Ion distribution function in a plasma with uniform electric field
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 {sigma} or a constant collision frequency {nu}. The constant-{sigma} model is found to accurately represent f(v) for any value of E, whereas the constant-{nu} results are qualitatively incorrect for large fields. Under the constant-{sigma} assumption, a simple, easily solvable ordinary differential equation is obtained which reproduces the MC results with good accuracy.