Effect of emittance and energy spread on a free-electron laser in the gain-focusing regime

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Abstract
A free-electron laser operating in the gain-focusing regime is discussed. The variation of growth rate, radius of curvature of wave fronts, filling factor and efficiency with emittance, and energy spread is derived. The reults, which are based on the Vlasov-Maxwell system of equations, are obtained by minimizing a variational functional. When plotted as a function of emittance, the efficiency at maximum growth rate peaks at a nonzero value of emittance. For small values of energy spread, the efficiency at maximum growth rate increases with energy spread, in contrast to intuitive expectations.

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