Numerical study of the first compression of a two-dimensional pinch

For studying the first compression phase of a Plasma Focus machine, we deve loped a 2-fluid, time-dependent, 2-D code. The code includes two species (i ons and electrons), two temperatures, radiation, thermal conductivity, elec trical conductivity, magnetic diffusion, and viscosity and is coupled to an external circuit. In order to get reasonable initial conditions for the pi nch phase, a simple 1-D model is used for the run-down phase. Under this so mewhat ideal Plasma Focus discharge condition, relatively simple scaling la ws 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) proportional to V-0(2); the thermonuclear production (Y-n) at these p ressures increases with the current (I-o) as Y-n proportional to I-0(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 regard less of the machine at the optimum conditions). These laws show a reasonabl e agreement with experimental data and can be explained with a dimensional analysis.