Numerical investigations and analysis on the effects of geometrical parameters on the group velocity of transverse magnetic pump mode and free electron laser instability

In this paper, we have numerically investigated the effects of various geometrical parameters of a backward wave oscillator, filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate R0 of a seeded free electron laser. On changing mean radius corrugation amplitude h and corrugation period z0 of backward wave oscillator; the ponderomotive potential of space charge wave changes. This in turn, changes the coupling strength of TM mode with negative beam space charge mode and hence the growth rate of parametric instability of free electron laser. A dispersion relation is derived and numerically solved for various geometrical parameters of backward wave oscillator and beam profile. A relation for Γ is also derived and computed numerically. The instability growth scales directly to the square root of beam density and inversely as seven power of relativistic gamma factor γ0.