The microbunching instability usually exists in the LINAC of a free electronlaser (FEL) facility. In many cases, the longitudinal space charge (LSC) is adominant factor that generates the instability. For the highly bright electronbeams, the plasma effect is found to be non-trivial in the development of theinstability. In this paper, starting from the Vlasov and Poisson equations inthe multiple-dimensional phase space, we perform the straightforward analysisof the microbunching instability based on the explicit formula of thelongitudinal electric field introduced by the density perturbation in thelongitudinal direction, in such a way to be highly comparable to thewell-developed method for higher energy beams. This method generally applies inboth the cases with and without acceleration and independent of latticecomponents. The results show that for a electron beam with small transverseemittance at low energies, which is always the case in the injector of a freeelectron laser device, the plasma effect results in the oscillation of thelongitudinal electric field in the modified plasma frequency that depends onthe transverse size of the beam, and the Landau damping effect in thelongitudinal electric field due to the uncorrelated longitudinal velocityspread during the beam transportation. These two effects both play importantroles in the development of the instability. As the result, the energymodulation driven by the LSC impedance differs from the regular valuesignificantly and the discrepancy leads to the noticeable change of the finalgain of the instability.
展开▼
