STABILITY OF RESONATOR CONFIGURATIONS IN THE PRESENCE OF FREE-ELECTRON LASER INTERACTIONS

The stability of empty resonators (or cold cavities) has been widely studied, and is well understood. Here we consider the stability of symmetric resonator systems when there is a free-electron laser (FEL) interaction present within the cavity. We first construct a linear thick-lens model of the FEL and analytically study the dependence of resonator stability on its geometry. Next, we employ a nonlinear, three-dimensional FEL oscillator code to study the dependence of FEL performance on the cavity configuration The analytic and numerical approaches are compared and it is shown that they agree quite well. It is found that the region of stability is shifted toward longer cavities, and beyond the concentric configuration. Between the confocal and the concentric configurations, where the empty-resonator analysis predicts stability, there now appear regions of instability. We find that operation near the concentric configuration is preferable, and operation very near the confocal should be avoided.