Resonant operation of the cross-field free-electron laser: Kinetic and fluid equilibria

Abstract

Multiple-scale perturbation theory is used to obtain periodic orbits of relativistic electrons in the external electric and magnetic fields of a planar cross-field free electron laser (FEL) operating near the fundamental resonance. The condition for this resonance is 2-yok.vo = (eBo/-yomo)(i +a2 )-1/ 2 , where k, is the wavenumber of the magnetic wiggler field, vo = E 0 /B 0 is the electron drift speed in the crossed uniform electric and magnetic fields, yo = (1 -vo/c 2 )'/ 2 is the relativistic factor associated with the Lorentz transformation between the laboratory frame and the drift frame, mo is the rest mass of the electron, aw = 2~'/ 2 (eBw/mockw) is the normalized r.m.s. vector potential of the wiggler field, and Bw is the magnitude of the wiggler field. The orbits are expressed in an approximate form suitable for use in linearized Vlasov stability analysis and are used to obtain Vlasov distribution functions which correspond to kinetic equilibria that are uniform and nonuniform (across the anode-cathode gap). Appropriate moments of these distribution functions yield corresponding fluid equilibria. These equilibria are developed as a basis for a linear stability analysis of the cross-field FEL operating near the fundamental resonance.t Present address: Thomson-CSF,