On the anti-resonance effect in the reversed field free electron laser

In their reversed field experiment, Conde and Bekefi observed a dramatic decrease in RF power output when the anti-resonance condition was satisfied, i.e., cyclotron frequency =−FEL frequency. They further noticed that even with no injected RF signal, beam transmission also fell at the anti-resonance. We show here 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 whose ratio is −2. That this would be a source of trouble was pointed out by Cherry in 1925. In the Conde-Bekefi experiment, the condition for anti-resonance coincided with the 2 : −1 ratio. By choosing wiggler parameters such that the two effects are dissociated, we demonstrate convincingly that the 2 : −1 condition causes the instability, and that a generalized version of Cherry's model provides an adequate analytic description of our numerical results.