Eigenmode dispersion relations in radially inhomogeneous helicon plasmas

The eigenmode dispersion relation is studied for a helicon plasma whose density varies in the radial direction. It is found that eigenmodes are strongly excited in a weakly collisional plasma when the dispersion relation obtained neglecting electron inertia is approximately satisfied and their orders vary as the magnetic field does for m=+1 (m is the azimuthal mode number) whether the density is uniform or not. But the inhomogeneity yields different results for m=-1. For sufficiently steep density profiles, the radial eigenmode of the lowest order is most strongly excited regardless of the magnetic field and a much higher density is required for m=-1 than m=+1 at a given magnetic field.