Ion distribution function in a plasma with uniform electric field

Abstract

For a homogeneous partially ionized plasma subject to a uniform electric field E, several methods and models are used to calculate the distribution function f(v) for ions subject to charge-exchange collisions. The exact solution for f(v), based on the energy-dependent cross section for Ar, is obtained by Monte Carlo (MC) simulation. This is compared to the MC results for f(v), based on either a constant cross section σ or a constant collision frequency ν. The constant-σ model is found to accurately represent f(v) for any value of E, whereas the constant-ν results are qualitatively incorrect for large fields. Under the constant-σ assumption, a simple, easily solvable ordinary differential equation is obtained which reproduces the MC results with good accuracy.