The linear growth rate of an electron cyclotron autoresonance maser (CARM) with a phase filter, constructed by imposing a transverse magnetostatic wiggler, is derived from relativistic kinetic theory. The theoretical results confirm previous findings from computer simulation showing substantial enhancement of the growth rate near the autoresonance condition. This theory provides an additional, more readily accessible tool for designing a novel phase filter-assisted CARM. The mathematical formalism developed to treat the complex electron motion in this device is introduced.
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