Plasma effect in the longitudinal space charge induced microbunching instability for low energy electron beams

TL;DR

This paper analyzes how plasma effects influence the development of microbunching instability in low-energy electron beams, revealing oscillations and damping effects that significantly alter instability growth and FEL performance.

Contribution

It introduces a comprehensive analysis of plasma effects on microbunching instability using explicit electric field formulas applicable to low-energy beams, including oscillation and damping phenomena.

Findings

Plasma effects cause oscillations in the longitudinal electric field.

Landau damping reduces electric field growth during transport.

Energy modulation and instability gain are significantly affected.

Abstract

The microbunching instability usually exists in the LINAC of a free electron laser (FEL) facility. In many cases, the longitudinal space charge (LSC) is a dominant factor that generates the instability. For the highly bright electron beams, the plasma effect is found to be non-trivial in the development of the instability. In this paper, starting from the Vlasov and Poisson equations in the multiple-dimensional phase space, we perform the straightforward analysis of the microbunching instability based on the explicit formula of the longitudinal electric field introduced by the density perturbation in the longitudinal direction, in such a way to be highly comparable to the well-developed method for higher energy beams. This method generally applies in both the cases with and without acceleration and independent of lattice components. The results show that for a electron beam with small transverse emittance at low energies, which is always the case in the injector of a free electron laser device, the plasma effect results in the oscillation of the longitudinal electric field in the modified plasma frequency that depends on the transverse size of the beam, and the Landau damping effect in the longitudinal electric field due to the uncorrelated longitudinal velocity spread during the beam transportation. These two effects both play important roles in the development of the instability. As the result, the energy modulation driven by the LSC impedance differs from the regular value significantly and the discrepancy leads to the noticeable change of the final gain of the instability.