Infrared-Raman-regime free-electron laser in the presence of helical wiggler and guide magnetic fields: analysis

A self-consistent kinetic theory of the free-electron laser is developed based on the method of characteristics in circularly polarized, periodic, static helical wiggler, and guide magnetic fields. The detailed relativistic particle trajectories obtained in wiggler and guide magnetic fields are used in linearized Vlasov–Maxwell equations having variations in perpendicular and parallel momenta to obtain the perturbed distribution function in terms of perturbed electric and magnetic fields. The perturbed distribution function thus obtained, having variations in perpendicular and parallel momenta for an arbitrary distribution function, is used to obtain current, conductivity, and dielectric tensors. The full dispersion relation is then obtained and further reduced to Raman-regime approximations for the case of a tenuous electron beam. The analysis is done for temporal and spatial growth rates in the infrared region. The temporal growth rate is higher than the spatial growth rate. The variation in dimensionless frequency is also depicted on the other axis of the graph for the case of temporal growth rate. This yields the frequency and hence wavelength corresponding to maximum growth rate. The effects of guide magnetic field, wiggler magnetic field, and electron density for temporal and spatial growth rates are also studied. Results are compared with those obtained by other techniques