Development of sidebands in tapered and untapered free-electron lasers

A time-dependent, axisymmetric code is employed to examine the development of sidebands in a free-electron laser. For the case where the input signal undergoes an extended period of exponential growth, a broad spectrum of sidebands with growth rates comparable to that of the signal is excited. In general, in an untapered system the optical field displays considerable modulation after several synchrotron periods. An analytical model, in qualitative agreement with a number of features of the simulations, is discussed. In a tapered system the amplitude of the sidebands approaches a quasisteady level that is several orders of magnitude below that of the untapered case, and the output optical field displays only a slight modulation. The optimal rate of tapering employed, to maximize efficiency, leads to substantial reduction in the growth rate of sidebands. This result is discussed in connection with the nonadiabatic nature of particle motion in the tapered system.