Notes on a 1-dimensional electrostatic plasma model

TL;DR

This paper introduces a 1D electrostatic plasma model using parallel charged disks to simplify the high-dimensional problem of plasma dynamics, aiming to facilitate numerical testing of the Vlasov equation assumptions.

Contribution

It proposes a novel 1D plasma model that captures both short-range 1D and long-range 3D features, reducing computational complexity for theoretical analysis.

Findings

Model combines 1D and 3D features effectively.

Potential to enable feasible numerical tests of plasma theories.

Provides a new framework for studying plasma interactions.

Abstract

A starting point for deriving the Vlasov equation is the BBGKY hierarchy that describes the dynamics of coupled marginal distribution functions. With a large value of the plasma parameter one can justify eliminating 2-point correlations in terms of the 1-point function in order to derive the Vlasov Landau Lenard Balescu (VLLB) theory. Because of the high dimensionality of the problem, numerically testing the assumptions of the VLLB theory is prohibitive. In these notes we propose a physically reasonable interaction model that lowers the dimensionality of the problem and may bring such computations within reach. We introduce a 1-dimensional (1-D) electrostatic plasma model formulated in terms of the interaction of parallelly-aligned charged disks. This model combines 1-dimensional features at short distances and 3-dimensional features at large distances.