Kinetic description of particle interaction with a gravitational wave

TL;DR

This paper develops a kinetic model for charged particles interacting with a gravitational wave in a magnetic field, deriving analytical expressions for resonance overlap and diffusion, and validating results through numerical simulations.

Contribution

It introduces an exact phase space analysis of particle resonance overlap and diffusion in gravitational wave fields using the FPK approach, providing new analytical and numerical insights.

Findings

Resonance overlap locations identified in phase space.

Analytical expressions for effective diffusion coefficients derived.

Numerical simulations confirm analytical diffusion results.

Abstract

The interaction of charged particles, moving in a uniform magnetic field, with a plane-polarized gravitational wave is considered using the Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact locations in phase space, where resonance overlapping occurs. We investigate the diffusion of orbits around each primary resonance of order (m) by deriving general analytical expressions for an effective diffusion coeficient. A solution to the corresponding diffusion equation (Fokker-Planck equation) for the static case is found. Numerical integration of the full equations of motion and subsequent calculation of the diffusion coefficient verifies the analytical results.