On the Anti-Resonance Effect in the Reversed Field Free Electron Laser

(WE-3-18)

J. T. Donohue, J. L. Rullier  

Centre d'Etudes Nucl$\acute{e}$aires de Bordeaux-Gradignan,CEA/Centre d'Etudes Scientifiques et Techniques d'Aquitaine

In their well-known reversed field experiment, Conde and Bekefi [1] observed a dramatic decrease in r-f power output when the anti-resonance condition was satisfied, i.e., cyclotron frequency =-Fel frequency. They further noticed that even with no injected r-f signal, beam transmission also fell at the anti-resonance. We show that the true cause of the observed orbital instability is not the anti-resonance, but rather the fact that the two independent oscillations about the ideal helical trajectory have frequencies in the ratio of 2:-1. That this would be a source of trouble was pointed out by Cherry in 1924, and a cautionary example is given in Whittaker's treatise [2]. Int the Conde-Bekefi experiment, the condition for anti-resonance coincided with the 2:-1 ratio. By choosing wiggler parameters such that these two distinct effects are dissociated, we demonstrate convincingly that the 2:-1 condition causes the instabilily, and that a generalized version of Cherry's model provides an adequate analytic description of our numerical results.

[1] M. E. Conde and G. Bekefi, Phys. Rev. Lett. 67 (1992), 3082.

[2] E. T. Whittaker, A Treatise on the Analytic Dynamics of Particles and Rigid Bodies, Cambridge Unive. Press, Cambridge, 1960).