A corrected method for Coulomb scattering in arbitrarily weighted particle-in-cell plasma simulations

•An accurate method for scattering with arbitrary particle weighting.•Validated through theory and numerical tests.•Tested within and between different particle groups over large weight ratios.•Errors in previous work Nanbu and Yonemura [J. Comput. Phys. 145 (1998) 639] identified. A physically and statistically accurate method to perform binary, pairwise Coulomb collisions for arbitrarily-weighted macroparticles in particle-in-cell simulations is described. The method is shown to conserve global energy and momentum on average and to produce physically accurate scattering frequencies. This is justified using the statistically expected values of the method and through a series of numerical tests showing that the method is valid independently of macroparticle weight. This novel method is required due to an error in previous work on binary scattering, initially by Nanbu and Yonemura (1998) [11] and applied to subsequent work, that causes inaccuracies in the scattering frequencies for unequally weighted simulations; a problem that occurs both for scattering within the group and between different groups.