Beam-tracing and profile evolution for localised beams in inhomogeneous plasmas

TL;DR

This paper develops a comprehensive beam-tracing method for localized beams in inhomogeneous plasmas, revealing how beam profiles evolve and differ from prior assumptions, with implications for plasma diagnostics.

Contribution

It introduces a PDE-based framework for beam profile evolution in inhomogeneous plasmas and provides exact solutions showing mode superpositions during propagation.

Findings

Hermite modes evolve into superpositions in inhomogeneous plasmas

The method generalizes Gaussian beam-tracing to arbitrary profiles

Exact expressions for beam profiles during propagation are derived

Abstract

We derive the beam tracing and profile evolution for the propagation of any localised beam with arbitrary profile through an inhomogeneous cold plasma. We recover standard Gaussian beam-tracing, with an additional PDE describing the evolution of the beam's profile as it propagates through the plasma. We then solve for generic families of solutions to the PDE using ladder operators, which can be chosen to reduce to Gauss-Hermite beams in homogeneous media. We importantly obtain an exact expression for the resulting beam profile, demonstrating that Hermite modes will generally evolve into a superposition of different modes during propagation through inhomogeneous plasmas, contrary to prior work on the subject. Importantly, this approach facilitates future analysis of the diagnostic signal received from arbitrary beams.