Quasi-linear approach to the propagation of Bernstein waves in an inhomogeneous plasma

The quasi-linear equations describing the resonant evolution of a weakly inhomogeneous plasma slab under the action of Bernstein modes resulting from linear conversion of an externally injected extraordinary wave are obtained, together with a tractable form of the pertinent dispersion relation. The coefficients of electron diffusion in velocity space are computed, and their effect is compared to the effect of Coulomb collisions.