High-frequency electrostatic waves in an inhomogeneous magnetized plasma

The paper investigates the propagation of HF electrostatic waves through an inhomogeneous plasma pervaded by uniform axial and variable azimuthal magnetic fields. A dispersion relation is obtained for nonaxisymmetric perturbations in an infinite cylinder in which the plasma density has a parabolic profile. Boundary conditions are determined for perfectly conducting as well as vacuum boundaries, the eigenvalue problem for both types of boundaries is solved numerically for nonzero azimuthal mode numbers, and the solutions are compared with the results of Lashmore-Davies (1969). An analytical solution to the eigenvalue problem is found for only one special case characterized by uniform density and zero wavenumber. The numerical results show that the presence of an azimuthal magnetic field allows nondegenerate azimuthal waves to exist for negative azimuthal mode numbers and that azimuthal waves will exist in a uniform plasma with a perfectly conducting boundary.