Diamagnetic and Paramagnetic Effects in Free-Electron Lasers

The effect of high-current relativistic electron beams (REB´s) on the undulator field amplitude in free-electron lasers (FEL´s) is investigated. Two mechanisms of excitation of periodic magnetostatic self-fields by REB are considered: 1) a static mechanism that is realized at stationary motion of REB in the undulator field; and 2) a dynamic mechanism that is realized at signal wave amplification. The static mechanism in the absence of an axial magnetic field leads to a decrease of the total undulator field amplitude (a diamagnetic effect). The dynamic mechanism for low-density beams leads to an increase of the total undulator field amplitude (a paramagnetic effect), with a subsequent increase of electron efficiency. For high-density beams, the effect of the phase shift of the total undulator field is most essential, due to which the growth of the signal wave amplitude is limited by nonlinear mismatch of synchronism.