Ion Bernstein waves in a plasma with a kappa velocity distribution

Abstract

Using a Vlasov-Poisson model, a numerical investigation of the dispersion relation for ion Bernstein waves in a kappa-distributed plasma has been carried out. The dispersion relation is found to depend significantly on the spectral index of the ions, κi, the parameter whose smallness is a measure of the departure from thermal equilibrium of the distribution function. Over all cyclotron harmonics, the typical Bernstein wave curves are shifted to higher wavenumbers (k) if κi is reduced. For waves whose frequency lies above the lower hybrid frequency, ωLH, an increasing excess of superthermal particles (decreasing κi) reduces the frequency, ωpeak, of the characteristic peak at which the group velocity vanishes, while the associated kpeak is increased. As the ratio of ion plasma to cyclotron frequency (ωpi/ωci) is increased, the fall-off of ω at large k is smaller for lower κi and curves are shifted towards larger wavenumbers. In the lower hybrid frequency band and harmonic bands above it, the frequency in a low-κi plasma spans only a part of the intraharmonic space, unlike the Maxwellian case, thus exhibiting considerably less coupling between adjacent bands for low κi. It is suggested that the presence of the ensuing stopbands may be a useful diagnostic for the velocity distribution characteristics. The model is applied to the Earth's plasma sheet boundary layer in which waves propagating perpendicularly to the ambient magnetic field at frequencies between harmonics of the ion cyclotron frequency are frequently observed.

One-dimensional particle-in-cell simulations of electrostatic Bernstein waves in plasmas with kappa velocity distributions

“…In particular, compared with Figure 8, Figure 9 shows a stronger tendency of the mode emanating from the lower hybrid frequency to "couple" to the mode immediately above it in the vicinity of the point (kk De $ 0.05, x/x ce $ 0.11). This coupling of the ion Bernstein modes is well known 3 and has been discussed recently in the context of the kappa theory by Nsengiyumva et al, 39 who pointed out its dependence on j i . Figure 10 illustrates the low frequency range of electric field fluctuation intensities for the Maxwellian plasma case.…”

“…Ion Bernstein waves in a plasma of kappa-distributed ions and electrons were recently investigated by Nsengiyumva et al 39 In that paper, the authors solved Equation (4) for a plasma of ions and electrons, each having a kappa distribution. Nsengiyumva et al 39 describe in detail how the parameters j i and j e affect the dispersion relation, and for that reason we give only a brief overview here.…”

“…Nsengiyumva et al 39 describe in detail how the parameters j i and j e affect the dispersion relation, and for that reason we give only a brief overview here. Figure 8 illustrates the electric field intensity, as a function of x and k, for the same simulation that was used to prepare Figure 3.…”

“…This paper presents the results of simulations of electrostatic Bernstein waves of both electron and ion types, where the electron and ion species are modelled by equilibrium (a) kappa and (b) Maxwellian velocity distributions. Results are compared with linear theory [36][37][38][39] for both the electron and ion cases.…”

Stimulated Raman scattering in nonextensive statistics

“…In recent years, a family of so-called kappa velocity distributions introduced by Vasyliunas [29] has been recognized to be appropriate for studying the nonequilibrium plasma systems [30][31][32][33][34][35][36][37]. It is important to mention that because of a lack of formal derivation, a nonextensive approach to kappa distributions has been suggested [38] and a reduced kappa distribution, which can be transformed into a nonextensive q-distribution by the expression κ = 1/(q − 1), has been obtained [39][40][41][42].…”