Relaxation times under pulsed ponderomotive forces and the Central Limit Theorem

TL;DR

This paper investigates plasma relaxation times under pulsed ponderomotive forces using a novel approach based on the moments of distribution functions and the Central Limit Theorem, validated against analytical solutions.

Contribution

It introduces a new technique employing moments and the Central Limit Theorem to analyze transient relaxation in plasma under pulsed forces, differing from traditional methods.

Findings

The new method accurately predicts relaxation times.

Validation against exact collision operator confirms the approach.

Numerical estimates show parameter impacts on relaxation time.

Abstract

We study the relaxation time of a generic plasma which is perturbed by means of a time-dependent pulsed force. This time pulse is modelled using a Gaussian superposition. During such a pulse two forces are considered: An inhomogeneous oscillating electric force and the corresponding ponderomotive force. The evolution of that ensemble is driven by the Boltzmann Equation, and the perturbed population is described by a power-law distribution function. In this work, as a new feature, instead the usual techniques the transient between both distributions is analysed using the moments of such distribution function and the Central Limit Theorem. This technique, together with the, ad hoc solved, equation of motion of the charges under this particular system of pulsed forces, allows to find the corresponding expressions relating the time pulse with the relaxation times and the dynamic conditions. We validate that new technique by comparison with the analytical expression using the corresponding relaxation time using an exact collision operator. Moreover, we parameterise this plasma to make numerical estimates in order to analyse the impact of relevant parameters involved in the physical process on such a relaxation time.