Weighted Particles in Coulomb Collision Simulations Based on the Theory of a Cumulative Scattering Angle

A cumulative property of Coulomb collisions in plasmas was formulated by Nanbu. A succession of small-angle binary collisions is grouped into a unique binary collision with a large scattering angle; the law of scattering is given by the exponential cosine function. Proposed here is a Coulomb collision algorithm for weighted particles, based on that work. Three cases of the weight algorithm are considered: (1) the weights of particles are the same; (2) the weights of particles are different from species to species; and (3) the weights are different from particle to particle. Sample calculations demonstrate the accuracy of the weight algorithm.