Collision rates estimated from exact N-body simulations of a one-dimensional plasma

Abstract

In a plasma, the charged particles interact via long-range forces, and this interaction causes the plasma to exhibit collective effects. If the graininess or coupling parameter g goes to zero (ideal collisionless plasma), two-body collisions are negligible, while collective effects dominate the dynamics. In contrast, when g≈1 collisions play a significant role. To study the transition between a collisionless and a collisional regime, a N-body code was developed and used in this work. The code solves exactly, in one spatial dimension, the dynamics of N infinite parallel plane sheets for both ion and electron populations. We illustrate the transition between individual and collective effects by studying two basic plasma phenomena, the two-stream instability and Langmuir waves, for different values of g. The numerical collision rates given by the N-body code increase linearly with g for both phenomena, although with proportionality factors that differ by roughly a factor of two, a discrepancy that may be accounted for by the different initial conditions. All in all, the usual collision rates published in the literature (Spitzer collisionality) appear to compare rather well with the rates observed in our simulations.