A conservative multi-species weighed-particle Takizuka-Abe Coulomb-Collision Algorithm

Takizuka-Abe’s Monte Carlo collision algorithm (TA77) [1] is widely used in PIC codes but conserves momentum and energy exactly only for equal particle weights. Weight variations typical of $\delta f$, minority species modeling, and gradient-driven problems therefore introduce secular errors. Built upon our earlier work [2], we extend TA77 to a conservative multi-species weighted-particle algorithm that enforces exact particle number, momentum, and energy conservation for arbitrarily weighted like- and unlike-species. Collision pairs are sampled proportional to weight and scattered in their center-of-mass frame. A deterministic correction step is then applied afterward to enforce conservation laws while recovering Landau-Fokker-Plank collision operator. The scheme reduses to TA77 for equal weights and binary species pairs, and can handle all intra and inter-species collisions within a single GPU kernel, avoiding multiple kernel launches. Benchmarks reproduce standard relaxation for maximum weight ratios exceeding 100. We present accuracy and performance comparisons between the new algorithm and TA77.

[1] Takizuka, T., Abe, H. Journal of computational physics, (1977) 25: 205-219.

[2] Chen, Guangye, et al. Journal of computational physics, (2025): 113771.