Modeling the thermal conduction in the solar atmosphere with the code MANCHA3D

Abstract

Context. Thermal conductivity is one of the important mechanisms of heat transfer in the solar corona. Within the limit of strongly magnetized plasma, it is typically modeled by Spitzer's expression, where the heat flux is aligned with the magnetic field. Aims. This paper describes the implementation of heat conduction into the MANCHA3D code, with an aim of extending single-fluid magnetohydrodynamic (MHD) simulations from the upper convection zone into the solar corona. Methods. Two different schemes for modeling heat conduction are implemented in this work: (1) a standard scheme where a parabolic term is added to the energy equation and (2) a scheme where the hyperbolic heat flux equation is solved. Results. The first scheme limits the time step due to the explicit integration of a parabolic term, which makes the simulations computationally expensive. The second scheme solves the limitations on the time step by artificially limiting the heat conduction speed to computationally manageable values. The validation of both schemes was carried out with standard tests in one, two, and three spatial dimensions. Furthermore, we implemented the model for heat flux derived by Braginskii (1965) in its most general form, where the expression for the heat flux depends on the ratio of the collisional to cyclotron frequencies of the plasma and, therefore, on the magnetic field strength. Additionally, our implementation takes into account the heat conduction in parallel, perpendicular, and transverse directions, and provides the contributions from ions and electrons separately. The model recovers Spitzer's expression for parallel thermal conductivity within the strongly magnetized limit but also transitions smoothly between field-aligned conductivity and isotropic conductivity for regions with a low or null magnetic field. We describe the details of the implementation of Braginskii's thermal conductivity using a combination of the first scheme for the perpendicular and transverse directions and the second scheme for the parallel component. Furthermore, we estimated the thermal conductivities in a quiet-Sun model. In this model, we find that the perpendicular and transverse components for electrons and ions and the parallel component for ions might have some significance below the transition region. Above the transition region only the parallel component for ions might be important. Finally, we present a 2D test for heat conduction using realistic values of the solar atmosphere where we prove the robustness of the two schemes implemented and show that our adaptation of the hyperbolic treatment offers a great advantage over the computational cost of the simulations.

Two-fluid numerical model of chromospheric heating and plasma outflows in a quiet-Sun

“…This dissipation leads to local heating of the background chromosphere. In comparison to the previous study by Martínez-Sykora et al (2017), Fleck et al (2021), Snow &Hillier (2021), andNavarro et al (2022), who adopted complex non-adiabatic MHD models, for a partiallyionized plasma, and Wójcik et al (2020) and Murawski et al (2020), who used a two-fluid numerical model including radiation, our results show that taking into account radiation, anisotropic thermal conduction, magnetic diffusivity, viscosity, ionization and recombination (Ballester et al 2018) leads to a solar atmosphere with a vertical temperature profile that resembles the semi-empirical data of Avrett & Loeser (2008). There were also attempts to assess the efficiency or feasibility of heating by waves by comparing the wave flux with the radiative loses.…”

Future prospects for partially ionized solar plasmas: the prominence case

“…It is clear from these works that it is necessary to go further, into the nonlinear regime and non-uniform plasmas with more complex models. For instance, significant progress has been achieved in this direction with the implementation of the full conductivity tensor in the MANCHA3D code [42,43] but only for fully ionized plasmas. In its two-fluid version, MANCHA3D-2F, only neutral conductivity is included [39][40][41].…”

MPI-AMRVAC 3.0: Updates to an open-source simulation framework

“…Both FLD and M1 radiative-(M)HD formulations have the distinct advantage that they in essence translate to fully hyperbolic PDE systems (with source term couplings), and this is readily adjustable to any framework, such as MPI-AMRVAC. Of course, in solar physics contexts, current state-of-the-art (non-AMR) codes such as Stagger (as used in Stein & Nordlund 2006), Bifrost (Gudiksen et al 2011;Nóbrega-Siverio et al 2020), MURaM (Vögler et al 2005), MANCHA3D (Khomenko et al 2018Navarro et al 2022), RAMENS (Iijima & Yokoyama 2017), and CO5BOLD (Freytag et al 2012) focus on 3D radiative-MHD simulations that include magneto-convection in optically thick sub-photospheric layers, use optically thin prescriptions for the corona, and have a more sophisticated treatment of the radiative effects known to be important in solar chromospheric layers. This includes handling partial ionization effects through MHD with ambipolar diffusion or two-fluid plasma-neutral modeling, as implemented in MPI-AMRVAC 3.0 (Popescu Braileanu & Keppens 2021.…”