Numerical Study of the First Compression of a Two-Dimensional Pinch

For studying the first compression phase of a Plasma Focus machine, we developed a 2-fluid, time-dependent, 2-D code. The code includes two species (ions and electrons), two temperatures, radiation, thermal conductivity, electrical conductivity, magnetic diffusion, and viscosity and is coupled to an external circuit. In order to get reasonable initial conditions for the pinch phase, a simple 1-D model is used for the run-down phase. Under this somewhat ideal Plasma Focus discharge condition, relatively simple scaling laws are obtained. In particular, for a given machine, the pressure (p_o) of maximum thermonuclear production scales with the charging voltage (V_o) as p_o V_{o 2}; the thermonuclear production (Y_n) at these pressures increases with the current (I_o) as Y_n I_o ⁴ and the mean energy per particle is almost independent of all parameters (note that this means that the converging speed should be almost the same regardless of the machine at the optimum conditions). These laws show a reasonable agreement with experimental data and can be explained with a dimensional analysis.