Self-Modulation Instability of a Long Proton Bunch in Plasmas

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 (wakefield), which can be used for acceleration of plasma electrons. Analytical expressions for the linear growth rates and the number of exponentiations are given. We use full three-dimensional particle-in-cell (PIC) simulations to study the beam self-modulation and 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.

Coupled beam hose and self-modulation instabilities in overdense plasma

“…In contrast to the predictions of Ref. [8], the growth of the beam hosing instability is comparable to that of the beam self-modulation. Figure 1 shows the centroid displacement given by the numerical solution of Eq.…”

“…Generating short proton beams (or proton beams with spatial structure at the plasma frequency) is challenging, for interesting plasma densities, and it has been proposed to rely on a beam-plasma instability to modulate the beam at the plasma wavelength λ p = 2πc/ω p , driving a large amplitude wave [8][9][10]. The growth and phase velocity of the self-modulation instability has been studied in Refs.…”

“…It was suggested in Ref. [8] that the self-modulation instability grows much faster than the hosing instability and that the self-modulation may alleviate the effects of hosing. In this work we calculate the hosing growth rate including return current effects (where the beam radius is of order the plasma skin depth k −1 p ).…”

Coherent seeding of self-modulated plasma wakefield accelerators

“…Generating short proton beams (or proton beams with spatial structure at the plasma frequency) is challenging, for interesting plasma densities, and it has been proposed to rely on a beam-plasma instability to modulate the beam at the plasma wavelength λ p = 2πc/ω p , driving a large amplitude wave. [10][11][12] Proof-of-principle experiments to study the physics of beam self-modulation using lepton beams have also been proposed. 13 The growth rate of the self-modulation instability was calculated in Ref.…”

Characterization of the equilibrium configuration for modulated beams in a plasma wakefield accelerator

“…Proton bunches are usually several times longer than λ p and such a requirement is achieved by using the self-modulation instability 8 , in which a long driver interacts with its own wake. At its final stage the modulation provides a train of bunches with the requested length whose periodicity is approximately λ p .…”