# Simulation of Parameters of Plasma Dynamics of a Magneto Plasma Compressor
## 3 Electrical Parameters and Power Regimes for Discharge
The \(A_{\rm m}\) values for some typical design variants of the magneto plasma compressor (with internal radius 0.8 \(\times\) 10\({}^{-2}\) m and external radius 5 \(\times\) 10\({}^{-2}\) m) in Ar are presented in Table 1. A generalized interpolation of the dependence \(\lambda_{\rm R}\) on the parameter \(A_{\rm m}\), calculated by equation, shown in Figure 1 (icons show some calculated values of the parameters \(\lambda_{\rm R}=\overline{R}_{\rm om}/\overline{R}_{\rm pl}\) and \(\lambda_{\rm E}=\overline{E}_{\rm kin}(t_{\rm m})/\overline{E}_{\rm int}(t_{ \rm m})\)). As can be seen, the role of the ohmic energy dissipation mechanism is significant over practically the whole range of power modes of magneto plasma compressor discharge and the surrounding gas densities. At values of A\({}_{\rm m}\) < 0.3-0.4, the ohmic resistance share in the total plasma load resistance is the main one (\(\lambda_{\rm R}\geq 0.8\)), and therefore it can be argued that the main mechanism of plasma heating in such modes is Joule heating. With an increasing A\({}_{\rm m}\) parameter, i.e., an increasing discharge current amplitude J\({}_{\rm m}\) and a decreasing gas density \(\rho_{0}\), a monotonic decrease in \(\lambda_{\rm R}\) is observed. For regimes characterized by values of A\({}_{\rm m}\) > 0.8, the part of ohmic resistance is relatively low (\(\lambda_{\rm R}\) = 0.2-0.4), and the plasma dynamic mechanism of plasma heating of the \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(\mathbf{p_{0}}\), \(\mathbf{MPa}\) & \(\mathbf{C,\,\mu F}\) & \(\mathbf{U_{0},\,kV}\) & \(\mathbf{W_{0},\,kJ}\) & \(\mathbf{A_{m}}\) \\ \hline \multirow{4}{*}{\(10^{-3}\)} & & 10 & 1.43 & 0.6 \\  & 28.6 & 30 & 12.9 & 0.9 \\  & & 50 & 35.7 & 0.93 \\ \cline{2-5}  & & 2 & 1.5 & 0.48 \\  & 750 & 5 & 9.37 & 0.78 \\  & & 10 & 37.5 & 0.91 \\ \hline \multirow{4}{*}{\(10^{-2}\)} & & 10 & 1.43 & 0.3 \\  & 28.6 & 30 & 12.9 & 0.65 \\  & & 50 & 35.7 & 0.76 \\ \cline{2-5}  & 750 & 5 & 9.37 & 0.6 \\  & 750 & 10 & 37.5 & 0.85 \\ \hline \multirow{4}{*}{\(10^{-1}\)} & & 30 & 12.9 & 0.36 \\  & 28.6 & 200 & 571 & 0.95 \\ \cline{2-5}  & & 2 & 1.5 & 0.25 \\ \cline{2-5}  & 750 & 5 & 9.37 & 0.4 \\ \cline{2-5}  & & 10 & 37.5 & 0.54 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mode parameter A\({}_{\rm m}\) dependent on gas pressure \(\rho_{0}\) and parameters of the power storage magneto plasma compressor discharge. magneto plasma compressor discharge becomes predominant. In the range of A\({}_{\rm m}\) = 0.4-0.8, the role of both mechanisms of plasma heating of the magneto plasma compressor discharge is commensurable. These results show that the value of the A\({}_{\rm m}\) parameter essentially defines the mode of IGC discharge plasma heating and, therefore, it can be called a mode parameter. In the region of A\({}_{\rm m}\) < 0.3-0.4, there is an ohmic mode of heating; in the region of A\({}_{\rm m}\) > 0.8, there is a plasma dynamic mode of heating; and at A\({}_{\rm m}\) \(\approx\) 0.4-0.8, there is a transitive mode (Figure 1). According to equation, the parameter A\({}_{\rm m}\) value depends on the main electric parameters of the discharge circuit and gas density as parameter A\({}_{\rm m}\)\(\sim\)\(\left(\rm{CW_{0}}/\rho_{0}L_{C}\right)^{1/6}\), and plasma heating mode control can be most effectively achieved by increasing the capacity of power storage C and the initial charging voltage U\({}_{0}\) (A\({}_{\rm m}\)\(\sim\)\(\left(\rm{CU_{0}}\right)^{1/3}\)), as well as by reducing the gas density \(\rho_{0}\). As the numerical simulations show, according to the proposed classification, discharges in rarefied spheres (\(\rho_{0}\) < 0.1 kg/m\({}^{3}\)) and a high level of power storage capacity (for C = 28.6 uF: U\({}_{0}\) > 30 kV, C = 750 uF: U\({}_{0}\) > 5 kV) can be attributed to the plasma dynamic modes of plasma heating of magneto plasma compressor discharges.