Generalized Harris Sheet Equilibrium in Regularized Kappa Distributed Plasmas

Abstract

Harris sheet models with antiparallel magnetic field are the equilibrium solutions to the steady Vlasov–Maxwell equations, which have been widely adopted for the study of plasma instabilities and magnetic reconnection in thin current sheets. The original Harris equilibrium model assumes the Maxwellian velocity distribution, which necessarily gives rise to the isothermal current sheets. Many observations have shown that the suprathermal populations are indispensable features of particle distribution profiles, which may well be fitted by the Kappa distribution (KD) functions with the free parameter κ . The Harris equilibrium based on the standard Kappa distribution (SKD), however, may become unphysical for $\kappa \leqslant \displaystyle \frac{3}{2}$ . Alternatively, the regularized KD (RKD) with two adjustable parameters, κ and α ^2 , has been proposed to replace the SKD in various studies. The RKD may recover the SKD for α ^2 = 0, and Maxwellian model for α ^2 = 0 and κ → ∞ . This paper presents the first results of adopting the nonthermal RKDs in the Harris equilibrium models. It is shown that the new RKD–Harris equilibrium is applicable for all κ values, and exhibits a stronger magnetic field associated with higher temperature in the asymptotic region. The proposed formulations for the generalized Harris sheet equilibrium may be applied to multiple component plasmas (e.g., electrons, protons) with different RKDs and temperatures.

Keywords

• Plasma physics
• Plasma astrophysics
• Space plasmas
• Planetary magnetospheres