A multiscale hybrid particle-Maxwellian Coulomb-Collision Algorithm for Hybrid Kinetic-Fluid Simulations

In many plasma systems, Coulomb collisions, the primary interactions between charged particles, often exhibit significant time-scale separation. Traditional Monte Carlo (MC) methods [1] have a timestep accuracy constraint ν∆t ≪ 1 to resolve the collision fre- quency (ν) effectively [2]. This constraint becomes particularly stringent in scenarios involving self-collisions in the presence of high-Z species or inter-species collisions with substantial mass disparities, rendering such simulations extremely expensive or impractical.

To overcome these challenges, we propose a multiscale hybrid particle-Maxwellian model for hybrid kinetic-fluid simulations. Specifically, we introduce a collisional al- gorithm that utilizes Maxwellians (i.e., isotropic Gaussians) [4] for both highly col- lisional kinetic species and fluid entities. We employ the Lemons method [3] for particle-Maxwellian collisions, enhanced with a more careful treatment of low-relative- speed particles. Additionally, we introduce a new scheme that extends the standard TA method for pairing particle-particle binary collisions to accommodate arbitrary particle weights without compromising conservation properties.

The method is strictly conservative and may significantly outperform standard MC methods, with orders of magnitude improvement in computational efficiency. We will substantiate the accuracy and performance of the proposed method through several examples of varying complexity, encompassing both relaxation and transport problems.

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

[2] Dimits, A. M., Wang, C., Caflisch, R., Cohen, B. I., & Huang, Y. Journal of Computational Physics (2009) 228: 4881-4892.

[3] Lemons, D.S., Winske, D., Daughton, W. and Albright, B., Journal of Computa- tional Physics, (2009) 228(5), pp.1391-1403.

[4] EchimMM,LemaireJ,&Lie-SvendsenØ.Surveysingeophysics(2011)32:1-70.