Investigation of the electron trajectories and gain regimes of the whistler pumped free-electron laser

A free-electron laser (FEL) scheme, which employs the whistler wave as a slow electromagnetic wave wiggler, was studied theoretically. Subjected to the transverse fields of whistler wave wiggler, the beam electrons are the source of the energy needed to produce electromagnetic radiation. The strength and the period of the wiggler field depend on the parameters of the magnetoplasma medium. This configuration has a higher tunability by controlling the plasma density, on top of the γ-tunability of the conventional FELs. The theory of linear gain and electron trajectories was presented and four groups (I, II, III, and IV) of electron orbits were found in the presence of an axial guide magnetic field. Using perturbation analysis, it is found that these groups of orbits were stable except small regions of group I and IV orbits. The function $Φ$ which determines the rate of change of axial velocity with beam energy was also derived. In the case in which $Φ<0$ represents a negative-mass regime in which the axial velocity accelerates as the electrons lose energy. Numerical solutions showed that by increasing the cyclotron frequency, the gain for group I and III orbits increased, while a gain decrement was obtained for group II and IV orbits.