Consistent transport properties in multicomponent two-temperature magnetized plasmas

Application to the Sun atmosphere

¹ Centre de Mathématiques Appliquées, Ecole Polytechnique, CNRS, Palaiseau, France
e-mail: quentin.wargnier@polytechnique.edu
² Laboratoire de Physique des Plasmas, Ecole polytechnique, CNRS, Palaiseau, France
³ Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Rhode-Saint-Genèse, Belgium
⁴ NASA Ames Research Center, Moffett Field, CA, USA

Received: 19 November 2018
Accepted: 25 December 2019

Abstract

Aims. We present a fluid model that has been developed for multicomponent two-temperature magnetized plasmas in chemical non-equilibrium for the partially to fully ionized collisional regimes. We focus on transport phenomena with the aim of representing the atmosphere of the Sun.

Methods. This study is based on an asymptotic fluid model for multicomponent plasmas derived from kinetic theory, yielding a rigorous description of the dissipative effects. The governing equations and consistent transport properties are obtained using a multiscale Chapman-Enskog perturbative solution to the Boltzmann equation based on a dimensional analysis. The mass disparity between free electrons and heavy particles is accounted for, as well as the influence of the electromagnetic field. We couple this model to the Maxwell equations for the electromagnetic field and derive the generalized Ohm’s law for multicomponent plasmas. The model inherits a well-identified mathematical structure leading to an extended range of validity for the Sun’s atmospheric conditions. We compute consistent transport properties by means of a spectral Galerkin method using the Laguerre-Sonine polynomial approximation. Two non-vanishing polynomial terms are used when deriving the transport systems for electrons, whereas only one term is retained for heavy particles.

Results. In a simplified framework where the plasma is fully ionized, we compare the transport properties for the lower solar atmosphere to conventional expressions for magnetized plasmas attributed to Braginskii, showing a good agreement between both results. For more general partially ionized conditions, representative of the lower solar atmosphere, we compute the muticomponent transport properties corresponding to the species diffusion velocities, heavy-particle and electron heat fluxes, and viscous stress tensor of the model for a helium-hydrogen mixture in local thermodynamic equilibrium. The model is assessed for the 3D radiative magnetohydrodynamic simulation of a pore at the Sun photosphere. The resistive term is found to dominate mainly the dynamics of the electric field at the pore location. The battery term for heavy particles appears to be higher at the pore location and at some intergranulation boundaries.