The gain of a free-electron laser may be multiplied by a very large factor when a uniform magnetic field B₀ is superimposed on the extant helical field. The effect is due to cyclotron resonance and requires B₀=10.6l(1-v_∥²c²)1/2 kG, where l is the period of the helical field and v_∥ is the streaming-electron velocity.
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Sprangle et al. (1978) studied this question.
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