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A linear theory based on Maxwell-Vlasov equations and the Laplace transform is presented to describe the large-orbit coaxial-waveguide cyclotron autoresonance maser (CARM) amplifier. A 35-GHz, TE5,1-mode large-orbit coaxial-waveguide CARM amplifier is specifically analyzed. Good agreement between the linear theory and the nonlinear simulations is found in the exponentially growing region of the wave...