Upper hybrid wave pumped free electron laser

A large amplitude upper hybrid wave has potential to be employed as a wiggler for the generation of high frequency coherent radiation via free electron laser (EEL) instability. At a density fluctuation level of a few percent, due to the upper hybrid wave, the growth time of FEL instability, with electron beam current of a few kilo ampere, turns out to be of the order of a nanosecond. The growth rate of FEL instability depends sensitively on ω₁ and this dependence comes through ν_osc the beam oscillatory velocity. ν_osc acquires large values at k_0z≃[ω₀-(ω_e/γ ₀⁰)]ν_b≃ω_c [1-(1/γ₀⁰)]ν_b. At this value of k_0z,ω≃2γ₀⁰²ω _c[2-(1/γ₀⁰)]. However, this scheme of FEL operation suffers from a severe limitation due to the parametric instability of the upper hybrid wave. The process of parametric decay into lower hybrid and upper hybrid waves may have growth rate comparable to that of the FEL instability