Higher harmonic inverse free-electron laser interaction.

We expand the theory of the inverse free electron laser (IFEL) interaction to include the possibility of energy exchange that takes place when relativistic particles traversing an undulator interact with an electromagnetic wave of a frequency that is a harmonic of the fundamental wiggler resonant frequency. We derive the coupling coefficients as a function of the IFEL parameters for all harmonics, both odd and even. The theory is supported by simulation results obtained with a three-dimensional Lorentz equation solver code. Comparisons are made between the results of theory and simulations, and the recent UCLA IFEL experimental results where higher harmonic IFEL interaction was observed.