# Simulation of Parameters of Plasma Dynamics of a Magneto Plasma Compressor
## 4 Plasma Dynamic Parameters for Discharge in Magneto Plasma Compressor  
The performed numerical simulation of erosive magneto plasma compressors has revealed the complex self-consistent nature of the processes of energy transfer from storage to plasma and the processes of erosive plasma formation, the dynamics of acceleration, the interaction of light erosive plasma streams between themselves and the surrounding gas, and, finally, the processes of transformation of energy W\({}_{1}\) dissipated in plasma into internal E\({}_{\rm int}\) and kinetic E\({}_{\rm kin}\) energy and into broadband E\({}_{\rm s,\Sigma}\) radiation energy, escaping from discharge plasma into the surrounding gas medium (in the \"transparency\" window). The character of the energy interconversions of the discharge is connected with the mechanism of energy dissipation of the storage device into plasma load and depends on the mode parameter A\({}_{\rm m}\). The dependence of the ratio of the total kinetic plasma energy \(\rm{E_{kin}}(t_{m})=\int\limits_{V}\left(\rho\left(\stackrel{{ \rightarrow}}{{V}}\right)^{2}/2\right)dV\) to the total internal energy \(\rm{E_{int}}(t_{m})=\int\limits_{V}\) edV (calculated at the moment of time \(t_{m}\) of the discharge current maximum), i.e., \(\upl_{\rm E}=E_{\rm kin}(t_{m})/E_{\rm int}(t_{m})\) from value A\({}_{\rm m}\) is presented in Figure 1 (for different energy power modes and densities of ambient gas; calculated values of \(\upl_{\rm E}\) are marked). The approximation curve \(\upl_{\rm E}(\upl_{\rm m})\) is a monotonically increasing function showing that the fraction of kinetic energy of plasma formation in relation to the internal one increases with the transition of plasma heating mode from an ohmic (\(\upl_{\rm E}\) < 0.15, A\({}_{\rm m}\) < 0.4) to a plasma dynamic (\(\upl_{\rm E}\) = 0.3-0.5, A\({}_{\rm m}\) > 0.8) regime. In other words, upon realization of the plasma heating, a significant portion (in the limit of parameters A\({}_{\rm m}\)\(\rightarrow\) 1, \(\upl_{\rm E}\)\(\rightarrow\) 1) of the energy input to the plasma is converted into kinetic energy of the moving erosive plasma and shock-compressed gas (plasma). In the region of magneto plasma compressor parameters corresponding to the ohmic heating mechanism (A\({}_{\rm m}\) < 0.4), the main part of the energy is concentrated into the internal energy of the erosive plasma, the kinetic energy of which is small due to the relative smallness of the accelerating ponderomotive forces. In the transition region where the joint action of ohmic and plasma dynamic regimes is carried out, the parameter A\({}_{\rm m}\)\(\approx\) 0.4-0.8 and the share of the total kinetic energy of the plasma in relation to the internal one is significant (\(\upl_{\rm E}\) = 0.2-0.4). In more powerful modes (i.e., at high values of discharge current amplitude J\({}_{\rm m}\) in the transition regime) and/or at a decrease in ambient gas density \(\rho_{0}\), the corresponding parameter A\({}_{\rm m}\) = 0.4-0.8 (ohmic-transient operation regime for discharge in the magneto plasma compressor). The strong gas dynamic shock wave in the surrounding gas (SWG) propagation velocity in the near-edge zone is higher than the SWG velocity in the peripheral zone. The transient regime has a shock front axial coordinate in the axial region; its value, by the time of the discharge current maximum, is about the size of the magneto plasma compressor midpoint, i.e., \(z_{\rm m}\approx\rm Dt_{\rm m}\geq 2r_{2}\). Velocity lines have shown in Figure 2.  
Figure 3 consists of the level lines for density and temperature at discharge current J = 353 kA for the magneto plasma compressor with the parameters C = 750 uF, and U\({}_{0}\) = 10 kV, R\({}_{1}\) = 0.8 \(\times\) 10\({}^{-2}\) m, and R\({}_{2}\) = 5 \(\times\) 10\({}^{-2}\) m for argon.