Green's Function Analysis of Free-electron Laser Amplifiers ;nd Oscillators

Theoretical analysis of the free-electron laser Green`s function has been made in two very distinct operating regimes. An analytic expression for the temporal Green`s function has been found for the strongly space-charge dominated (Raman) regime for a single pass FEL amplifier. The expression is shown to reduce to the expected steady-state result when the initial system parameters are time-independent. Frequency shifting is seen to arise from slippage and finite length electromagnetic pulses, as well as from better known causes such as variations in the beam energy and voltage. An explicit criterion for using the local gain approximation is presented. A new formalism for analyzing the temporal and spectral evolution in an oscillator is developed. Variations in both the beam and radiation profiles are included in the analysis. An exact expression for the Green`s function of the n`th pass in an oscillator is derived and can be explicitly evaluated using a fast numerical algorithm. The algorithm yields the n`th pass Green`s function directly, without requiring calculation of the Green`s function at previous passes. The calculation does not involve non-causal truncations utilized in supermode theory.