Vlasov simulation in multiple spatial dimensions

TL;DR

This paper introduces the Vlasov Multi Dimensional (VMD) model, an efficient alternative to particle-in-cell methods for simulating plasma dynamics in multiple spatial dimensions, especially when plasma waves are confined to narrow cones.

Contribution

The VMD model leverages solution properties in specific regimes to reduce computational resources significantly compared to standard PIC methods, particularly in 2D and 3D simulations.

Findings

VMD reduces computational resources by an order of magnitude in 2D.

VMD achieves further reduction in 3D simulations.

VMD results qualitatively agree with PIC in modeling localized Langmuir waves.

Abstract

A long-standing challenge encountered in modeling plasma dynamics is achieving practical Vlasov equation simulation in multiple spatial dimensions over large length and time scales. While direct multi-dimension Vlasov simulation methods using adaptive mesh methods [J. W. Banks et al., Physics of Plasmas 18, no. 5 (2011): 052102; B. I. Cohen et al., November 10, 2010, http://meetings.aps.org/link/BAPS.2010.DPP.NP9.142] have recently shown promising results, in this paper we present an alternative, the Vlasov Multi Dimensional (VMD) model, that is specifically designed to take advantage of solution properties in regimes when plasma waves are confined to a narrow cone, as may be the case for stimulated Raman scatter in large optic f# laser beams. Perpendicular grid spacing large compared to a Debye length is then possible without instability, enabling an order 10 decrease in required computational resources compared to standard particle in cell (PIC) methods in 2D, with another reduction of that order in 3D. Further advantage compared to PIC methods accrues in regimes where particle noise is an issue. VMD and PIC results in a 2D model of localized Langmuir waves are in qualitative agreement.