A linear growth rate fluid formulation for large orbit, annular electron layers with finite thickness

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Abstract
The macroscopic fluid equations are used to study the effect of beam thickness on the linear growth rates of a large orbit gyrotron. The chosen equilibrium models a rotating annular electron beam produced by a magnetic cusp. Two methods are used to calculate the growth rates. The analytic approach solves the problem to first order in the ratio of beam thickness to average beam radius and recovers the zero thickness limit. The numeric approach uses complete orthonormal systems comprised of the homogeneous wave equation solutions to calculate the growth rates for beams with arbitrary thicknesses. It is concluded that thick, tenuous beams in resonant systems must be operated near the cutoff of the electromagnetic wave. The decrease in growth rate as the wavelength decreases is attributed to the loss of synchronism in systems where the beam has a spread in its canonical angular momentum.