Electrostatic waves in a magnetized plasma with nonextensive distribution

The generalized dispersion relation for warm electrostatic waves in magnetized plasmas is derived in the context of the nonextensive q-distribution of Tsallis statistics. The dispersion relation is expressed as a function of different values of the nonextensive parameter q, which quantifies the degree of nonextensivity of the system. The dispersion relation of cold plasma electrostatic waves is obtained in terms of generalized hypergeometric functions by keeping the lowest order thermal terms. It is shown that Landau damping appears both at the wave frequency and also at cyclotron harmonics and depends on the q-parameter. The combination of warm plasma effects and a magnetic field leads to the existence of Bernstein waves in nonextensive plasmas. In general, the nonextensive distribution significantly alters the dispersion relation for Bernstein waves. For a wave with a frequency close to the upper hybrid frequency, diminishing q gives rise to faster frequency fall-off. Bernstein waves which propagate at frequencies higher than the upper hybrid frequency occupy a decreasing range of frequencies above nearest cyclotron harmonics as q is reduced. In the limit q→1, the warm and cold magnetized plasma electrostatic dispersion relation and also Bernstein dispersion are recovered based on the standard Maxwellian distribution.