Numerical thermalization timescales in electrostatic particle-in-cell simulations

Numerical thermalization is a form of error in particle-in-cell (PIC) simulations that drives the electron velocity distribution function (EVDF) towards a Maxwellian. It is essentially caused by Coulomb collisions between macroparticles, and it can occur on timescales much more rapid than numerical heating or cooling. In 1D simulations the numerical thermalization rate is often slow due to some degree of kinetic blocking – though the addition of a Monte Carlo collision scheme has been shown to break the kinetic blocking and enhance the rate of thermalization. [1]



The situation is quite different in multidimensional PIC simulations. In 2D and 3D simulations, many standard electrostatic PIC schemes with grid spacings that resolve the Debye length will have numerical collisions which modify the EEDF more rapidly than real electron-electron collisions for any reasonable macroparticle weight. [2] The aim of this talk is to discuss this numerical thermalization error and several possible strategies for mitigating its effects.



[1] M. M. Turner, "Kinetic properties of particle-in-cell simulations compromised by Monte Carlo collisions," Phys. Plasmas 13, 033506 (2006). doi: 10.1063/1.2169752



[2] S. Jubin, A. T. Powis, W. Villafana, D. Sydorenko, S. Rauf, A. V. Khrabrov, S. Sarwar and I. D. Kaganovich, "Numerical thermalization in 2D PIC simulations: Practical estimates for low-temperature plasma simulations," Phys. Plasmas 31, 023902 (2024). doi: 10.1063/5.0180421