Dispersion curves for the generalized Bernstein modes

Abstract

Dispersion curves are plotted for the extraordinary branch of the electron- and ion-cyclotron harmonic waves propagating perpendicularly to the static magnetic field in a non-relativistic, hot Maxwellian plasma, without invoking the electrostatic approximation. It is found that, except in the vicinity of the cyclotron harmonics and the hybrid resonances, either the cold-plasma or the electrostatic approximation are accurate representations of the exact solution. The hybrid resonances of the cold-plasma model become monotonically shrinking regions of low group velocity as the temperature is increased, till all discernible evidence of these resonances disappears as the parameters corresponding to the thermonuclear plasmas are approached.

Ion Bernstein waves in a plasma with a kappa velocity distribution

“…The fact that their frequency structure is governed by the ion gyrofrequency and its harmonics and that they propagate perpendicularly to the magnetic field make the ion Bernstein 5 wave a strong candidate for the production of these waves. Ion Bernstein waves have been the subject of several theoretical studies, both within the context of space [6][7][8] and laboratory 5,9,10 plasmas. Most of these studies have relied on the Maxwellian distribution to provide the equilibrium plasma state.…”

“…The Bernstein waves that propagate under such conditions are often referred to as generalised Bernstein waves. He found that the full electromagnetic dispersion relation asymptotically approaches the electrostatic approximation at large values of k. Puri et al 9 obtained the dispersion curves for the generalised ion Bernstein waves in a Maxwellian plasma, and found that the waves are predominantly electrostatic and that they exhibit an electromagnetic character only where the phase velocity becomes superluminal, i.e., where k ! 0, in agreement with the earlier findings of Fredricks.…”

“…6,7,9 However, this is not necessarily true if the plasma has a different velocity (energy) distribution. For instance, Tataronis and Crawford 10 considered perpendicularly propagating electron cyclotron harmonic waves in a plasma whose electrons had, inter alia, a ring distribution, a spherical shell distribution and a mixed ring-Maxwellian distribution.…”

Maser-beam instability of Bernstein waves

“…[23][24][25] However, in the present case such effects on the real part of the dispersion relation are insignificant. Thus we will follow the traditional nonrelativistic approach 5,6 and adopt Eq. ͑3͒, whereas relativistic effects are necessary for the discussion of the growth rate ͓see Eq.…”

“…2, 5,6 An important point is that there exist numerous ''windows'' at gyroharmonic frequencies via which Bernstein waves can be converted to fast (X) mode. Such a conversion is likely to be a natural consequence of a plasma immersed in a nonuniform magnetic field.…”