Effect of beam emittance on self-modulation of long beams in plasma wakefield accelerators

TL;DR

This paper investigates how initial beam emittance limits the maximum wakefield amplitude in plasma wakefield accelerators, revealing a critical emittance beyond which self-modulation is suppressed.

Contribution

It derives a simple formula linking critical emittance to beam and plasma parameters, clarifying its impact on self-modulation development.

Findings

Wakefield amplitude decreases linearly with increasing emittance.

A critical emittance value exists beyond which self-modulation does not develop.

Experimental observations support the theoretical predictions.

Abstract

The initial beam emittance determines the maximum wakefield amplitude that can be reached as a result of beam self-modulation in the plasma. The wakefield excited by the fully self-modulated beam decreases linearly with the increase of the beam emittance. There is a value of initial emittance beyond which the self-modulation does not develop even if the instability is initiated by a strong seed perturbation. The emittance scale at which the wakefield is twice suppressed with respect to the zero-emittance case (the so called critical emittance) is determined by inability of the excited wave to confine beam particles radially and is related to beam and plasma parameters by a simple formula. The effect of beam emittance can be observed in several discussed self-modulation experiments.