The Michelson resonator free-electron laser. II. Supermode structure and mirror detuning effects

For pt.I, see ibid., vol.29, no.2, p.452-64 (1993). Conventional mode-locked laser theory is applied to the longitudinal mode structure in an RF linac-driven Michelson resonator free-electron laser (FEL). A greatly simplified derivation of the small-signal small-gain FEL coupled mode equations is obtained. These equations are solved numerically in the frequency domain to study the supermode evolution in the presence of mode dependent cavity losses. The results are compared with simulations of the detuned Michelson resonator FEL using a pulse propagation code based on the Maxwell-Lorentz equations of motion. Increasing the interferometer detuning broadens and shifts the cavity detuning curve, narrows the supermode spectrum, and decreases the hypermode decay rates. The practical consequences of each of these effects are discussed. A simple theory describing the dependence of the hypermode decay rates on interferometer detuning, in which the decay rates are abruptly decreased beyond a critical detuning that depends primarily on the slippage length, is outlined