Exact and paraxial Airy propagation of relativistic electron plasma wavepackets

TL;DR

This paper explores exact and paraxial Airy solutions for relativistic electron plasma wavepackets, demonstrating their structured propagation and generalizing their forms based on spectral functions in both time and space domains.

Contribution

It introduces the most general solutions for relativistic electron plasma wavepackets using Airy functions, including exact and paraxial approximations, with arbitrary spectral dependence.

Findings

Wavepackets exhibit accelerated transverse propagation.

Structured wavepackets are maintained in the transverse plane.

Generalized Airy wavepackets depend on arbitrary spectral functions.

Abstract

The different forms of propagation of relativistic electron plasma wavepackets in terms of Airy functions are studied. It is shown that exact solutions can be constructed showing accelerated propagations along coordinates transverse to the thermal speed cone coordinate. Similarly, Airy propagation is a solution for relativistic electron plasma waves in the paraxial approximation. This regime is considered in time-domain, when paraxial approximation is considered for frequency, and in space-domain, when paraxial approximation is considered for wavelength. In both different cases, the wavepackets remains structured in the transverse plane. Using these solutions we are able to define generalized and arbitrary Airy wavepackets for electron plasma waves, depeding on arbitrary spectral functions. Examples of this construction are presented. These electron plasma Airy wavepackets are the most general solutions of this kind.