A comparison of some particle-in-cell plasma simulation methods

Abstract

Comparisons between four particle-in-cell methods for plasma simulation in one dimension have been made with the objectives of investigating (a) the utility of using a higher-order representation of the scalar potential than piecewise linear, and (b) the effects of smoothing the electric field as opposed to simply calculating it from the gradient of the scalar potential at every point. The potential is represented either as a continuous piecewise linear function of position or as a smooth piecewise quadratic function. Numerical comparisons were made using a simple test problem in which a Maxwellian distribution of positrons streams stably through a Maxwellian distribution of electrons. With various numbers of simulation particles per Debye length, time steps and grid spacings, the time variation of the relative stream velocity of the positrons and electrons was used to determine a collision time, and fluctuations in total energy and momentum were monitored. The investigations with this test problem indicate that the four methods are similar to one another with regard to collisional effects, although the collisional effects are usually somewhat less pronounced with the smoothed electric field and the piecewise linear representation of the potential. All of the methods exhibit a strong dependence on initial conditions and time step with this test problem. With regard to fluctuations of total energy and momentum, the comparison of the methods depends very much on the grid spacing and time step.