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

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 ∝ kzz, 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 2ndorder 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 was obtained. These modes reveal also non-reciprocal behavior with respect to θ and obey a quadratic dispersion law in strongly non-uniform plasma. A particular objective is mode coupling (MC) occurring when the helicon and the ES dispersion branches merge in a certain layer. For m=1 modes, mode coupling may arise at rather low density when the radial density gradient is steep enough. In any case, new modes, denoted as localized-coupled (LC) modes, may occur in the presence of an MC layer within the plasma. As for helicon and ES modes, the m=1 LC modes exhibit quadratic scaling in strongly non-uniform plasma. As a particular case, we examined the propagation of m=1 modes in a plasma column with a peaked density distribution in the center. The field distribution was found to be drastically altered due to mode coupling, thus leading to strongly enhanced wave absorption near the axis. [ABSTRACT FROM AUTHOR]