Implicit kinetic solvers with Adaptive Mesh in Phase Space for simulations of low-temperature plasmas

The disparity of time scales calls for using implicit methods in plasma simulations [1]. This paper describes the development of implicit kinetic solvers for electrons with Adaptive Mesh in Phase Space (AMPS). We have previously developed AMPS solvers with splitting velocity and configuration scape (for 6D phase space [2]) and without splitting (for 2D and 3D phase space [3]) using explicit and multi-grid implicit solvers for diffusion. In this paper, we describe the implementation of an implicit AMPS solver with adaptive Cartesian mesh using spherical coordinates in velocity space and different coordinate systems in configuration space. Splitting velocity and configuration spaces facilitates coupling of the kinetic solver for electrons with Poisson solver for the electric field and fluid solvers for ions. We will illustrate the new solvers for spherical expansion of weakly collisional non-magnetized and magnetized (solar wind) plasma and for capacitively coupled collisional gas discharge plasma. The benefits of the implicit treatment of electrons for kinetic plasma simulations will be explained. 

[1] R. R. Arslanbekov and V. I. Kolobov, Plasma Sources Sci. Technol. 30, 045013 (2021)

[2] R. R. Arslanbekov, V. I. Kolobov, and A. A. Frolova, Phys. Rev. E 88, 063301 (2013)

[3] V. Kolobov, R. Arslanbekov and D. Levko, AIP Conference Proceedings 2132, 060011 (2019)