Nonlocal theory of a whistler pumped free electron laser

A cylindrical waveguide loaded with a magnetized plasma supports a short wavelength whistler mode. In the presence of a relativistic electron beam the whistler mode couples to a negative energy beam mode and a high-frequency electromagnetic mode giving coherent radiation. A nonlocal theory of the process reveals that larger beam cross section is preferable for better coupling. The phase matching conditions give the frequency of operation as ω1=(ck0z/η0)[(η0-η)/(η-η1)] where ω1 is the frequency of the free electron laser radiation, k0z is the wave number of the pump wave, c is the velocity of light in free space, and ηj=ckj/ωj, ηj=η0, η1, η correspond to the pump, radiation signal, and the beam mode, respectively. The frequency of radiation is maximum when it propagates in the transverse magnetic TM01 mode. As the frequency of the whistler approaches electron cyclotron frequency, the frequency of radiation is enhanced while the growth time also increases. The growth time scales as γ9/20k3/20zω1/2 [ω2c-γ20(ω0-k0zvb)2]1/2 /(ω2pbω1/21)