In the present paper, it is argued that non-Maxwellian distribution functions are better suited to model space plasmas. A new model distribution function called the generalized (r,q) distribution function which is the generalized form of the generalized Lorentzian (kappa) distribution function has been employed to carry out theoretical investigation for parallel propagating waves in general and for Alfvén waves in particular. New plasma dispersion functions have been derived and their properties investigated. The new linear dispersion relation for Alfvén waves is investigated in detail.
Dust grains immersed in a plasma can exhibit charge fluctuations in response to the oscillatory plasma currents flowing onto them. The fluctuation electrodynamics of dusty plasmas are determined by taking into account the dynamics of charging processes associated with plasma currents. Expressions for the charging currents are derived using kappa and generalized (r, q) distribution functions. The dispersion relation of dust-acoustic waves is modified while taking into account these distribution functions. Further, it is found that in the limit (i) r = 0, q → ∞ and (ii) κ → ∞, the expressions of the current modified with (r, q) and kappa distributions reduce to the Maxwellian current.
In the present paper, comparison of characteristic shielding distance is determined by using a non-Maxwellian plasma. A modified version of the generalized Lorentzian distribution function, which is referred to as the (r, q) distribution, has been employed to derive the shielding distance with a modified power-law. The most surprising feature of a plasma containing superthermals is the strong dependence of plasma Debye length λD on spectral indices κ, r and q. It is observed that these spectral indices frustrate the Debye shielding distance. In the case of kappa, it is much smaller than that found for a Maxwellian plasma. We adopt the (r, q) distribution because it gives better data fit results, especially when there are shoulders in the profile of the distribution function along with a high-energy tail.
The Weibel instability in an unmagnetized plasma is investigated for non-Maxwellian distribution functions. In particular, analytical expressions are derived for the real and imaginary parts of the dielectric constant for the Maxwellian, kappa (κ), and (r,q) distribution functions under the conditions of ξ=ω∕k‖θ‖⪢1 and ⪡1. The real frequency and the growth rate of the instability now depend upon the values of the spectral indices of the distribution functions. In general, the growth rate is suppressed for small values of κ and q (keeping r fixed) and for negative values of r (keeping q fixed) instability transforms into damping. In the limiting cases (i) κ→∞ and (ii) r=0, q→∞, the results approach to the Maxwellian situation.
By using the full electromagnetic drift kinetic equations for electrons and ions, the general dispersion relation for geodesic acoustic modes (GAMs) is derived incorporating the electromagnetic effects. It is shown that m = 1 harmonic of the GAM mode has a finite electromagnetic component. The electromagnetic corrections appear for finite values of the radial wave numbers and modify the GAM frequency. The effects of plasma pressure βe, the safety factor q, and the temperature ratio τ on GAM dispersion are analyzed.
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