Propagation of electrostatic modes in strongly non-uniform helicon plasma

The propagation of electrostatic waves in the region of strong radial non-uniformity of a magnetized plasma column in the helicon frequency range is analyzed. The eigenfunctions and values of the modes are found for a Gaussian density profile analytically and numerically. It is demonstrated that the plasma density gradient perpendicular to the external magnetic field is essential for the propagation of non-axially symmetric (m≠0) waves. In the low-frequency limit, the modes scale as kz2 and depend on the sign of the azimuthal mode number m, thus revealing non-reciprocal behavior with respect to the azimuthal direction. In contrast, the symmetric mode (m=0), which is affected by the inhomogeneity of the plasma as well, exhibits linear dispersion. The possibility of radio-frequency power coupling and deposition through the excitation of m=+1 electrostatic modes is discussed.