The non-linear theory and efficiency enhancement of free electron lasers

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 (FELs) include, among other things, continuous frequency tunability, very high power of operations and high efficiency. The free electron laser 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. We present a general self-consistent non-linear theory of the free electron laser process. The non-linear formulation of the temporal steady state free electron laser 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 II spatial scale which is comparable to a growth length of the output radiation. A number of numerical/analytical illustrations are presented ranging from the optical to the submillimetel wavelength regime. Our non-linear 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 non-linear numerical solutions. Efficiency curve is obtained for an optical PEL example with fixed magnetic pump parameters. We show that the 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 greater than 20% by appropriately decreasing the pump period and increasing the pump magnetic field.