Since the electron cyclotron auto-resonance maser (CARM) is operated with the wave refractive index being very close to unity, a little variation of the refractive index in the CARM calculations might be crucial. Therefore, a modified self-consistent one-dimensional nonlinear model was developed by exactly setting the evolving wave refractive index and keeping all second-order terms to examine the inadequacy induced by the simplification of the earlier one-dimensional models. Comparisons of the numerical results obtained by the earlier models and the modified model for a CARM amplifier reveal that the inadequate relaxation of the limited azimuthal and axial bunching region for electrons to lose energy in the earlier models was the main reason for the overestimate of the linear gain and the saturated efficiency for the fast (the slow) wave branch with initial refractive index n0<1 (n0>1). However, the earlier model with fixed n0=1 is an excellent approximation whatever linear or saturated state is considered. The efficiency dependence of a CARM amplifier on some basic operating parameters was reexamined by the modified formulations.
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