Effects of electron energy spread on self-excitation of free-electron lasers

The performance parameters of free-electron lasers when the particle parameters differ widely and there is a kinetic stage of interaction are analyzed. Expressions are given for the energy transfer efficiency in free-electron lasers from a monoenergetic electron beam to the laser wave in the small-signal approximation assuming a fixed rf field structure, as well as for the initial current in a free-electron laser with a high-Q resonator. The contributions to the laser wave energy from electron bunches having different velocities are summed, assuming a Gaussian spread, and an expression is derived which is then integrated and numerically evaluated. It is found that the particle energy spread does not seriously constrain the length, but that starting at a certain reduced length the rate of dropoff of the initial current is greatly reduced. The maximum length and smallest possible laser current are determined by the minimum acceptable efficiency.