Gas Discharge Sustained by Potential Surface Waves in Magnetized Waveguide Structure Filled by Radially Non–Uniform Plasma

The report presents the results of theoretical investigation of axial structure of gas discharge that is sustained by the travelling slightly–attenuating potential surface wave (SW) in diffusion gas–discharge regime. Plasma density axial distribution along the discharge was studied in the framework of electrodynamic approach [1,2] and the main attention was devoted to the phase properties of the SW that sustains the discharge. The SW considered propagates along radially non–uniform plasma column with radius pR that is bounded by the glass tube with permittivity dε and outer radius gR. This tube is surrounded by the vacuum region and is enclosed by the waveguide metal wall with radius mR. External steady magnetic field 0B is directed along the axis of the waveguide system. Plasma is considered in hydrodynamic approximation as cold and slightly absorbing medium with the effective collisional frequency of momentum transfer ν, that much less than generator frequency ω and is constant in the whole discharge volume. Radial profile of electron density ()rn was chosen in the Bessel–like form, given by ( ) ( ) ()100 −µ = prRJnrn, where)0(n is plasma density value on the axis of the discharge structure, oJ – Bessel function of the zero order, µ is non–unifomity parameter. Such choice of a radial density profile allows one to model different discharge regimes with the help of changing nonuniformity parameter µ. The propagation of the nonsymetric potential SW along the discharge structure is governed by the Poisson equation. Let us consider the case when plasma density, SW amplitude and wavelength vary slightly along the discharge column at the distances of wavelength order. Then the solution of the Poisson equation for the wave potential Ψ in the cylindrical coordinate system ()z,,r ϕ can be found in WKB form [3] and the equation itself can be written in the following local form: 0