A simplified Vlasov–Landau treatment of electron motion in the orbitron maser

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Abstract
An electron ring trapped in a logarithmic potential well (orbitron) is studied. The electrons in the ring possess a spread in angular velocity. A forward traveling-wave line is used to simulate a cavity resonator. For a Maxwellian, or monotonically increasing electron distribution function with increasing orbital frequency, sinusoidal perturbations are damped. For an inverted energy distribution, they grow. The growth rate at harmonics of the orbital frequency increases linearly with harmonic number.