On the gravitational stratification of multi-fluid-multi-species plasma

TL;DR

The paper presents a method to construct gravitationally stratified MFMS plasmas that are simultaneously in ionization equilibrium and hydrostatic balance by enforcing collisional coupling in a static state and allowing SE or NEQ ionization inputs. It introduces a simple 1D numerical integration scheme to solve the hydrostatic balance with a stratified ionization state, yielding a coupled hydrostatic equilibrium (cHE) that accounts for multiple species and their pressure contributions. Through isothermal and SE/NEQ tests, the authors show that cHE stratifications remain near equilibrium and avoid the instabilities seen with independent pHE stratifications, while enabling physically meaningful drift between fluids in the transition region. The work demonstrates the Ebysus MFMS framework for constructing robust initial conditions and explores the impact of ponderomotive forcing, indicating that cHE stratifications support realistic multi-fluid dynamics and chemical fractionation, with potential applications to wave propagation, reconnection, and FIP-related phenomena.

Abstract

Context. The solar atmosphere is gravitationally stratified and consists of several layers at temperatures different by orders of magnitude. Consequently, the solar atmospheric plasma changes from weakly ionized in the photosphere, partially ionized in the chromosphere, to eventually fully ionized in the corona. However, it is still not trivial to integrate ionization and recombination processes into multi-fluid solar plasma models with gravitational stratification. Aims. We intend to provide a method for constructing multi-fluid-multi-species gravitational stratification that satisfies ionization equilibrium and hydrostatic equilibrium at the same time, avoiding causing non-physical disturbances and numerical instability due to initial in-equilibria. Methods. We assume that collisional interactions between fluids are sufficient for coupling all fluids when there is no high-frequency external driving force imposed. Ionization fractions can be (I) calculated assuming ionization in statistical equilibrium at any given temperature, or (II) extracted from other atmospheric models. A simple numerical integration routine is then designed and used to construct multi-fluid-multi-species gravitational stratifications. Results. A gravitational stratification constructed using the present numerical integration routine can be in hydrostatic equilibrium with any given ionization fractions of multi-species plasmas. Meanwhile, without any dynamic driving force, fluid decoupling appears in the transition region of the constructed stratification, while the total velocity of all fluids remains zero. Conclusions. A gravitational stratification constructed using the present routine can be used in multi-fluid-multi-species models to study specific dynamics without being affected by initial in-equilibria.

Figures (10)

• Figure 1: Density stratifications of hydrogen-helium isothermal mixtures. The solid lines are the cHE stratification and the dashed lines are the pHE stratification, both having the same ionization fractions at the reference height ($z=0$ Mm).
• Figure 2: The cHE stratification of a hydrogen-helium-iron-neon mixture under the Model C7 temperature distribution.
• Figure 3: A snapshot of a rMHD simulation with NEQ ionization. Top: density; middle: temperature; bottom: magnetic field strength. Loops and spicules are observed in the snapshot. These structures are dynamic but also relatively steady compared to, e.g., high-frequency waves that may be responsible for local heating or the FIP effect.
• Figure 4: Two cHE stratifications calculated based on the rMHD simulation snapshot. Left: ionization fractions are calculated assuming SE and using the averaged total density and temperature from the rMHD model; right: NEQ ionization fractions are directly given as the averaged ionization fractions from the rMHD model. A small value is used as the floor when calculating ionization fractions in SE, which is a practical treatment for simulations but serves here only for the convenience of visualization, without affecting our conclusions.
• Figure 5: Left: density distributions at $t=0$ s and $t=0.5$ s when using the cHE stratification as the initial condition for a simulation with NEQ ionization/recombination, but without any dynamic driving force; right: the pHE stratification (viz. at $t=0$ s). Using the pHE stratification as the initial condition leads to numerical instability in simulations with ionization/recombination, and thus the results are not included.