Vlasov model using kinetic phase point trajectories

TL;DR

This paper introduces a novel method for solving the collisionless Vlasov equation by tracking phase point trajectories, improving accuracy and handling fine structures efficiently without increasing grid resolution.

Contribution

It presents a new phase point trajectory approach with an effective interpolation scheme and randomization to prevent recurrence effects in Vlasov simulations.

Findings

Enhanced simulation accuracy with more phase points.

Effective interpolation reduces computational operations.

Randomization prevents recurrence effects.

Abstract

A method of solution of the collisionless Vlasov equation, by following collisionless phase point trajectories in phase space, is presented. It is shown that by increasing the number of phase points, without enhancing the resolution of phase space grid, the accuracy of simulation will be improved. Besides, the phase points spacing introduces a smaller scale than grid spacing on which fine structures might be more conveniently handled. In order to perform simulation with a large population of phase points, an effective interpolation scheme is introduced that reduces the number of operations. It is shown that by randomizing initial position of the phase points along velocity axis, the recurrence effect does not happen. Finally, the standard problem of linear Landau damping will be examined.