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In this paper we numerically investigate the effects of various geometrical parameters of a backward wave oscillator (BWO), filled with a magnetized plasma of uniform density and driven by a mild relativistic solid electron beam, on the instability growth rate (Γ) of a free electron laser (FEL). The FEL instability is numerically calculated and the result is compared with the instability growth rate of an annular electron beam for the same set of parameters. The instability growth for a solid electron beam scales inversely to the seventh power of relativistic gamma factor γ0 and directly proportional to the corrugation amplitude.

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A non-local theory is used to study the effects of the corrugation parameter ε of a plasma-filled slow wave structure, the cyclotron frequency of a pumped magnetic field Ω and the relativistic gamma factor γ0 on the instability growth Γ of a free electron laser in the presence of an external finite axial magnetic field. The dispersion relation is derived and the growth rate is formulated in the Raman regime. The growth rate is approximately proportional to ε. There is a considerable decrease in the instability growth when the cyclotron frequency is close to ω0. The growth rate approximately scales inversely as the 19/2 power of the relativistic gamma factor.

A mathematical model for salt transport by a cylindrical root in an infinite extent of soil is derived and solved analytically by asymptotic matching of the inner and outer solutions. By asymptotic analysis it is shown that the salt solution uptake by a single cylindrical root in the absence of competition does not influence the overall salt concentration in the soil even when the soil moisture concentration is less than full saturation.

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