Simulation of Electron Beam Emission in Argon–Neon Mixture Pinch Using the Nonrelativistic 6-D Valsov–Maxwell System Solved by the Forward Semi-Lagrangian Approach

The 6-D Vlasov–Maxwell equations in the cylindrical coordinates have been solved to calculate the electron beam emission from mixtures of argon and neon. The forward semi-Lagrangian approach was used for solutions. The simulation of the electron velocity field has shown that at the early stage of the pinch evolution of a 4-mbar 90% Ar–10% Ne mixture, the sausage instabilities began to develop from the top parts of the pinch due to bigger $B_{\theta }$ with respect to $B_{z}$ . In the turbulence regions, the electrons could accelerate up to speeds of $905 \times 10^{5}$ and $2387.5 \times 10^{5} \,\,{\text {m}}/{\text {s}}$ at 90.9 and 181.82 ns, respectively. It has been observed that in the high turbulence region, $E_{z}=-2.04\times {10}^{7}\,\,{\text {V}}/{\text {m}}$ , while in the weak turbulence region, $E_{z}=-1.46\times {10}^{7}\,\,\text {V}/{\text {m}}$ . Increasing the neon percentage in the mixture changed the turbulence regions and the upstream and downstream emissions.