Space-charge effects in high-density plasmas

The electron and ion continuity equations and Poisson's equation are solved for the motion of a pulse of plasma of peak density up to 1013 cm-3, in nitrogen at 12 kPa, with an initially uniform electric field of -5.58 kV/cm. Slight movement of the electrons causes the electric field to be reduced to almost zero throughout the plasma and enhanced outside the plasma. The net charge has a positive peak near the cathode and a negative peak near the anode and varies smoothly from one to the other throughout the plasma. It is possible to obtain results at these higher densities by (i) the use of the flux-corrected transport algorithm of Boris and Book. ''Phoenical LPE Shasta,'' together with Zalesak's flux limiting algorithm, and (ii) the limiting of the time step to avoid a numerical instability. The numerical instability at these high densities is found to be an oscillation in the calculated electric current due to too great a change in the electric field in one time step. With a suitable limitation in the time step, calculations can be performed at much higher plasma densities