Small-angle Coulomb collision model for particle-in-cell simulations

We construct and investigate a set of stochastic differential equations that incorporate the physics of velocity-dependent small-angle Coulomb collisions among the plasma particles in a particle-in-cell simulation. Each particle is scattered stochastically from all the other particles in a simulation cell modeled as one or more Maxwellians. Total energy and momentum are conserved by linear transformation of the velocity increments. In two test simulations the proposed “particle-moment” collision algorithm performs well with time steps as large as 10% of the relaxation time – far larger than a particle-pairing collision algorithm, in which pairs of particles are scattered from one another, requires to achieve the same accuracy.