A grid-based binary model for coulomb collisions in plasmas

Both binary and grid-based Langevin equations models for Coulomb collisions are used in particle simulation of plasmas. We introduce a variant of the conventional binary collision algorithm for performing Coulomb collisions. In this algorithm particles in a configuration space cell are not paired for collisions. Instead, for every test particle in the cell, a unique field particle is defined by randomly sampling a velocity distribution defined on the grid by accumulating moments of the particle distribution function(s). The test and field particle pair then undergoes a collision using the standard methodology for binary collisions. The performance of the new algorithm is illustrated in example computations and compared to a drag-diffusion Langevin equations algorithm. The grid-based algorithms do not conserve momentum and energy, although with good particle statistics the non-conservation is relatively small. Conservation can be restored after collisions using a shift and scaling of the momenta. The comparative merits of the new algorithm are discussed.