Exact and paraxial Airy propagation of relativistic electron plasma waves

Abstract

It is shown that relativistic electron plasma waves can propagate in an Airy-like form. These solutions are possible even for relativistic temperatures. These waves can be constructed in an exact manner, showing that they propagate in an accelerated fashion along coordinates transverse to the thermal speed cone coordinate. Similarly, we show that Airy-like propagation is also a solution for relativistic electron plasma waves in the paraxial approximation. This regime is considered in time-domain, when the paraxial approximation is taken for frequency, and in space-domain when the paraxial approximation is taken for wavelength. In these two different cases, the waves remains structured in the transverse plane. Finally, we show that these solutions allow us to define general and arbitrary Airy-like wavepackets for electron plasma waves.