Abstract
An efficient grid-based Langevin formulation is developed for treating electron–electron (e-e) and electron–ion collisions within a particle-in-cell plasma simulation code. The formulation is energy- and momentum-conserving. If the thermal part of the electron velocity distribution is reasonably close to isotropy in any local frame of reference, the basic scattering algorithm is quantitatively accurate for electrons with any value of energy. This is particularly important in calculating the approach to equilibrium of the high-energy tail, or the equilibrium under the competing influences of e-e collisions, inelastic electron–neutral collisions, and end losses through sheaths. If the electron velocity distribution is multi-peaked or very anisotropic, accurate calculations can be performed by representing the electrons as a superposition of several beams. Computational examples are given illustrating both equilibrium energy distribution and approach to equilibrium.
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