Electron Bernstein waves in nonextensive statistics

The propagation of electron Bernstein waves in a magnetized plasma is investigated in the context of nonextensive q-distribution of Tsallis statistics. The dispersion relation is expressed as a function of generalized hypergeometric function. It is shown that the generalized dispersion relation significantly depends on the q-parameter, which quantifies the degree of nonextensivity of the system. The reduced number of superthermal particles shifts the Bernstein wave curves to higher wavenumbers. For harmonics whose frequency lies above the upper hybrid frequency, an increase in the value of q increases the maximum frequency and the wavenumber at which the group velocity vanishes. For Bernstein waves which propagate at frequencies lower than the upper hybrid frequency or close to it, diminishing q, or increasing the number of superthermal particles, gives rise to faster frequency fall-off. The generalized electron Bernstein waves are studied in both the strongly and weakly magnetized regimes and for both small and large wavenumbers compared with the Larmor radius. It is found that for the weak magnetic field, the frequency range occupied by the mode spans the complete intraharmonic frequency, and the q value significantly affects the dispersion curves. On the other hand, in strongly magnetized regimes the frequency variation domain is extremely restricted and has little dependence on the q value.