Efficient Numerical Treatment of Ambipolar and Hall Drift as Hyperbolic System

Partially ionized plasmas, such as the solar chromosphere, require a generalized Ohm’s law including the effects of ambipolar and Hall drift. While both describe transport processes that arise from the multifluid equations and are therefore of hyperbolic nature, they are often incorporated in models as a diffusive, i.e., parabolic process. While the formulation as such is easy to include in standard MHD models, the resulting diffusive time-step constraints do require often a computationally more expensive implicit treatment or super-time-stepping approaches. In this paper we discuss an implementation that retains the hyperbolic nature and allows for an explicit integration with small computational overhead. In the case of ambipolar drift, this formulation arises naturally by simply retaining a time derivative of the drift velocity that is typically omitted. This alone leads to time-step constraints that are comparable to the native MHD time-step constraint for a solar setup including the region from photosphere to lower solar corona. We discuss an accelerated treatment that can further reduce time-step constraints if necessary. In the case of Hall drift we propose a hyperbolic formulation that is numerically similar to that for the ambipolar drift and we show that the combination of both can be applied to simulations of the solar chromosphere at minimal computational expense.

Acoustic/shock wave heating in the gravitationally stratified partially ionized plasmas: the two-fluid effects

<p> The chromospheric heating problem is a long-standing intriguing topic of solar physics, and the acoustic wave/shock wave heating in the chromospheric plasma has been investigated in the last several decades. It has been confirmed that acoustic waves, and the shock waves induced by the steepening acoustic waves in the gravitationally stratified chromospheric plasma, are able to transport energy to the chromosphere, but the energy supplied in this way is not necessarily sufficient for heating the chromosphere. Here, we further investigate the acoustic/shock wave heating process while taking into account the two-fluid effects.</p><p> As the plasma in the chromosphere is weakly or partially ionized,  neutrals play an important role in wave propagation in this region. Therefore,  a two-fluid computational model treating neutrals and charged particles (electrons and ions) as two separate fluids is used for modelling the acoustic/shock wave propagation in idealised partially ionized plasmas, while taking into account the ion-neutral collisions, ionization and recombination. We have thus investigated  the collisional and reactive interactions between separated ions and neutrals, as well as the resulting effects in the acoustic/shock wave propagation and damping. In the numerical simulations, both the initial hydrostatic equilibrium and chemical equilibrium are taken into account to provide different density profiles for comparison.</p><p>We have found that the shock heating in the partially ionized plasmas strongly depends on the ionization fraction. In particular, the relatively smaller ionization fraction resulting from the initial chemical equilibrium significantly enhances the shock wave heating, which dominates the overall heating effect according to an approximated quantitative comparison. Moreover, the decoupling between ions and neutrals is also enhanced while considering ionization and recombination, resulting in stronger collisional heating.</p>

Magnetic reconnection in partially ionized plasmas

Magnetic reconnection has been intensively studied in fully ionized plasmas. However, plasmas are often partially ionized in astrophysical environments. The interactions between the neutral particles and ionized plasmas might strongly affect the reconnection mechanisms. We review magnetic reconnection in partially ionized plasmas in different environments from theoretical, numerical, observational and experimental points of view. We focus on mechanisms which make magnetic reconnection fast enough to compare with observations, especially on the reconnection events in the low solar atmosphere. The heating mechanisms and the related observational evidence of the reconnection process in the partially ionized low solar atmosphere are also discussed. We describe magnetic reconnection in weakly ionized astrophysical environments, including the interstellar medium and protostellar discs. We present recent achievements about fast reconnection in laboratory experiments for partially ionized plasmas.