Turbulent Gravito-Electrostatic Sheath (GES) Structure with Kappa-Distributed Electrons for Solar Plasma Characterization

Abstract

We report on new characteristic features of the plasma-based gravito-electrostatic sheath (GES) model for solar plasma equilibrium characterization through nonthermal ($\kappa$-distributed) electrons composed of both a thermal halo (low-speed) and a suprathermal (high-speed) energy tail. The constituent ions are treated collectively as inertial species. The presence of intrinsic fluid turbulence is included with the help of a proper logatropic equation of state in the ionic momentum conservation law. The analysis is based on the basic physics of space-charge polarization effects, collectively evolving as a plasma sheath, but previously known only for laboratory plasma-scales. We show that the radial location of the solar surface boundary (SSB, inner boundary, diffused), formed by the counteracting GES force balancing, becomes slightly enhanced (by 0.5 on the Jeans scale). The net electric current densities, in both the solar interior and exterior, confirm the universal law of total charge conservation in the presence of geometrical curvature effects. The relevant properties of the new $\kappa$-modified equilibrium GES structure are numerically illustrated and discussed. The results are finally compared in the light of existing reports based on the Maxwell–Boltzmann electron distribution. The new outcomes can be extensively expanded to analyze the realistic thermostatistical dynamics of the Sun and its ambient atmosphere, as predicted earlier from various space-based observations.

Appendix A: Derivation of the \(\kappa\)-Distribution Law for Electrons

The Lorentzian $\kappa$-distributed population density distribution for plasma electrons with all the customary notational symbols [Equation 4 in Baluku and Hellberg 2008] is well known, the expression for which in the customary form is given as

$$ n_{\mathrm{e}}(\phi) = n_{0} \biggl( 1 - \frac{2e\phi}{m_{\mathrm{e}} \kappa V_{\kappa \mathrm{e}}^{2}} \biggr) ^{-\kappa+ 1/2}. $$

(11)

Here, for instant reference in addition to that given in the text, $n_{\mathrm{e}}$ is the electron population density, $n_{0}$ the equilibrium plasma population density, $e$ the electronic charge, $m_{\mathrm{e}}$ the electron mass, and $\kappa$ the thermostatistical spectral index. Furthermore, $V_{\kappa \mathrm{e}}$ is the thermostatistically modified electron thermal speed, given by $V_{\kappa \mathrm{e}}= [ (\kappa- 3/2)/\kappa ] ^{1/2} v_{\mathrm{th}}$, where $v_{\mathrm{th}} = (2k_{\mathrm{B}} T_{0}/m_{\mathrm{e}})^{1/2}$ is the usual electron thermal speed. We now introduce the normalized symbols as $N = n_{\mathrm{e}}/n_{0}$, $\theta= e\phi /k_{\mathrm{B}} T_{0}$. After simplification, Equation 11 finally reduces to

$$ N = \biggl( 1 - \frac{\theta}{\kappa-3/2} \biggr) ^{-\kappa+1/2}. $$

(12)

Equation 12 describes the real thermostatistical behavior of the plasma electrons, as has been explained in the main text, in the Sun and its atmosphere.