Nonlinear theory of free-electron lasers and efficiency enhancement

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Abstract
The development of lasers in which the active medium is a relativistic stream of free electrons has recently evoked much interest. The potential advantages of such free-electron lasers include, among other things, continuous frequency tunability, very high operating power, and high efficiency. The free-electron laser (FEL) is characterized by a pump field, for example, a spatially periodic magnetic field which scatters from a relativistic-electron beam. The scattered radiation has a wavelength much smaller than the pump wavelength, depending on the electron-beam energy. The authors present a general self-consistent nonlinear theory of the FEL process. The nonlinear formulation of the temporal steady-state FEL problem results in a set of coupled differential equations governing the spatial evolution of the amplitudes and wavelength of the radiation and space-charge fields. These equations are readily solved numerically since the amplitude and wavelength vary on a spatial scale which is comparable to a growth length of the output radiation. A number of numerical and analytical illustrations are presented, ranging from the optical to the submillimeter-wavelength regime. Our nonlinear formulation in the linear regime is compared with linear theory, and agreement is found to be excellent. Analytical expressions for the saturated efficiency and radiation amplitude are also shown to be in very good agreement with our nonlinear numerical solutions. Efficiency curves are obtained for both the optical and submillimeter FEL examples with fixed magnetic-pump parameters. It is shown that these intrinsic efficiencies can be greatly enhanced by appropriately contouring the magnetic-pump period. In the case of the optical FEL, the theoretical single-pass efficiency can be made greater than 20% by appropriately decreasing the pump period and increasing the pump magnetic field.