A numerical integration scheme for vectorised phase-space of one-dimensional collision-free, electrostatic systems

TL;DR

This paper introduces a novel, fast, and accurate numerical integration scheme for 1D collisionless electrostatic systems based on a fluid-analogy of phase-space, outperforming traditional methods in speed and precision.

Contribution

The work presents a new numerical scheme for Vlasov-Poisson equations that models phase-space as a 2D fluid vector space, improving accuracy and computational speed.

Findings

The new scheme demonstrates higher speed than finite splitting methods.

It achieves comparable or better accuracy in phase-space integration.

Simulation results confirm its effectiveness for plasma studies.

Abstract

The kinetic analyses of many-particle soft matter often employ many simulation studies of various physical phenomena which supplement the experimental limitations or compliment the theoretical findings of the study. Such simulations are generally conducted by the numerical integration techniques of the governing equations. In the typical case of collisionless electrostatic systems such as electrostatic plasmas, the Vlasov-Poisson (VP) equation system governs the dynamical evolution of the particle phase-space. The one-dimensional position-velocity (1D-1V) particle phase-space, on the other hand, is known to exhibit direct analogy with ordinary two-dimensional fluids, wherein the Vlasov equation resembles the fluid continuity equation of an in-compressible fluid. On the basis of this fluid-analogy, we present, in this work, a new numerical integration scheme which treats the 1D-1V phase-space as a two-dimensional fluid vector space. We then perform and present analyses of numerical accuracy of this scheme and compare its speed and accuracy with the well-known finite splitting scheme, which is a standardised technique for the numerical Vlasov-Poisson integration. Finally, we show some simulation results of the 1D collisionless electrostatic plasma which highlight the higher speed and accuracy of the new scheme. This work presents a fast and sufficiently accurate numerical integration technique of the VP system which can be directly employed in various simulation studies of many particle systems, including plasmas.