Linear and non-linear theory of the Doppler-shifted cyclotron resonance maser based on TE and TM waveguide modes

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Abstract
This paper presents a comprehensive theory of the cyclotron resonance maser (CRM) interaction in a circular waveguide. The kinetic theory is used to derive the dispersion relationships for both TE and TM modes. The TE mode case has been investigated by several authors, but there has been comparatively little work on the TM mode case. However, the TM mode interaction competes effectively with the TE mode interaction at relativistic electron energies. The conditions for maximum temporal and spatial growth rates are shown. The TM mode growth rates are found to vanish when the RF wave group velocity equals the beam axial velocity (‘grazing incidence’). The single particle theory is used to derive a compact set of self-consistent non-linear equations for the TE and TM mode interactions. These equations are particularly appropriate for the cyclotron auto-resonance maser (CARM) regime but applicability extends to other regimes as well. The conditions for optimum efficiency are investigated for oscillator and amplifier configurations at the fundamental and low order harmonic interactions. In the case of a beam with delta function distributions in position and momentum the single particle results in the small signal limit are shown to be equivalent to the kinetic theory results. Design parameters are given for a high power amplifier and oscillator.

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