Wave interaction in gyrotrons with off-axis electron beams

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The effect of displacement of an annular electron beam with respect to the resonator axis on gyrotron operation is studied. The coupling between co- and counter-rotating TEm,p waves caused by eccentricity is analyzed both in the linear and nonlinear regimes. Nonlinear regimes are studied first in the quasilinear approximation, when the dependence of the electron gain functions on the field amplitude is described by a polynomial approximation. This makes it possible to study analytically some nonlinear effects caused by eccentricity. Then a self-consistent set of equations is studied numerically in the case of the MIT gyrotron [Blank et al., IEEE Trans. Plasma Sci. PS-22, 883 (1994)] operating in the TE16,2 mode at the fundamental cyclotron harmonic, where such effects have been studied experimentally, and of a gyrotron operating in the TE1,2 mode at the second harmonic.