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An external alternating electric field in the range of ion–cyclotron frequencies is shown to excite extraordinary polarized surface electromagnetic waves at the second harmonic of ion–cyclotron frequencies. The kinetic model of a uniform semi-bounded plasma is applied. Plasma electrodynamical properties are described by using the Vlasov–Boltzmann kinetic equation in the approach of weak spatial plasma dispersion. Two components of these modes’ wave vector, which are oriented across an external steady magnetic field, are taken into account. Fields of these ion–cyclotron modes are described by Maxwell equations. Their phase velocity is assumed to be much lower than light velocity. The external alternating electric field is assumed to be uniform and monochromatic. The nonlinear boundary condition is formulated for the tangential magnetic field of the studied surface waves (SW). An infinite set of equations is derived for the values of tangential electric field harmonics on the plasma interface. This set is solved using the approach to the wave packet consisting of the main harmonic and two nearest satellite harmonics. Simple analytical expressions for the growth rates of parametric instability of these SW are derived. The influence of plasma parameters on their parametric excitation is numerically analyzed.

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Abstract-Excitation of extraordinarily polarized azimuthal eigen modes by modulated annular electron beam is shown to be characterized by the increase of instability growth rates compared with the case of non-modulated electron beam. Interaction between the modulated beam and azimuthal eigen modes happens in the range of electron cyclotron frequency in waveguides with metal walls, which are partially filled with cold magneto-active plasma. Nonlinear set of differential equations, which describs excitation of these azimuthal modes by an annular electron beam is derived and analyzed numerically. Different scenarios of the beam-plasma interaction depending on relation between azimuthal mode number of the exited waves and periodicity of azimuthal modulation of the beam density, degree and manner of the beams' modulation are studied numerically.

The application of an external alternating electric field in the range of ion cyclotron frequencies is a well-known method for the excitation of surface electromagnetic waves. The present paper is devoted to the development of a kinetic theory of parametric excitation of these eigenwaves propagating across an external steady magnetic field along the plasma boundary at the second harmonic of the ion cyclotron frequency. Unlike previous papers on this subject, parametric excitation of surface ion cyclotron X-modes is studied here under the condition of non-monochromaticity of an external alternating electric field. Non-monochromaticity of the external alternating electric field is modeled by the superposition of two uniform and monochromatic electric fields with different amplitudes and frequencies. The nonlinear boundary condition is formulated for a tangential magnetic field of the studied surface waves. An infinite set of equations for the harmonics of a tangential electric field is solved using the approximation of the wave packet consisting of the main harmonic and two nearest satellite harmonics. Two different regimes of instability have been considered. If one of the applied generators has an operation frequency that is close to the ion cyclotron frequency, then changing the amplitude of the second generator allows one to enhance the growth rate of the parametric instability or to diminish it. But if the operation frequencies of the both generators are not close to the ion cyclotron frequency, then changing the amplitudes of their fields allows one to decrease the growth rate of the instability and even to suppress its development. The problem is studied both analytically and numerically.