A Three Dimensional Calculation of Electron Energy Loss in a Variable Parameter Free-Electron Laser

Abstract

A single-pass free-electron laser (FEL) using a wiggler magnet with either the period, and/or the magnetic field, varying along the magnet axis has been proposed. The main advantage of this system over a conventional free-electron laser, having a constant period and magnetic field wiggler, is in the higher efficiency of the energy transfer from the electron beam to the laser radiation field. This efficiency, which is of the order of 1% in a conventional FEL, can be of the order of 30% in a variable wiggler FEL. The theory of the variable wiggler FEL is based on a one dimensional model, in which the electron motion transverse to the laser axis is assumed to be given and only the motion parallel to the axis is studied. In this paper, the effect on the laser efficiency of the electron transverse motion is studied and the electron energy loss is evaluated for a beam having a spread in angle and in the transverse position at the wiggler entrance. The complete three dimensional equations of motion for an electron interacting with the laser field and the wiggler field are integrated numerically. Only the case of a small gain regime, assuming that the laser field intensity remains constant, is considered. Also, this study is limited to the case of a helical wiggler. The results are compared with the one dimensional model. The effect of the initial position and angular spread can, to a good approximation, be considered equivalent to an increase in the energy spread. The limits for this increased energy spread that must not be exceeded in order to avoid a loss in efficiency are nearly the same as in the one dimensional model.