Implementations of mesh refinement schemes for Particle-In-Cell plasma simulations

Abstract

Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation region, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations and present two implementations in more detail, with examples.

Electromagnetic full particle code with adaptive mesh refinement technique: Application to the current sheet evolution

“…(15) must be executed to maintain $ AE E = q/e 0 on each level cells. The electromagnetic fields obtained by this procedure without recalculating under the corrected boundary conditions, however, do not give proper solutions on each refinement level, because they are not continuously differentiable at the boundaries of the refined regions [17,37]. Nevertheless, the test simulations described in Section 3 indicate that numerical errors in association with the cell refinement are almost negligible, so that we consider that the influence of the inconsistency in the field solutions between refined regions is not significant.…”

“…Although their code is adaptive only in space, recently developed codes [20,35,40] are adaptive not only in space but also in time. Plasma simulations using an electrostatic PIC code with the AMR have been recently examined in order to describe the ion beam transport in a heavy ion fusion [37].…”

Study of electric and magnetic field fluctuations from lower hybrid drift instability waves in the terrestrial magnetotail with the fully kinetic, semi-implicit, adaptive multi level multi domain method

“…The Multi-Level Multi-Domain (MLMD) method is a way of reducing the computational cost of fully kinetic PIC simulations by simulating at increasingly higher spatial and temporal resolutions increasingly smaller fractions of the domain. In this regards, it is similar in concept to Adaptive Mesh Refinement methods for PIC codes 70,71 . The computational cost becomes the main limiting factor to what simulations can achieve in cases, such as Innocenti et al 72 , where the aim is to study kinetic processes at large temporal (hundreds of inverse ion cyclotron fequency) and spatial (hundreds of ion skin depth) scales.…”

Particle-based simulation of plasmas

“…To avoid the finite grid instability, uniform grids need to resolve the smallest Debye length in the system. Adaptive schemes can be devised to resolve in each region only the local Debye length, resulting in considerable savings [23,29,66]. However, even in this case, often the local scales of interest are much larger than the Debye length and the local grid resolution would be more desirably chosen according to other consideration than the need to resolve the Debye length.…”