Self-modulation instability of a long proton bunch in plasmas

TL;DR

This paper develops an analytical model for the self-modulation instability of long proton bunches in plasmas, demonstrating how it excites plasma waves for particle acceleration and proposing a method to control it.

Contribution

It introduces a new analytical framework for understanding proton bunch self-modulation and proposes a seeding method to suppress competing instabilities.

Findings

Analytical expressions for growth rate and exponentiation of the instability.

PIC simulations confirm the competition between self-modulation and hosing instability.

Seeding method effectively suppresses hosing instability in simulations.

Abstract

An analytical model for the self-modulation instability of a long relativistic proton bunch propagating in uniform plasmas is developed. The self-modulated proton bunch resonantly excites a large amplitude plasma wave (wake field), which can be used for acceleration of plasma electrons. Analytical expressions for the linear growth rate and the number of exponentiations are given. We use the full three-dimensional particle-in-cell (PIC) simulations to study the beam self-modulation and the transition to the nonlinear stage. It is shown that the self-modulation of the proton bunch competes with the hosing instability which tends to destroy the plasma wave. A method is proposed and studied through PIC simulations to circumvent this problem which relies on the seeding of the self-modulation instability in the bunch.