Abstract
The linear stability of sideband modes for a one-dimensional free electron laser is investigated in detail. The dependence on wiggler taper, slippage between optical pulse and electrons, and trapped electron distribution functions are included in the analysis. Nyquist plots are used to delineate the parameter space in which sideband instabilities occur and approximate analytic expressions for the linear growth rate are derived. In special cases a complete analytic solution is given. Essentially all equilibria are unstable to sideband growth. The linear growth rates agree well with numerical simulations.
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