Multi-Moment Advection scheme for Vlasov simulations

TL;DR

This paper introduces a novel multi-moment advection scheme for Vlasov simulations that improves conservation and accuracy in plasma modeling, especially for long-term rotation problems.

Contribution

The paper develops a new multi-moment advection scheme that incorporates higher-order moments, enhancing accuracy and conservation in Vlasov simulations compared to existing methods.

Findings

Accurately solves solid body rotation of Gaussian profiles over 100 periods

Provides high-accuracy solutions with reasonable computational resources

Demonstrates effectiveness in electrostatic and electromagnetic plasma simulations

Abstract

We present a new numerical scheme for solving the advection equation and its application to Vlasov simulations. The scheme treats not only point values of a profile but also its zeroth to second order piecewise moments as dependent variables, for better conservation of the information entropy. We have developed one- and two-dimensional schemes and show that they provide quite accurate solutions within reasonable usage of computational resources compared to other existing schemes. The two-dimensional scheme can accurately solve the solid body rotation problem of a gaussian profile for more than hundred rotation periods with little numerical diffusion. This is crucially important for Vlasov simulations of magnetized plasmas. Applications of the one- and two-dimensional schemes to electrostatic and electromagnetic Vlasov simulations are presented with some benchmark tests.