This paper is devoted to the theory of surface waves propagating across axis of symmetry in non-uniform cylindrical metal waveguides with plasma filling. The presented results are devoted to: first, studying an influence of plasma density non-uniformity on the features of these waves; second, studying an influence of an external magnetic fields' non-uniformity on their dispersion properties; third, studying possibility to sustain gas discharge by propagation of these waves under different operating regimes. The problems have been solved both analytically and numerically. Plasma particles are described in the framework of hydrodynamics; fields of the studied waves are determined by a set of Maxwell equations. Analytical research of the obtained equations is carried out by the method of successive approximation; adequacy of such approach is proved here as well. Numerical evaluations of the possibilities to observe experimentally the phenomena, which accompany propagation of these waves, are carried out.

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Using the model of uniform semi-bounded plasma, it is shown that the influence of an external alternating electric field in the range of electron cyclotron frequencies leads to excitation of eigen ordinary polarized waves at the first harmonic of electron cyclotron frequency. The external electric field was assumed to be uniform and monochromatic; electro-dynamical properties of the plasma were described by the kinetic Vlasov–Boltzmann equation in the approach of a weak spatial dispersion of plasma. Two components of these modes’ wave vector oriented across an external magnetic field are taken into consideration. Fields of these electron cyclotron O-modes are described by the Maxwell equations; their phase velocity is assumed to be less than the velocity of light. Nonlinear boundary condition-described discontinuity of the modes’ tangential magnetic field is formulated using the concept of a nonlinear surface electric current. The infinite set of equations for harmonics of these O-modes’ tangential electric field has been derived with the aid of this nonlinear boundary condition. It is solved using a wave packet consisting of the basic harmonic and two nearest satellite harmonics. A simple analytical expression for growth rates of these surface waves’ parametric instability is obtained; the influence of plasma parameters on their excitation is numerically analyzed.

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