Alignment and performance of almost concentric resonators for low gain free-electron lasers

The propagation of mismatched and misaligned laser beams bouncing back and forth between the mirrors of an almost concentric resonator is investigated with reference to the alignment of the cavities used for low gain free-electron lasers. In addition, the excitation of the cavity modes by the spontaneous radiation of a linear undulator is analyzed by considering the reduction of their coupling factors due to the misadjustment of the optical cavity with respect to the axis and the center of the undulator. In particular, analytical expressions are given for the coupling coefficients of two misaligned sets of Gauss-Laguerre or Gauss-Hermite modes and for the coupling factors between the cavity modes and the spontaneous radiation.