Saturation of the hosing instability in quasi-linear plasma accelerators

TL;DR

This paper analyzes the beam hosing instability in quasi-linear plasma accelerators, revealing that it saturates at lower levels than previously predicted due to natural focusing force variations, with derived analytic expressions matching numerical results.

Contribution

It provides the first theoretical analysis showing saturation of the hosing instability in the quasi-linear regime, including analytic formulas for saturation distance and amplitude.

Findings

Hosing instability saturates at lower levels than standard predictions.

Analytic expressions for saturation distance and amplitude are derived.

Numerical results agree with the theoretical analysis.

Abstract

The beam hosing instability is analyzed theoretically for a witness beam in the quasi-linear regime of plasma accelerators. In this regime, the hosing instability saturates, even for a monoenergetic bunch, at a level much less than standard scalings predict. Analytic expressions are derived for the saturation distance and amplitude and are in agreement with numerical results. Saturation is due to the natural head-to-tail variations in the focusing force, including the self-consistent transverse beam loading.