Scattering of electromagnetic waves by a cylindrical plasma in a steady magnetic field: I. Anisotropy effects

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Abstract
The experimental resonance pattern of a cylindrical plasma in a steady magnetic field is compared to theory. The scattering of a plane homogeneous wave by a cold plasma column with a glass wall is studied theoretically. The Poynting vector of this wave is perpendicular to the axis of the cylinder. The static magnetic field B0 is parallel either to the axis or to the Poynting vector S, or perpendicular to both the axis and S. The equilibrium density of the cold plasma is assumed constant in this paper and the anisotropy effects due to the homogeneous steady magnetic fields are studied through the equivalent tensorial permittivity. This permittivity is written in a general form so that the treatment also includes the anisotropie dielectric rod. When B0 lies in the cross-section of the cylinder, the partial differential equations cannot be solved in cylindrical co-ordinates. The solution is however obtained to second order in β (dimensionless parameter proportional to B0) in a Cartesian co-ordinate system and it is then transformed to a cylindrical system in which the boundary conditions are stated. It is found in most cases that the effect of B0 is much greater for the experimental phenomena than that predicted by the theoretical approach. This discrepancy arises from Laplace forces due to B0 in the cross-section and to the drift velocity of the electrons along the axis of the cylinder, and results in an inhomogeneity of magnetic origin studied in part II. This magnetically induced inhomogeneity accounts for the data not explained by the anisotropie approach. When B0 is parallel to the cylinder axis, the problem is solved exactly. The aforesaid Laplace forces do not intervene as B0 is then parallel to the drift velocity. The quantitative agreement is very satisfactory for relatively small values of B0 and poorer results for higher B0 are probably linked to non-proportionality between equilibrium electron density and the discharge current in the plasma column.