Abstract
The linear theory of axial injection orbitron maser (AXIOM) oscillators is formulated analytically for circular electron orbits using the relativistic Vlasov equation and Maxwell’s equations. The theory treats transverse electric (TE) or transverse magnetic (TM) modes with sinusoidal axial field profiles. Owing to the simplicity of modeling circular electron orbits the theory is fully relativistic. The power transferred from the electron beam to the cavity fields is calculated in terms of a general distribution function and the cavity parameters. A cold beam distribution function is used to evaluate the theory. The results of the theory are presented in terms of the threshold value of the cavity Q times the electron beam current required for self-oscillation. The results show that TE modes with small azimuthal mode numbers have the strongest interaction and that modes with large azimuthal mode numbers resonate at lower electrostatic fields but require larger electron beam currents for self-oscillation.
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