Spatiotemporal dynamics of ultrarelativistic beam-plasma instabilities

TL;DR

This paper develops a spatiotemporal theory for ultrarelativistic beam-plasma instabilities, revealing that finite-length beams exhibit slower growth and that wakefield self-focusing can influence instability dynamics, with implications for accelerator experiments.

Contribution

It introduces a novel spatiotemporal framework for beam-plasma instabilities, extending beyond traditional temporal models and incorporating self-focusing effects.

Findings

Spatiotemporal effects slow instability growth in finite-length beams.

PIC simulations validate the theoretical predictions.

Self-focusing from plasma wakefields can compete with oblique instabilities.

Abstract

An electron or electron-positron beam streaming through a plasma is notoriously prone to micro-instabilities. For a dilute ultrarelativistic infinite beam, the dominant instability is a mixed mode between longitudinal two-stream and transverse filamentation modes, with a phase velocity oblique to the beam velocity. A spatiotemporal theory describing the linear growth of this oblique mixed instability is proposed, which predicts that spatiotemporal effects generally prevail for finite-length beams, leading to a significantly slower instability evolution than in the usually assumed purely temporal regime. These results are accurately supported by particle-in-cell (PIC) simulations. Furthermore, we show that the self-focusing dynamics caused by the plasma wakefields driven by finite-width beams can compete with the oblique instability. Analyzed through PIC simulations, the interplay of these two processes in realistic systems bears important implications for upcoming accelerator experiments on ultrarelativistic beam-plasma interactions.