{d}\mathrm{V}}\right)\mathrm{d}\mathrm{t}}/{\displaystyle \underset{0}{\overset{{\mathrm{t}}_1}{\int }}\left(\frac{1}{{\mathrm{J}}^2\left(\mathrm{t}\right)}{\displaystyle \underset{\mathrm{V}}{\int }\left(\overrightarrow{\mathrm{j}}\overrightarrow{\mathrm{E}}\right)\mathrm{d}\mathrm{V}}\right)\mathrm{d}\mathrm{t}}$$

This relation is proportional to the ratio of the Joule heating power to the total power supplied to the plasma load, directly reflecting the contribution of the ohmic and dynamic plasma heating mechanisms.

Depending on the Am value (Am is a dimensionless criterion determining the energy–power mode of MPC discharge in a gas), i.e., depending on the heating mode, there are three different plasma structures that are characterized by different formation mechanisms and dynamics; these show different types of quasi-stationary plasma parameter spatial distributions. This makes it possible to identify the plasma regions (and parameters) that are the main sources of the radiation generated by MPC discharge. The influence of metal vapor light-erosion plasma on the formation processes of the internal structure and the parameters of the light-erosion flow are then established.

The brightness temperatures (averaged over the entire surface of the external UV boundary) of the MPC discharge plasma are functions of the mode parameter, the electrical power (P_el), and the density of the surrounding gas. In terms of practical applications, it is important to note that the maximum brightness radiation temperatures in the spectral region hν = 3.14–5.98 eV for MPC discharge under atmospheric pressure (Ar) at P_el/F_m = 10¹² W/m² (${\mathrm{F}}_{\mathrm{m}}=\pi {\mathrm{r}}_2^2$) can be 35 kK.

3. Estimation of Photodissociation Gas OQG Characteristics with Optical Pumping

In cases of limited brightness temperature in the radiation source, one of the ways to influence large volumes of gas medium is the use of several radiation sources that trigger simultaneously, performing photo-effects on the gas from different sides. This radiation source arrangement has a number of advantages compared to the one-sided arrangement of the radiator surface.

According to the characteristics of optimal spectral, structural, and technological energy, such irradiation schemes allow, firstly, the provision of the required quantum fluxes (for a given volume of processed medium), and secondly, their appropriate arrangement in space. They make it possible to symmetrize the distributions of all the main parameters arising from the spatially inhomogeneous decomposition of impurity molecules during photolysis (particularly the gradient dynamics of the refractive index, which reduces the refractive losses associated with this effect in gas OQG optical pumping systems).

These processes are possible if short-wave radiation (affecting the volumes of the gaseous medium) in the ultraviolet region of the spectrum has a high energy, causing chemical reactions. In this case, the photon energy must be sufficient in order to break the molecule’s chemical bond and initiate the decomposition process. In this case, the main chemical reaction is photodissociation, i.e., it is possible to create a photodissociation laser in which the molecules of the active medium dissociate. Under the influence of optical pumping (with the formation of a photodissociation wave in the active medium, provided it is “illuminated” for optical pumping radiation), they dissociate into two parts, one of which turns out to be in an excited state and is used later in the creation of laser radiation.

The selective photoexposure method is based on the implementation of processes of direct photodissociation (or photoexcitation) of certain (impurity) molecules of a gas mixture exposed to broadband UV radiation from an electric discharge source. When exposed to broadband UV radiation on a gas mixture, the method can be implemented, provided that the absorption bands of the impurity molecules, whose photolysis must be initiated, and the molecules of the base (buffer) gas differ.

In this section, we mathematically describe the process (which is a scheme of optically pumping the active medium of a photodissociation optical quantum generator by MPC discharge) of impurity molecule photodissociation M in a layer of a gas mixture under the action of collimated oncoming streams of UV radiation quanta from two stationary, mutually parallel flat light sources (based on MPC discharge) located at a distance L from each other (Figure 1a). In this case, we assume that a gas mixture, containing impurity molecules M with an initial concentration of ${\mathrm{N}}_0$ and buffer gas molecules with a concentration of ${\mathrm{N}}_{\mathrm{Б}}$, is exposed to quasi-monochromatic radiation with a quantum energy $\mathrm{h}{\nu }_0$ corresponding to the maximum photodissociation cross-section σ of the impurity molecules M. At the same time, the active radiation fluxes are not absorbed by the buffer gas molecules.

Taking into account the assumptions made regarding the coordinate system (Figure 1a), the beginning of which (x = 0) is located at distance L/2 from the chosen surface of the radiation source (RS) (see Figure 1), the basic system of photodissociation dynamics equations takes the following form:

$${\displaystyle \frac{\partial {\mathrm{S}}^{+}}{\partial \mathrm{x}}}=-\mathrm{N}\sigma {\mathrm{S}}^{+},{\displaystyle \frac{\partial {\mathrm{S}}^{-}}{\partial \mathrm{x}}}=\mathrm{N}\sigma {\mathrm{S}}^{-},{\displaystyle \frac{\partial \mathrm{N}}{\partial \mathrm{t}}}=-\sigma \mathrm{N}\left({\mathrm{S}}^{+}+{\mathrm{S}}^{-}\right),$$

(2)

where ${\mathrm{S}}^{\pm }\left(\mathrm{x}, \mathrm{t}\right)$ is the unit density of the flow of pumping quanta at a point with a coordinate $\mathrm{x}\in [-\mathrm{L}/2, \mathrm{L}/2]$ at time t, with ${\mathrm{S}}^{+}$ in the positive direction of the X-axis (from the left RS) and ${\mathrm{S}}^{-}$ in the negative direction (from the right edge of the RS). $\mathrm{N}\left(\mathrm{x}, \mathrm{t}\right)$ is the concentration of impurity molecules (M) at point X and moment t. The boundary and initial conditions for (2) are as follows: ${\mathrm{S}}^{+}\left(\mathrm{x}=-\mathrm{L}/2, \mathrm{t}\right)={\mathrm{S}}^{-}\left(\mathrm{x}=\mathrm{L}/2, \mathrm{t}\right)={\mathrm{S}}_0\left(\mathrm{t}\right),\mathrm{N}\left(\mathrm{x}, \mathrm{t}=0\right)={\mathrm{N}}_0$, where ${\mathrm{S}}_0\left(\mathrm{t}\right)={\mathrm{S}}_{\mathrm{m}}\phi \left(\mathrm{t}\right)$ is the time dependence of the quantum flux density from the RS surface; $\phi \left(\mathrm{t}\right)$ is an arbitrary bell-shaped function of time having a maximum value of 1 at some point in time ${\mathrm{t}}_{\mathrm{m}}$, i.e., $\phi \left({\mathrm{t}}_{\mathrm{m}}\right)=1$, and tending toward 0 as $\mathrm{t}\to \infty$, or $\phi \left(\mathrm{t}\right)=1$ on the interval $\mathrm{t}\in \left[0÷{\mathrm{t}}_{\mathrm{m}}\right]$.

The solution of the system for the degree of decomposition $\mathsf{\delta }\left(\stackrel{\sim }{\mathrm{x}}, \tau \right)=\mathrm{N}\left(\stackrel{\sim }{\mathrm{x}}, \tau \right)/{\mathrm{N}}_0$ and the dimensionless photodissociation (PD) rate $\stackrel{\sim }{\mathrm{F}}\left(\stackrel{\sim }{\mathrm{x}}, \tau \right)=\left(-\partial \mathrm{N}/\partial \mathrm{t}\right)/{\mathrm{F}}^{*}$ of particles M, as outlined in Equation (2), has the following form:

$$\begin{array}{c}\mathsf{\delta }\left(\stackrel{\sim }{\mathrm{x}}, \tau \right)=4\mathsf{\eta }\mathrm{f}\left(\tau \right){\left[{\left(\mathsf{\eta }+1\right)}^2-{\left(\mathsf{\eta }-1\right)}^2{\mathrm{f}}^2\left(\tau \right)\right]}^{-1},\\ \stackrel{\sim }{\mathrm{F}}\left(\stackrel{\sim }{\mathrm{x}}, \tau \right)={\stackrel{\sim }{\mathrm{F}}}_0\left(\tau \right){\displaystyle \frac{4\mathsf{\eta }\left[{\left(\mathsf{\eta }+1\right)}^2+\left(\mathsf{\eta }-1\right){\mathrm{f}}^2\left(\tau \right)\right]}{{\left[{\left(\mathsf{\eta }+1\right)}^2-{\left(\mathsf{\eta }-1\right)}^2{\mathrm{f}}^2\left(\tau \right)\right]}^2}},\end{array}$$

(3)

where $\stackrel{\sim }{\mathrm{x}}=\mathrm{x}/\mathrm{L}, \tau =\mathrm{t}\sigma {\mathrm{S}}_{\mathrm{m}}$ corresponds to the dimensionless coordinate $\mathrm{x}\in [-1/2, 1/2]$ and time; ${\mathrm{y}}_0={\mathrm{N}}_0\sigma \mathrm{L}$ is the initial optical thickness of the gas layer; ${\mathrm{F}}^{*}=2{\mathrm{N}}_0{\mathrm{S}}_{\mathrm{m}}\sigma$ is the characteristic value of the photodissociation (PD) rate of molecules M; and ${\stackrel{\sim }{\mathrm{F}}}_0\left(\tau \right)={\displaystyle \frac{\phi \left(\tau \right)\mathrm{f}\left(\tau \right)}{\sqrt{1+\Omega \mathsf{\xi }\left(\tau \right)}}}$ is the dimensionless velocity in the plane of symmetry of the system with $\Omega =\exp ({\mathrm{y}}_0)-1$, $\mathsf{\xi }\left(\tau \right)=\exp \left(-2{\displaystyle \underset{0}{\overset{\tau }{\int }}\phi \left(\tau \right)\mathrm{d}\tau }\right)$, and $\mathrm{f}\left(\tau \right)=\mathrm{c}\mathrm{t}\mathrm{h}\left({\displaystyle \frac{{\mathrm{y}}_0}{4}}\right){\displaystyle \frac{{\left(\sqrt{1+\Omega \mathsf{\xi }\left(\tau \right)}-1\right)}^2}{\Omega \mathsf{\xi }\left(\tau \right)}}, \mathsf{\eta }=\exp \left(\stackrel{\sim }{\mathrm{x}}\right)$.

The analysis of F(x, τ) shows that, over the duration of the light pulse action, three successive stages of PD can take place; these are characterized by different spatial distributions F(x, τ). The first stage takes place up to a certain point ${\tau }_1={\tau }_1\left({\mathrm{y}}_0\right)$, with F(x, τ) having the greatest value on the RS surface and the lowest at point x = 0. The value τ₁ at the end of this stage depends on the initial optical thickness of the gas layer y₀ and is calculated based on the following ratio:

$${\mathrm{R}}_1=\mathrm{R}\left({\tau }_1\right)={\displaystyle \underset{0}{\overset{{\tau }_1}{\int }}\phi \left(\tau \right)\mathrm{d}\tau }=\mathcal{l}\mathrm{n}\left\{{\displaystyle \frac{\sqrt{\Omega }\left(1-{\mathrm{G}}_1\left({\mathrm{y}}_0\right)\right)}{2\sqrt{{\mathrm{G}}_1\left({\mathrm{y}}_0\right)}}}\right\},$$

(4)

where ${\mathrm{G}}_1({\mathrm{y}}_0)={\left\{{\displaystyle \frac{\left(\sqrt{8+\mathrm{c}{\mathrm{h}}^2\left({\mathrm{y}}_0/2\right)}-3\right)}{\left[\left(\mathrm{c}\mathrm{h}\left({\mathrm{y}}_0/2\right)-1\right)\mathrm{c}\mathrm{t}{\mathrm{h}}^2\left({\mathrm{y}}_0/4\right)\right]}}\right\}}^{1/2}$.

The following ratios allow us to draw the following qualitative conclusion about the stages of photodissociation wave formation.

At t∈[0, t₁], the dimensionless photodissociation wave velocity is a monotonously decreasing function (the stage of photodissociation wave formation). At t > t₁, a photodegradation mode with a local maximum occurs (a photodissociation wave is formed and moves towards the system’s geometric axis of symmetry). With a further increase in time, the photodegradation waves (meaning the local maximum) move towards the axis of the system, reaching it at time t₂. This point has one local maximum on the axis of the system (the stage of nonlinear photolysis rate amplification). A further increase in time corresponds to a distribution with one maximum on the system’s axis.

Thus, with the gas layer’s two-way irradiation scheme, depending on the irradiation conditions (i.e., the temporal shape of the pump pulse φ(t) and the parameters of the absorbing layer), the photodegradation of gas molecules can occur in three different, successively alternating stages (see Figure 2 and Figure 3).

Figure 3 presents the integral of the time function of the external pumping radiation effect Ri and the dimensionless (non-physical) time τ_i, that is, the time for which the effect is carried out. Using Formula (4), the values of Ri from the dimensionless time τ_i are found.

The time to reach the maximum value of the PD speed is determined by the condition ${\left.{\displaystyle \frac{\mathrm{d}{\stackrel{\sim }{\mathrm{F}}}_0}{\mathrm{d}\tau }}\right|}_{\tau ={\tau }_{\mathrm{m}\mathrm{F}}}=0$ or

$${\left.{\displaystyle \frac{\mathrm{d}}{\mathrm{d}\tau }}\left(-{\displaystyle \frac{1}{\phi }}\right)\right|}_{\tau ={\tau }_{\mathrm{m}\mathrm{F}}}={\displaystyle \frac{2\sqrt{1+\Omega {\mathsf{\xi }}_{\mathrm{m}\mathrm{F}}}-\Omega {\mathsf{\xi }}_{\mathrm{m}\mathrm{F}}}{1+\Omega {\mathsf{\xi }}_{\mathrm{m}\mathrm{F}}}},$$

(5)

where ${\mathsf{\xi }}_{\mathrm{m}\mathrm{F}}=\exp \left(-2{\displaystyle \underset{0}{\overset{{\tau }_{\mathrm{m}\mathrm{F}}}{\int }}\phi \left(\tau \right)\mathrm{d}\tau }\right)$. As can be seen in Equation (4), the time to reach the maximum F₀ on the system’s axis can be either less or more than the time ${\tau }_{\mathrm{m}}$ at which the quantum flux from the surface RS reaches its maximum value. The greatest value F_0m for an arbitrary bell-shaped $\phi \left(\tau \right)$ with a maximum chance of $\tau ={\tau }_{\mathrm{m}}$ can be achieved when the moment of the maximum luminous flux ${\tau }_{\mathrm{m}}$ coincides with the moment ${\tau }_{\mathrm{m}}$ reaching the F₀ value, i.e., when $\Omega {\mathsf{\xi }}_{\mathrm{m}\mathrm{F}}=2(1+\sqrt{2})$, or

$${\mathrm{R}}_3={\displaystyle \underset{0}{\overset{{\tau }_{\mathrm{m}}}{\int }}\phi \left(\tau \right)\mathrm{d}\tau =\mathcal{l}\mathrm{n}\sqrt{\frac{\Omega \left({\mathrm{y}}_0\right)}{2\left(1+\sqrt{2}\right)}}}={\mathrm{R}}_3\left({\mathrm{y}}_0\right).$$

(6)

When condition (5) is met, the maximum value of the dimensionless velocity is reached at the moment when $\tau ={\tau }_{\mathrm{m}}={\tau }_{\mathrm{m}\mathrm{F}}$ on the system’s axis:

$${\stackrel{\sim }{\mathrm{F}}}_{0\mathrm{m}}={\displaystyle \frac{\sqrt{2}}{\left(1+\sqrt{2}\right)\left(2+\sqrt{2}\right)}}\mathrm{c}\mathrm{t}\mathrm{h}\left({\displaystyle \frac{{\mathrm{y}}_0}{4}}\right).$$

A scheme with irradiation sources on opposite sides of the target plasma at appropriate time intervals (depending on y₀) allows us to achieve conditions when the PD velocity value of gas molecules exceeds that under the same conditions, but under the influence of only one RS.

Equation (6) can be considered as a condition determining, for a given y₀, the optimal time form of the illumination pulse $\phi \left(\tau \right)$ during the phase when the luminous flux increases to its maximum value. Conversely, for the given parameters of the leading edge of the radiation pulse, it is necessary to choose the optimal parameters $({\mathrm{N}}_0, \mathrm{L})$ at which it is possible to provide a local (in space and in time) increase in the PD velocity of gas molecules.

Next, we consider the features of the kinetic processes of photoexcitation of excimer-like lasers on mercury halides. In these lasers, in the vapor phase, the working molecules are mercury halide molecules (HgCl₂, HgBr₂, and HgI₂). Inert gases (Ar, Ne, He, etc.) and their mixtures with nitrogen are used as buffer gases. A mercury halide laser with optical pumping operates according to a four-level scheme: the photoexcitation of radiation quanta from a broadband source that pumps the initial HgG₂ molecules from the ground state ${}^1\mathsf{\Sigma }_{\mathrm{g}}^{+}$ to unstable electronically excited states and their subsequent dissociation with the formation of HgG radicals in X, B, C, and D excited states; the settlement of the upper laser level as a result of HgG radical quenching from the D to the B state and vibrational relaxation of B-state HgG radicals; the laser transition ${\mathrm{B}}^2{\mathsf{\Sigma }}_{1/2}^{+}\to {\mathrm{X}}^2{\mathsf{\Sigma }}_{1/2}^{+}$ is carried out between the lower vibrational levels of the B-state HgG radicals (${\mathsf{\vartheta }}^{\prime }=0, 1, 2, 3$) and the highly excited vibrational levels of the ground X-state HgG radicals; and the rapid vibrational relaxation of the X-state HgG radicals in collision with the buffer gas molecules, which is the main mechanism for emptying the lower laser level.

The absorption spectrum of HgBr₂ has four main absorption bands in the UV region [13,14,15]. HgBr₂ molecule photodissociation in the region of these four short-wave continuums, with maxima of absorption cross-sections, specifically, 5.4 eV, 6.26 eV, 7.3 eV, and 7.8 eV, proceeds according to the following scheme:

$$\begin{array}{l}\mathrm{H}\mathrm{g}\mathrm{B}{\mathrm{r}}_2+\mathrm{h}{\nu }_{\mathrm{a}}\stackrel{{\sigma }_{\mathrm{a}}}{\to }\mathrm{B}\mathrm{r}+\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}({\mathrm{X}}^2{\mathsf{\Sigma }}_{1/2}^{+}),\\ \mathrm{H}\mathrm{g}\mathrm{B}{\mathrm{r}}_2+\mathrm{h}{\nu }_{\mathrm{b}}\stackrel{{\sigma }_{\mathrm{b}}}{\to }\mathrm{B}\mathrm{r}+\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}({\mathrm{B}}^2{\mathsf{\Sigma }}_{1/2}^{+}),\\ \mathrm{H}\mathrm{g}\mathrm{B}{\mathrm{r}}_2+\mathrm{h}{\nu }_{–}\stackrel{{\sigma }_{\mathrm{c}}}{\to }\mathrm{B}\mathrm{r}+\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}({\mathrm{C}}^2{\mathsf{П}}_{1/2}),\\ \mathrm{H}\mathrm{g}\mathrm{B}{\mathrm{r}}_2+\mathrm{h}{\nu }_{\mathrm{d}}\stackrel{{\sigma }_{\mathrm{d}}}{\to }\mathrm{B}\mathrm{r}+\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}({\mathrm{D}}^2{\mathsf{П}}_{3/2}^{+}),\end{array}$$

(7)

where ${\sigma }_{\mathrm{i}}$ is an absorption cross-section of HgBr₂ by quanta with energy $\mathrm{h}{\nu }_{\mathrm{i}}$, and HgBr(j) denotes radical molecules in the corresponding ($\mathrm{j}=\mathrm{X}, \mathrm{B}, \mathrm{C}, \mathrm{D}$) excited states.

The complete system of differential equations describing the kinetics of the molecules of the main working components of the laser medium, as well as the time evolution of the laser radiation density inside the resonator, can be written as follows:

$${\displaystyle \frac{\mathrm{d}{\mathrm{n}}_1}{\mathrm{d}\mathrm{t}}}={\mathrm{F}}_1-\left\{{\displaystyle \frac{{\mathrm{n}}_1}{{\tau }_{\mathrm{s}\mathrm{p}}}}+{\mathrm{K}}_{\mathrm{H}\mathrm{g}\mathrm{B}{\mathrm{r}}_2}^{\mathrm{T}}{\mathrm{n}}_1\mathrm{N}+{\mathrm{K}}_{\mathrm{b}}^{\mathsf{Т}}{\mathrm{n}}_1{\mathrm{n}}_{\mathrm{b}}+\mathsf{\rho }\mathrm{c}{\sigma }_{\mathrm{i}\mathrm{n}\mathrm{d}}({\mathrm{n}}_1-{\mathrm{n}}_2)\right\},$$

(8)

$${\displaystyle \frac{\mathrm{d}{\mathrm{n}}_2}{\mathrm{d}\mathrm{t}}}=\mathrm{c}\mathsf{\rho }{\sigma }_{\mathrm{i}\mathrm{n}\mathrm{d}}({\mathrm{n}}_1-{\mathrm{n}}_2)-{\mathrm{n}}_2({\mathrm{K}}_{\mathrm{b}}^{\mathrm{r}}{\mathrm{n}}_{\mathrm{b}}+{\mathrm{K}}_{\mathrm{M}}^{\mathrm{R}}{\mathrm{n}}_3{\mathrm{n}}_{\mathrm{b}}),$$

$${\displaystyle \frac{\mathrm{d}\mathrm{N}}{\mathrm{d}\mathrm{t}}}=-({\mathrm{F}}_1+{\mathrm{F}}_2)+{\mathrm{K}}_{\mathrm{M}}^{\mathrm{R}}{\mathrm{n}}_{\mathrm{g}\mathrm{l}}({\mathrm{n}}_1+{\mathrm{n}}_{\mathrm{g}\mathrm{l}}){\mathrm{n}}_{\mathsf{б}},$$

$${\displaystyle \frac{\mathrm{d}\mathsf{\rho }}{\mathrm{d}\mathrm{t}}}={\displaystyle \frac{{\mathrm{n}}_1}{{\tau }_{\mathrm{s}\mathrm{p}}}}\mathsf{\alpha }+\mathrm{c}\mathsf{\rho }\left[{\sigma }_{\mathrm{i}\mathrm{n}\mathrm{d}}({\mathrm{n}}_1-{\mathrm{n}}_2)-\gamma \right],$$

$${\mathrm{n}}_{\mathrm{g}\mathrm{l}}={\mathrm{n}}_1+{\mathrm{n}}_2+{\mathrm{n}}_3, {\mathrm{n}}_{\mathrm{b}}=\mathrm{N}+{\mathrm{n}}_{\mathrm{g}\mathrm{l}}+{\mathrm{n}}_{\mathrm{b}0}$$

where $\mathrm{N},{ \mathrm{n}}_1,{ \mathrm{n}}_2,{ \mathrm{n}}_3$ denote the concentrations of MeG₂, $\mathrm{M}\mathrm{e}\mathrm{G}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=0)$, $\mathrm{M}\mathrm{e}\mathrm{G}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=\mathrm{L})$, and $\mathrm{M}\mathrm{e}\mathrm{G}(\mathrm{X}, {\mathsf{\vartheta }}^{″}=0, \mathrm{L}-1)$, respectively; ${\mathrm{n}}_{\mathrm{b}0}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ is the buffer gas concentration; $\mathsf{\rho }$ is the unit density of laser radiation quanta inside the resonator; ${\mathrm{F}}_1=\mathrm{c}\mathrm{N}{\sigma }_1{\mathrm{U}}_1, {\mathrm{F}}_2=\mathrm{c}\mathrm{N}{\sigma }_2{\mathrm{U}}_2$ describe the rates of formation of the corresponding components ($\mathrm{M}\mathrm{e}\mathrm{G}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=0), \mathrm{M}\mathrm{e}\mathrm{G}(\mathrm{X}, {\mathsf{\vartheta }}^{″}=\mathrm{L})$) during the photodissociation of MeG₂ by radiation with a piece density ${\mathrm{U}}_{\mathrm{i}}$ in the first band; $\gamma ={\gamma }_{\mathrm{p}}+{\gamma }_{\mathrm{s}\mathrm{v}}$ cm⁻¹ describes the constant of the total losses of generation quanta in the resonator (${\gamma }_{\mathrm{p}}$ denotes the losses on the opacity of the resonator, and ${\gamma }_{\mathrm{s}\mathrm{v}}$ denotes the losses inside the resonator); α represents a portion of all spontaneously emitted photons at a small solid angle corresponding to the divergence of the laser beam; ${\tau }_{\mathrm{s}\mathrm{p}}$ denotes the time of spontaneous transition (${\tau }_{\mathrm{s}\mathrm{p}}$ = 2.3 × 10⁻⁸ s); ${\mathrm{K}}_{\mathrm{M}}^{\mathrm{T}}$ and ${\mathrm{K}}_{\mathrm{M}}^{\mathrm{r}}$ are the rate constants of the quenching reaction states $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=0)$ (${\mathrm{K}}_{\mathrm{M}}^{\mathrm{T}}$ = 1.3 × 10⁻¹³ cm³/s) and $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{X},{\mathsf{\vartheta }}^{″}=\mathrm{L}) ({\mathrm{K}}_{\mathrm{M}}^{\mathrm{r}}=6\cdot {10}^{-13})$ cm³/s, respectively, with the latter also being the rate constant of the triple recombination reaction (${\mathrm{K}}_{\mathrm{M}}^{\mathrm{R}}={10}^{-32}$ cm⁶/s); ${\sigma }_{\mathrm{i}\mathrm{n}\mathrm{d}}$ denotes the cross-section of the induced transition; and $\mathrm{h}{\nu }_{\mathrm{g}}$ denotes the generation quantum ($\mathrm{h}{\nu }_{\mathrm{g}}$ = 2.47 eV, ${\sigma }_{\mathrm{i}\mathrm{n}\mathrm{d}}$ = 1.1 × 10⁻¹⁶ cm²).

During the calculations, it is assumed that the spectral distribution of pumping quanta in the i-th band of an end-type MPC discharge with effective brightness temperature ${\mathrm{T}}_{\mathrm{b}\mathrm{r}}$ obeys Planck’s law with time-variable intensity:

$${\mathrm{U}}_{\mathrm{i}}={\displaystyle \frac{2\pi {\left(\mathrm{h}{\nu }_{\mathrm{i}}\right)}^3\Delta \mathrm{h}{\nu }_{\mathrm{i}, 1/2}}{{\mathrm{c}}^3\mathrm{h}{\nu }_{\mathrm{i}}\left[\exp \left(\mathrm{h}{\nu }_{\mathrm{i}}/\mathrm{k}{\mathrm{T}}_{\mathrm{b}\mathrm{r}}\right)-1\right]}}\phi \left(\mathrm{t}\right),$$

where φ(τ) is a dimensionless function of time that determines the shape of the radiation pulse; 0.47 eV and 0.31 eV are, correspondingly, the half-widths of the i-th absorption line at frequency ${\nu }_{\mathrm{i}} \left(\mathrm{i}=1, 2\right)$. The initial conditions are as follows: $\mathrm{t}=0,{ \mathrm{N}=\mathrm{N}}_0,{ \mathrm{n}}_1={\mathrm{n}}_2={\mathrm{n}}_3={\mathrm{n}}_{\mathrm{g}\mathrm{l}}=0$, and ${\mathrm{n}}_{\mathrm{b}}={\mathrm{n}}_{\mathrm{b}0}+{\mathrm{N}}_0$.

By taking its “rigidity” using the Geer numerical method at various values of the initial concentrations of the active medium ${\mathrm{N}}_0$ and buffer gas molecules ${\mathrm{n}}_{\mathrm{b}0}$, the effective brightness temperature ${\mathrm{T}}_{\mathrm{b}\mathrm{r}}$ of the radiation source from the MPC discharge, the temporal form of the pump pulse φ(t), and the loss constants γ and α into account, the system of Equation (8) is solved.

Let us briefly focus on the main results of the calculations performed for the pump pulse φ(t) = 1. As a typical example (${\mathrm{N}}_0$ = 8.6 × 10¹⁶ cm⁻³, ${\mathrm{n}}_{\mathrm{b}0}$ = 4.05 × 10¹⁹ cm⁻³, ${\mathrm{T}}_{\mathrm{b}\mathrm{r}}=25$ kK, and $\gamma ={\gamma }_{\mathrm{p}}+{\gamma }_{\mathrm{s}\mathrm{v}}=2\cdot {10}^{-3}+7\cdot {10}^{-3}=9\cdot {10}^{-3}$ cm⁻¹), Figure 4 shows the graphical dependences of changes in concentrations over time (HgBr₂—N(t), $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=0)$—${\mathrm{n}}_1$, $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=\mathrm{L})$—${\mathrm{n}}_2$, and ρ(t)—radiation densities in the resonator of a photodissociation laser).

The minimum degree of PD decomposition (at $\mathrm{t}\to \infty$) of the initial molecules ${\mathsf{\delta }}_{\min }=\mathrm{N}\left(\mathrm{t}\to \infty \right)/{\mathrm{N}}_0\le {10}^{-2}$ is limited by the corresponding processes (7). However, the concentration of the remaining undecomposed HgBr₂ molecules is small as $\mathrm{N}\left(\infty \right)\ll {\mathrm{N}}_0$. With the excited gas layer of the active medium parameters corresponding to small initial optical thicknesses ${\mathrm{y}}_0=\sigma {\mathrm{N}}_0\mathrm{L}\le 10÷30$, the magnitude of the optical thicknesses of the layers with a concentration of $\mathrm{N}\left(\infty \right)$ is, consequently, ${\mathrm{y}}_{\infty }=\sigma \mathrm{N}(\infty )\mathrm{L}\ll 1$; thus, this practically does not affect the spatiotemporal dynamics of radiation propagation from the surface of the radiation source into the depth of the gas layer. The rate of PD decomposition of MeG₂ molecules is $\mathrm{F}=\partial \mathrm{N}/\partial \mathrm{t}$, which is maximal over a time interval of 4 µs and can be approximated by the dependence $\mathrm{F}\approx {\mathrm{N}}_0{\displaystyle \frac{\partial \mathsf{\delta }}{\partial \mathrm{t}}}\approx {\displaystyle \frac{\mathsf{\delta }(\mathrm{t})}{{\mathrm{t}}_{*}}}$. These calculations show that, without taking into account recombination reactions, the characteristic time scale at which F is the maximum value is 3–3.5 µs. A comparison of ${\mathrm{t}}_{*}$ and ${\mathrm{t}}_{*\mathrm{i}\mathrm{n}\mathrm{d}}$ also indicates that, in the laser radiation generation phase, the quantitative effect of recombination processes on the PD velocity of the initial molecules at a given point in space does not exceed 20%.

From the graphical results of Figure 4, it can be seen that the intensive decomposition (with the formation of $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=0)$ and $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=\mathrm{L})$ radicals) of the active medium molecule ($\mathrm{H}\mathrm{g}\mathrm{B}{\mathrm{r}}_2$ denoted as N in Figure 4) occurs in the time interval of t ∈ [0, 4] microseconds. At the same time, radical molecules $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=0)$ and $\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{B}, {\mathsf{\vartheta }}^{″}=\mathrm{L})$ are in an excited state. The decay of these states is accompanied by the generation of laser radiation quanta $\mathsf{\rho }$ inside the resonator.

With the “instantaneous” inclusion of radiation sources with a flux density exceeding a certain threshold value, generation also begins instantly. The generation period is characterized by a monotonous decrease in the density of laser radiation quanta, while $\mathrm{d}\mathsf{\rho }/\mathrm{d}\mathrm{t}\sim \left(-\mathrm{d}\mathrm{N}/\mathrm{d}\mathrm{t}\right)$. The moment of termination of generation practically coincides with the moment of time ${\mathrm{t}}_{\ast }$ at which the degree and rate of PD of the initial molecules become minimal ($\mathrm{N}({\mathrm{t}}_{*})\to {\mathrm{N}}_{\infty }, \mathrm{F}\to 0$). It follows that the threshold generation condition depends primarily on the PD rate of the initial HgBr₂ molecules, with $\mathrm{F}=\mathrm{d}\mathrm{N}/\mathrm{d}\mathrm{t}$; this can be represented as $\mathrm{F}>{\mathrm{F}}_{\mathrm{p}}$. It is important to note that the concentration of HgBr₂ molecules at the lower laser level ${\mathrm{n}}_2\ll {\mathrm{n}}_1$ does not affect either the fulfillment of the threshold generation conditions or the amount of energy and power created by the generation radiation pulse. At the same time, in a number of practically interesting cases, the efficiency of the laser (that is, its generation characteristics) is determined. Firstly, this is mainly achieved according to the settlement rate of the upper laser level due to the photodissociation processes of the original HgBr₂ molecules; then, according to the first approximation, it is determined by the recombination processes (i.e., the restoration of the original HgBr₂ molecules during the generation process can be neglected when calculating the laser’s characteristics); and, finally, there is sufficiently effective emptying of the lower laser level $(\mathrm{H}\mathrm{g}\mathrm{B}\mathrm{r}(\mathrm{X}, {\mathsf{\vartheta }}^{″}=\mathrm{L}))$ so that its settlement does not constitute a “narrow throat” in the induced transition.

Thus, an analysis of the elementary physicochemical photoexcitation processes of the active medium of mercury bromide vapor lasers (HgBr₂) shows that end-type MPC discharge can be used for the optical pumping of the active medium of the optical quantum generator (OQG).

4. Evaluation of Plasma Dynamic Parameters of End-Type MPC Discharge Required for Emergency Combustible Mixture Ignition

The results of the work described above indicate that, depending on the Am value, there are three different types of quasi-stationary spatial distribution of plasma parameters. These can be used to judge the features of emerging structures and the dynamics of plasma propagation, and, consequently, interpret the discharge modes. In this section, we consider only the radiation–plasma dynamic structure features and the behavior of the main parameters of the plasma from MPC discharge in the ohmic mode. This end-type MPC discharge mode is most suitable for emergency combustible mixture ignition.

According to the MPC discharge energy–power parameters and the density of the surrounding gas corresponding to the region of variations in the parameter Am < 0.4, the ohmic mode is implemented; in this mode, the acting gas and dynamic forces exceed the pondermotor forces, and the ohmic heating mechanism is predominant (λ > 0.8). At the same time, the proportion of kinetic energy is relatively small compared to the plasma’s internal energy (λ_E < 0.2).

The outer boundary of the discharge is a dynamic SW gas with a weakly expressed cone shape and relatively low non-uniformity in terms of its velocity along the front: the velocity of the head part of the SW is ~1.1 km/s, and the velocity in the area of the outer electrode is ~0.6 km/s. The degree of gas compression in the SW decreases from the maximum ${\mathsf{\rho }}_{\mathrm{S}\mathrm{W}}/{\mathsf{\rho }}_0\approx 4$ (near the system axis) to ${\mathsf{\rho }}_{\mathrm{S}\mathrm{W}}/{\mathsf{\rho }}_0\approx 3$ in the peripheral regions. This SW intensity non-uniformity is caused by the non-uniformity of Joule energy-release power distribution along the surface of the magnetoplasma compressor’s electrode system. A weak cone shape of the outer shock-wave boundary of the discharge is a distinctive feature of this mode, indicative of the Joule mechanism of plasma heating. Additionally, in spite of the rather sharp attenuation of Joule energy-release power along the radius ($\sim 1/{\mathrm{r}}^2$), the velocity and parameters of SW depend on r being rather weak, at approximately $\mathrm{D}\sim {\left({\mathrm{j}}^2\right)}^{1/3}\sim {\mathrm{r}}^{-2/3}$.

The propagation velocity of the near-axis portion of the SWG roughly corresponds to the value of the SW velocity formed during a planar “explosion”, with $\mathrm{D}\sim {\left({\mathrm{P}}_{\mathrm{e}\mathrm{l}1}/\pi {\mathrm{r}}_2^2{\mathsf{\rho }}_0\right)}^{1/3}$. A characteristic feature of this mode is the relatively small value of the coordinate of the head SW position by the time of discharge. The current maximum is ${\mathrm{z}}_{\mathrm{m}}\approx \mathrm{D}{\mathrm{t}}_{\mathrm{m}}\ll 2{\mathrm{r}}_2$, where ${\mathrm{r}}_2$ is the interelectrode dielectric insert’s radius.

The magnitude of the SWG propagation velocity is approximately constant during the first half-period of the discharge current, which is caused by the continuous supply of Joule energy with little time-varying power to the discharge plasma. A typical feature of these modes with A_m < 0.3 for the values of SW intensities is that the ionization effects behind the SW front are insignificant—the discharge current does not flow through the shock-compressed gas region. The current is distributed in the high-temperature (T_pl~15–40 kK) zone of the light-emitting vapor plasma adjacent to the region of shock-compressed gas. The overall contact boundary of the vapor plasma (PG) has a shape close to that of the SWG (see Figure 5a).

In the range of specific electric power values (per unit area of MPC midsection) of <5·10⁵ W/cm², which is characteristic of the ohmic mode, the delay time of light-erosion evaporation in the central electrode is at a maximum (in comparison with more powerful energy modes) of t_s = 0.3–0.4 t₁.

At t = t_d, intense surface evaporation from the central electrode begins. By this time, the jet of light-erosion metal plasma has entered the region occupied by the dielectric plasma, forcing it out of the near-edge discharge zone. The radial dispersal of the metallic plasma jet is mainly restrained by the discharge current’s magnetic pressure. Under Joule heating, metal plasma is accelerated in the z-direction up to a speed of 5 km/s. The magnitude of the axial velocity of the metallic plasma jet significantly exceeds the velocity of the external SW boundary of the plasma from magnetoplasma compressor discharge. As a result, for 2–3 μs after evaporation from the central electrode has started, the metallic plasma jet completely fills the near-axis zone. From this point in time, the axial area with a radial size of r < 5–6 mm is filled with plasma from the central electrode’s vapor, and the surrounding light-erosion plasma zone is filled with plasma by inserted erosion products. The position of the contact boundary, which separates the areas of light-erosion dielectric plasma and metal plasma (MD), at the time of the maximum discharge current is shown in Figure 5a. The shape of the CB (MD) is close to cylindrical with a slight degree of contraction around z = Dt/2.

The light-erosion metal plasma’s density reaches maximum values at the magnetoplasma compressor’s axis and decreases along the 0Z axis from 0.9 kg/m³ (near the surface of the central electrode) to 0.15 kg/m³ before the shock-wave SWP (Figure 5a). In the peripheral regions filled with dielectric plasma, the density varies between 0.05 and 0.2 kg/m³. For the ohmic mode, the ratio of plasma to ambient gas densities is 0.1–0.2, and this varies weakly with ambient gas density ρ₀ and the thermophysical properties of the materials of the structural elements of the magnetoplasma compressor’s electrode system.

The maximum temperature of the discharge plasma (40–60 kK) in this mode of operation is reached in the near-edge zone in the discharge phase (t < t_d), where there is no metallic plasma. With developing surface evaporation from all structural elements of the magnetoplasma compressor, in the discharge phase, the temperature of the near-side metal plasma is 10–30 kK. This increases with distance from the surface of the central electrode, which is caused by the gradual Joule heating of “cold” vapors coming from the electrode surface. The region of light-erosion dielectric plasma surrounding the metal plasma has a slightly higher temperature of 30–40 kK (Figure 5b). In the peripheral regions (r > 25 mm), where the Joule heat release rate is reduced, the plasma temperature is reduced to values of 15–20 kK.

The light-erosion plasma mainly moves in the direction perpendicular to the surface of the electrode system, reaching velocity values of u = 1.5–5 km/s. In this case, the maximum values of the z component of the velocity (5 km/s) are reached in the axial region of the light-erosion metal plasma (Figure 5d), where the Joule heating intensity is the highest. The dielectric plasma flux in the zone (8 mm < r < 15 mm) immediately adjacent to the metal plasma is accelerated in the axial direction to a velocity of 4 km/s. In the peripheral regions (r > 20 mm) with a lower Joule heating power, the velocity is lower at ~1.5 km/s. The braking of the light-erosion plasma flow, which is accelerated in the z-direction of the surrounding gas, leads to the formation of a typical plasma dynamic structure with an external discharge boundary region consisting of gas and a dynamic shock wave in plasma, a shock wave in gas, and a contact boundary CB (PG) separating the areas of shock-compressed gas and light-erosion plasma (Figure 5a). The ohmic mode of magnetoplasma compressor discharge characteristically has a relatively low maximum velocity of light-erosion plasma, and the effects of its plasma dynamic braking in a gas medium are insignificant: in plasma, a weak SWP is formed, and the temperature and density behind its front do not differ from the corresponding parameters of the incoming flow.

The axial acceleration of the metal plasma is driven by the gas and dynamic forces in the “heat nozzle” (due to Joule heating) to the level of local sonic velocities ($\mathrm{M}=\mathrm{u}/{\mathrm{a}}_{\mathsf{з}\mathsf{в}}\sim 1$), which is achieved just before the SWP. The radial plasma motion $\left|\mathrm{v}\right|\ll \mathrm{u}$ is mostly weak throughout the plasma region. The subsonic nature of the light-erosion plasma flow results in the absence of internal shock-wave ruptures, which is a typical feature of this mode.

The effects of electromagnetic forces are generally insignificant. The degree and areas of influence of electromagnetic forces can be judged (Figure 5c) based on the magnitudes and spatial distributions of local Alfvén velocities ${\mathrm{V}}_{\mathrm{A}}={\left({\mathrm{H}}_{\phi }^2/4\pi \mathsf{\rho }\right)}^{1/2}$. A characteristic feature of this mode is that the Alfvén velocity is at a maximum (2.6 km/s) in the region of the dielectric surface adjacent to the central electrode of the magnetoplasma compressor (r = 8–15 mm). It is in this region that the electromagnetic acceleration effect of the dielectric plasma is most noticeable. In peripheral regions (r > 15 mm), dielectric plasma acceleration exhibits a gas-dynamic character.

At the temperatures and densities achieved in the ohmic mode, the entire plasma region of the light-erosion vapor is a source of thermal radiation, with flux densities on the order of 1 MW/cm² escaping into the surrounding gas from the SW boundary of the discharge.

In [18,19,20,21,22,23,24,25,26], experimental and theoretical studies were carried out to determine the operability of a small-sized MPC functioning in the frequency mode, and the possibility of its use for initiating the volumetric ignition and combustion of a fuel mixture in a supersonic flow was investigated. Overall, the experimental results (in terms of plasma dynamic characteristics) are in accordance with the results of the calculations performed here. Thus, a preliminary (estimated) conclusion can be drawn: it is possible to initiate the volumetric ignition of combustible mixtures with the frequency mode of operation when using end-type MPC discharge. The development of magneto-gas dynamics with instabilities is also possible [27,28,29,30,31,32,33,34,35].

From the known experimental results [36,37], it follows that MPC discharge plasma generates thermal radiation with brightness temperatures of 30–35 kK in the visible range of the spectrum. Such brightness temperatures correspond to radiation fluxes at the level of 10⁵–10⁶ W/cm². These flows heat the electrodes and the interelectrode insert to temperatures (electrode T > 1000 K, interelectrode insert (fluoroplast) T > 300 K) at which their evaporation is possible.

5. Conclusions

A qualitative analysis of the plasma dynamic modes of operation of an end-type MPC discharge has been performed. We have shown that the most acceptable mode for the optical pumping of gas lasers in the UV ranges of the spectrum is inhibiting MPC discharge plasma on a gas barrier (ohmic mode). We carried out numerical modeling of erosive MPCs, which revealed the complex and self-consistent nature of energy transfer processes from the storage device to the plasma; the processes of erosive plasma formation; the dynamics of acceleration and light-erosive plasma flux interactions with other fluxes and surrounding gas; and, ultimately, the processes of converting energy dissipated into plasma into internal and kinetic energy and into broadband radiation from discharge plasma into the surrounding gas environment, the so-called transparency window. The spatial distributions of plasma parameters were obtained for ohmic and transient heating modes.

This study provides a theoretical justification for the use of a two-way irradiation scheme, which ensures increased OQG efficiency. In order to obtain high-energy OQG generation, it is necessary to use several sources of active laser medium exposure based on MPC-type discharge. The simplest variant of the schematic solution of such laser installations is the several light sources mounted around plasma; this can be considered a starting point for considering more complex configurations. In this regard, we showed that the spatiotemporal dynamics of the concentration N(x,t) and the rate of the photolysis decomposition F(x,t) = ∂N(x,t)/∂t of molecules M of a gas layer with a thickness L under the action of radiation sources provide a “counter action” (a light source may be mounted “opposite” or on the other side of the target plasma) of simultaneous irradiation of the layer with specified S_O fluxes. Duration t is the pulse of UV radiation in the absorption band of molecules M (with an effective cross-section σ) at their initial concentration of N_O. Our analysis was carried out on the basis of a joint solution for physicochemical kinetics and radiation transfer equations.

Also, in this work, the characteristic phases and modes of dynamics of the photolysis decomposition of M molecules in a layer were analyzed depending on the initial optical thickness of σN_OL and the parameters of the radiation source S_O, t. The effect of the nonlinear enhanced photolysis rate of F in the layer volume was established. Based on the results, we calculated the energy–power parameters of a photodissociable gas laser. The result demonstrated enhanced plasma performance, showing that such a scheme (that is, the opposite of a “counter action”) makes it possible to increase the laser generation energy and efficiency by 10–20% compared with the one-way pumping scheme when choosing the initial optical thickness of the active medium layer, σN_OL ≈ (1–8). The initial estimations for the ranges of pump pulse parameters (half-width and amplitude) and active laser medium layer parameters (initial concentration of HgBr₂ molecules and thickness of the excited layer) are given; according to these, the maximum laser radiation energy and energy efficiency values can be obtained.