Growth and phase velocity of self-modulated beam-driven plasma waves

TL;DR

This paper analyzes the self-modulation instability of a relativistic beam in plasma, calculating growth rates and phase velocity, revealing limitations on energy gain due to dephasing in plasma accelerators.

Contribution

It provides a detailed analysis of the growth rate and phase velocity of self-modulated plasma waves, highlighting the dephasing limitation on energy gain.

Findings

Phase velocity is significantly less than beam velocity.

Dephasing occurs in less than four e-foldings in the long-beam regime.

Energy gain is severely limited by dephasing.

Abstract

A long, relativistic charged particle beam propagating in a plasma is subject to the self-modulation instability. This instability is analyzed and the growth rate is calculated, including the phase relation. The phase velocity of the accelerating field is shown to be significantly less than the drive beam velocity. These results indicate that the energy gain of a plasma accelerator driven by a self-modulated beam will be severely limited by dephasing. In the long-beam, strongly-coupled regime, dephasing is reached in less than four e-foldings, independent of beam-plasma parameters.