# Mitigation of the hose instability in plasma-wakefield accelerators

## TL;DR

This paper presents an analytical model showing that energy loss, initial energy spread, and tapered plasma profiles can significantly mitigate hose instability in plasma-wakefield accelerators, enabling stable long-distance propagation.

## Contribution

The work introduces a new analytical model that accounts for the evolution of hose instability and demonstrates mitigation strategies for stable beam acceleration.

## Key findings

- Inherent drive-beam energy loss reduces hose instability.
- Initial beam energy spread detunes betatron oscillations.
- Tapered plasma profiles can suppress initial hosing seeds.

## Abstract

Current models predict the hose instability to crucially limit the applicability of plasma-wakefield accelerators. By developing an analytical model which incorporates the evolution of the hose instability over long propagation distances, this work demonstrates that the inherent drive-beam energy loss, along with an initial beam energy spread detune the betatron oscillations of beam electrons, and thereby mitigate the instability. It is also shown that tapered plasma profiles can strongly reduce initial hosing seeds. Hence, we demonstrate that the propagation of a drive beam can be stabilized over long propagation distances, paving the way for the acceleration of high-quality electron beams in plasma-wakefield accelerators. We find excellent agreement between our models and particle-in-cell simulations.