Self-modulation instability of ultra-relativistic particle bunches with finite rise times

TL;DR

This paper investigates how finite rise times in ultra-relativistic particle bunches affect the self-modulation instability, revealing that sharp rise times are crucial for stable wakefield acceleration.

Contribution

It demonstrates through simulations that finite rise times cause large wake variations, emphasizing the importance of sharp rise times for stable self-modulation.

Findings

Finite rise times lead to large wake amplitude variations.

Sharp rise times are essential to seed the instability.

Stable acceleration requires bunches with sharp rise times.

Abstract

We study the evolution of the self-modulation instability using bunches with finite rise times. Using particle-in-cell simulations we show that unlike long bunches with sharp rise times, there are large variations of the wake amplitudes and wake phase velocity when bunches with finite rise times are used. These results show that use of bunches with sharp rise times is important to seed the self-modulation instability and to ensure stable acceleration regimes.