Abstract
The free electron laser instability for a solid relativistic electron beam propagating in combined transverse helical wiggler and uniform axial guide fields is investigated within the framework of the linearized Vlasov–Maxwell equations. It is assumed that ν/γb≪1, where ν is Budker’s parameter and γbmc2 is the electron energy. Stability properties are investigated for the choice of equilibrium distribution function in which all electrons have the same value of the linear combination of transverse and helical invariants, C⊥ −2γbmωbCh =const., and a Lorentzian distribution in the axial invariant Cz. (Here ωb is a constant.) The instability growth rate is calculated including a determination of the optimum value of the ratio of beam radius to conducting wall radius (R0/Rc) for maximum growth. It is found that the maximum growth rate for a solid electron beam is comparable to that for a hollow beam with similar parameters. Moreover, the introduction of a small axial momentum spread (Δ/γbmc≊ a few percent) significantly reduces the instability growth rate.
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