Electron energy and electron trajectories in an inverse free-electron laser accelerator based on a novel electrostatic wiggler

We expand here a theory of a high-gradient laser-excited electron accelerator based on an inverse free-electron laser (inverse-FEL), but with innovations in the structure and design. The electrostatic wiggler used in our scheme, namely termed the Paul wiggler, is generated by segmented cylindrical electrodes with applied oscillatory voltages $V_{\text{osc}}\left(t\right)$ over ${90}^{\circ }$ segments. The inverse-FEL interaction can be described by the equations that govern the electron motion in the combined fields of both the laser pulse and Paul wiggler field. A numerical study of electron energy and electron trajectories has been made using the fourth-order Runge–Kutta method. The results indicate that the electron attains a considerable energy at short distances in this device. It is found that if the electron has got sufficient suitable wiggler amplitude intensities, it can not only gain higher energy in longer distances, but also can retain it even after the passing of the laser pulse. In addition, the results reveal that the electron energy gains different peaks for different initial axial velocities, so that a suitable small initial axial velocity of e-beam produces substantially high energy gain. With regard to the transverse confinement of the electron beam in a Paul wiggler, there is no applied axial guide magnetic field in this device. (paper)