Abstract
A gyrating relativistic electron beam supports negative energy modes near the harmonics of the electron cyclotron frequency. An electromagnetic wave passing through such a beam parametrically up-converts into high frequency electromagnetic radiation, producing a beam cyclotron mode. In the case when pump frequency ω0 is away from the harmonics of cyclotron frequency, ω≠lωc/γ0 and ω≫ωc/γ0, the beam response to the pump and sideband waves is obtained by the fluid theory whereas the response at the beam cyclotron mode is kinetic. In the case when ω0∼lωc/γ0 the beam response to all three interacting waves is taken to be fully kinetic. It is seen that the normalized growth rate decreases as ω0−ωc/γ0 increases for Raman as well as Compton regimes of operation.
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