Propagation of guided modes in strongly non-uniform helicon-produced plasma

Abstract

Theoretical as well as numerical analysis of the full set of Maxwell's equations was carried out to study axisymmetric (m = 0) as well as non-axisymmetric (m ≠ 0) guided modes in a helicon discharge (radius R). In detail, the propagation of various guided modes for conditions of strong radial inhomogeneity was treated. The m = 1 helicon dispersion exhibits for kzR≪1 a quadratic frequency dependence on the axial wavenumber, ω∝kz2, if the radial density gradient is steep enough. These modes reveal non-reciprocal behavior with respect to the azimuthal (θ) direction, that is, only modes with positive azimuthal mode numbers, m > 0, can propagate. This is in contrast to the linear dispersion relation, ω∝kz (kzR≪1), for common helicon mode propagation in weakly non-uniform plasma. The results agree reasonably with those obtained from the 2nd-order helicon wave equation derived for Ez = 0. Furthermore, guided electrostatic (ES) modes were analyzed using the 2nd-order wave equation and their eigen mode spectrum wa...