Mode theory of FEL oscillator with the open plane Fabry-Perot resonator, helical undulator and axisymmetric electron beam

Abstract

This paper presents an analytic method of finding the eigenvalue problem solution for the FEL oscillator with the open plane Fabry-Perot resonator. The method is based on the self-consistent solution of Maxwell's equations and the kinetic equation. To take into account diffraction effects we apply the impedance boundary conditions of resonance type at the open resonator ends. As an example of using the general approach we consider the systems with axial symmetry. The rigorous solution of the eigenvalue problem is found for the case when the electron beam has a bounded parabolic profile. The multilayer approximation method is used when the electron beam has an arbitrary gradient profile.