Single-fluid Approximation Research Articles

Magnetoacoustic cutoff effect in numerical simulations of thepartially ionized solar atmosphere.

The cutoff effect is a significant determinant of solar magnetohydrodynamic wave propagation and hence pivotal in energy transfer studies, such as solar plasma heating and seismological diagnostics. Despite continuous efforts, no good agreement between observed waveperiods and theory or numerical simulations was found. Our objective is to investigate the magnetoacoustic cutoff effect in the partially ionized solar atmosphere, factoring in the two-fluid effects. We developed a two-fluid MHD numerical model and used it to simulate a quiet region of the Sun from the top of the convective zone to the low corona. Our findings show that the ongoing granulation excites a wide range of waves propagating into the upper atmospheric layers. The cutoff waveperiods strongly depend on the height. Two-fluid waveperiods obtained with numerical simulations reproduce the recent observations at avery good level of compliance. Furthermore, direct comparison with strongly coupled cases that imitate the single-fluid approximation have shown that the waveperiod propagation pattern is only present in fully two-fluid simulations. We conclude that the presence of neutrals and therefore collisional terms change the dynamics of the magnetized plasma, in comparison with the single-fluid approximation. This effect is more prominently seen in the upper photosphere and chromosphere. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.

Simulation of the Knudsen Pump by means of Quasi Gasdynamic Equation System

The use of miniature micropumps based on the effect of thermal gas sliding along the walls with an applied temperature gradient (Knudsen pump) is very relevant when creating modern miniature devices. Currently, algorithmically complex methods such as DSMC are usually used to simulate gas flows in such pumps. Progress in the development of algorithms based on a quasi-gasdynamic system of equations, pushed the authors to apply such algorithm to modeling the flow of a binary gas mixture gases in one variant of a micropump. The equations of the QGD system are conservation laws with additional dissipative terms. These terms contain a coefficient determined by the characteristic time between particles collisions. In this paper, the problem of flow in a rectangular Knudsen pump is solved based on this algorithm for a gas mixture in a single-fluid approximation. Different variants of the composition of the gas mixture are considered. The Knudsen numbers for which it is possible to describe gas flows by the QGD system correspond to flows of dense or moderately rarefied gases. Calculations for not too large Knudsen numbers demonstrated a good agreement with the results obtained by the DSMC method which is much more complex and expensive.

Phase Mixing of Propagating Alfvén Waves in a Single-fluid Partially Ionized Solar Plasma

The phase mixing of Alfvén waves is one of the most promising mechanisms for the heating of the solar atmosphere. The damping of waves in this case requires small transversal scales, relative to the magnetic field direction; this requirement is achieved by considering a transversal inhomogeneity in the equilibrium plasma density profile. Using a single-fluid approximation of a partially ionized chromospheric plasma, we study the effectiveness of the damping of phase-mixed shear Alfvén waves and investigate the effect of varying the ionization degree on the dissipation of waves. Our results show that the dissipation length of shear Alfvén waves strongly depends on the ionization degree of the plasma, but more importantly, in a partially ionized plasma, the damping length of shear Alfvén waves is several orders of magnitude shorter than in the case of a fully ionized plasma, providing evidence that phase mixing could be a large contributor to heating the solar chromosphere. The effectiveness of phase mixing is investigated for various ionization degrees, ranging from very weakly to very strongly ionized plasmas. Our results show that phase-mixed propagating Alfvén waves in a partially ionized plasma with ionization degrees in the range μ = 0.518–0.657, corresponding to heights of 1916–2150 km above the solar surface, can provide sufficient heating to balance chromospheric radiative losses in the quiet Sun.

Non-ideal magnetohydrodynamics on a moving mesh I: ohmic and ambipolar diffusion

ABSTRACT Especially in cold and high-density regions, the assumptions of ideal magnetohydrodynamics (MHD) can break down, making first order non-ideal terms such as ohmic and ambipolar diffusion as well as the Hall effect important. In this study, we present a new numerical scheme for the first two resistive terms, which we implement in the moving-mesh code arepo using the single-fluid approximation combined with a new gradient estimation technique based on a least-squares fit per interface. Through various test calculations including the diffusion of a magnetic peak, the structure of a magnetic C-shock, and the damping of an Alfvén wave, we show that we can achieve an accuracy comparable to the state-of-the-art code athena++ . We apply the scheme to the linear growth of the magnetorotational instability and find good agreement with the analytical growth rates. By simulating the collapse of a magnetized cloud with constant magnetic diffusion, we show that the new scheme is stable even for large contrasts in the spatial resolution. Thanks to the Lagrangian nature of the moving mesh method the new scheme is thus well suited for intended future applications where a high resolution in the dense cores of collapsing protostellar clouds needs to be achieved. In a forthcoming work, we will extend the scheme to include the Hall effect.

Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation

We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of ${N}_{\mathrm{spec}}$ particle species with ${N}_{q}$ intrinsic quantum numbers (e.g., electric charge, baryon number, and strangeness) using the method of moments. We obtain the continuity equations for multiple conserved charges as well as the conservation equations for the total energy and momentum in the single-fluid approximation. These $4+{N}_{q}$ conservation laws are closed by deriving the second-order equations of motion for the dissipative quantities in the $(10+4{N}_{q})$-moment approximation. The resulting fluid-dynamical equations are formally similar to those of a single-component system, but feature different thermodynamic relations and transport coefficients. We derive general relations for all transport coefficients and compute them explicitly in the ultrarelativistic limit.

Alfvén wave heating in partially ionized thin threads of solar prominences

There is observational evidence of the presence of small-amplitude transverse magnetohydrodynamic (MHD) waves with a wide range of frequencies in the threads of solar prominences. It is believed that the waves are driven at the photosphere and propagate along the magnetic field lines up to prominences suspended in the corona. The dissipation of MHD wave energy in the partially ionized prominence plasma is a heating mechanism whose relevance needs to be explored. Here we consider a simple 1D model for a non-uniform thin thread and investigate the heating associated with dissipation of Alfvén waves. The model assumes an ad hoc density profile and a uniform pressure, while the temperature and ionization degree are self-consistently computed considering either local themodynamical equilibrium (LTE) or non-LTE approximations for the hydrogen ionization. A broadband driver for Alfvén waves is placed at one end of the magnetic field line, representing photospheric excitation. The Alfvénic perturbations along the thread are obtained by solving the linearized MHD equations for a partially ionized plasma in the single-fluid approximation. We find that wave heating in the partially ionized part of the thread is significant enough to compensate for energy losses due to radiative cooling. A greater amount of heating is found in the LTE case because the ionization degree for core prominence temperatures is lower than that in the non-LTE approximation. This results in a greater level of dissipation due to ambipolar diffusion in the LTE case. Conversely, in the hot coronal part of the model, the plasma is fully ionized and wave heating is negligible. The results of this simple model suggest that MHD wave heating can be relevant for the energy balance in prominences. Further studies based on more elaborate models are required.

Conditions for Justifying Single-fluid Approximation for Charged and Neutral Dust Fluids and a Smoothed Particle Magnetohydrodynamics Method for Dust–Gas Mixture

Abstract We describe a numerical scheme for magnetohydrodynamics simulations of dust–gas mixture by extending smoothed particle magnetohydrodynamics. We employ the single-species particle approach to describe dust–gas mixture with several modifications from the previous studies. We assume that the charged and neutral dust can be treated as single-fluid, that the electromagnetic force acts on the gas, and that that acting on the charged dust is negligible. The validity of these assumptions in the context of protostar formation is not obvious and is extensively evaluated. By investigating the electromagnetic force and electric current with terminal velocity approximation, it is found that as the dust size increases, the contribution of dust to them becomes smaller and negligible. We conclude that our assumption that the electromagnetic force on the dusts is negligible is valid for the dust size with a d ≳ 10 μm. On the other hand, they do not produce the numerical artifact for the dust a d ≲ 10 μm in the envelope and disk, where the perfect coupling between gas and dust is realized. However, we also found that our assumptions may break down in outflow (or under an environment with very strong magnetic field and low density) for the dust a d ≲ 10 μm. We conclude that our assumptions are valid in almost all cases where macroscopic dust dynamics is important in the context of protostar formation. We conduct numerical tests of dusty waves, dusty magnetohydrodynamics shocks, and gravitational collapse of magnetized cloud cores with our simulation code. The results show that our numerical scheme well reproduces the dust dynamics in the magnetized medium.

Numerical investigations of Rayleigh–Taylor instability with a density gradient layer

The Rayleigh-Taylor instability (RTI) with a density gradient layer was investigated by implicit large eddy simulations (ILES) in a framework of three dimensional compressible multiphase flow with the single fluid approximation. The simulations are firstly initialized by multi-mode random perturbations in classic RTI and the associated case with a premixed layer. It is found that the late time behaviours of the turbulent mixing layer in classic and premixed cases are similar although an initial premixed layer slows down the growth of the turbulent mixing layer significantly. A variety of flow quantities for different cases are compared and studied at different time. In addition, the turbulent mixing caused by RTI with a single-mode dominated perturbation is investigated in classic and premixed cases. Different stages are identified for the time evolution of turbulent mixing layer. The dynamics of bubble-spike structures at early time, and the production and transfer of turbulent kinetic energy at late time are expatiated. Typical quantities of turbulent mixing are also summarized. It is found that there is an inactive stage before the fast growth of bubble-spike structures with an initial premixed layer and the spectra need more time to adjust until the flow turns to a self-similar regime.

Cosmological perturbations for two cold fluids in ΛCDM

ABSTRACT The cosmic large-scale structure of our Universe is comprised of baryons and cold dark matter (CDM). Yet it is customary to treat these two components as a combined single-matter fluid with vanishing pressure, which is justified only for sufficiently large scales and late times. Here, we go beyond the single-fluid approximation and develop the perturbation theory for two gravitationally coupled fluids while still assuming vanishing pressure. We mostly focus on perturbative expansions in powers of D (or D+), the linear structure growth of matter in a ΛCDM Universe with cosmological constant Λ. We derive in particular (1) explicit recursion relations for the two fluid densities, (2) complementary all-order results in the Lagrangian-coordinates approach, as well as (3) the associated component wavefunctions in a semiclassical approach to cosmic large-scale structure. In our companion paper, we apply these new theoretical results to generate novel higher order initial conditions for cosmological hydrodynamical simulations.

Numerical modeling of electric arc motion in external constant magnetic field

The paper generalizes to the three-dimensional case the previously proposed two-dimensional mathematical model of the motion of a plasma formation in a constant transverse magnetic field. The complete system of single-fluid magnetogasdynamic approximation of the equations of the hydrodynamic method for plasma description under conditions of local thermodynamic equilibrium is simplified in the electromagnetic part. Instead of solving the complete system of Maxwell’s equations, Ohm’s integral law is applied to the conducting region with usage of empirical data. Earlier studies in a two-dimensional version of this model as applied to the problem of describing the motion of an arc showed its effectiveness and efficiency for the class of problems under consideration. The simulation results with proposed extended model are compared with previously obtained calculated and experimental data. Main integral and local features of flow structure are highlighted.

On Beltrami states near black hole event horizon

In this article, we study Beltrami equilibria for plasmas near the horizon of a spinning black hole and develop a framework for constructing the magnetic field profile in the near horizon limit for Clebsch flows in the single-fluid approximation. We find that the horizon profile for the magnetic field is shown to satisfy a system of first-order coupled ODEs dependent on a boundary condition for the magnetic field. For states in which the generalized vorticity vanishes (the generalized “superconducting” plasma state), the horizon profile becomes independent of the boundary condition and depends only on the thermal properties of the plasma. Our analysis makes use of the full form for the time-independent Ampère's law in the 3 + 1 formalism, generalizing earlier conclusions for the case of vanishing vorticity, namely, the complete magnetic field expulsion near the equator of an axisymmetric black horizon assuming that the thermal properties of the plasma are symmetric about the equatorial plane. For the general case, we find and discuss additional conditions required for the expulsion of magnetic fields at given points on the black hole horizon. We perform a length scale analysis, which indicates the emergence of two distinct length scales characterizing the magnetic field variation and the strength of the Beltrami term, respectively.

A transient phase in cosmological evolution : A multi-fluid approximation for a quasi-thermodynamical equilibrium

This article presents the study of a multi-species fluid characterised by a freeze-out or break-away of one or more species. Whereas single-fluid approximation suffices for modelling of the pre {\it freeze-out} period, multi-fluid approximation is required for the post freeze-out period. Embedded in this is a transition period where neither one of the two approximations is singly appropriate. We examine the thermodynamics of this fluid and find that the second law holds before, during and after the freeze-out. Our application to cosmological modelling involving interacting dark-section species indicates that the species' equations of state are modified.

Ambipolar diffusion in large Prandtl number turbulence

ABSTRACT We study the effects of ambipolar diffusion (AD) on hydromagnetic turbulence. We consider the regime of large magnetic Prandtl number, relevant to the interstellar medium. In most of the cases, we use the single-fluid approximation where the drift velocity between charged and neutral particles is proportional to the Lorentz force. In two cases we also compare with the corresponding two-fluid model, where ionization and recombination are included in the continuity and momentum equations for the neutral and charged species. The magnetic field properties are found to be well represented by the single-fluid approximation. We quantify the effects of AD on total and spectral kinetic and magnetic energies, the ohmic and AD dissipation rates, the statistics of the magnetic field, the current density, and the linear polarization as measured by the rotationally invariant E and B mode polarizations. We show that the kurtosis of the magnetic field decreases with increasing AD. The E mode polarization changes its skewness from positive values for small AD to negative ones for large AD. Even when AD is weak, changes in AD have a marked effect on the skewness and kurtosis of E, and only a weak effect on those of B. These results open the possibility of employing E and B mode polarizations as diagnostic tools for characterizing turbulent properties of the interstellar medium.

3D Magnetic Holes in Collisionless Plasmas

Recent multispacecraft observations in the Earth’s magnetosphere have revealed an abundance of magnetic holes—localized magnetic field depressions. These magnetic holes are characterized by the plasma pressure enhancement and strongly localized currents flowing around the hole boundaries. There are several numerical and analytical models describing 2D configurations of magnetic holes, but the 3D distribution of magnetic fields and electric currents is studied poorly. Such a 3D magnetic field configuration is important for accurate investigation of charged particle dynamics within magnetic holes. Moreover, the 3D distribution of currents can be used for distant probing of magnetic holes in the magnetosphere. In this study, a 3D magnetic hole model using the single-fluid approximation and a spatial scale hierarchy with the distinct separation of gradients is developed. It is shown that such 3D holes can be obtained as a generalization of 1D models with the plasma pressure distribution adopted from the kinetic approach. The proposed model contains two magnetic field components and field-aligned currents. The magnetic field line configuration resembles the magnetic trap where hot charged particles bounce between mirror points. However, the approximation of isotropic pressure results in a constant plasma pressure along magnetic field lines, and the proposed magnetic hole model does not confine plasma along the field direction.

MHDSTS: a new explicit numerical scheme for simulations of partially ionised solar plasma

The interaction of plasma with magnetic field in the partially ionised solar atmosphere is frequently modelled via a single-fluid approximation, which is valid for the case of a strongly coupled collisional media, such as solar photosphere and low chromosphere. Under the single-fluid formalism the main non-ideal effects are described by a series of extra terms in the generalised induction equation and in the energy conservation equation. These effects are: Ohmic diffusion, ambipolar diffusion, the Hall effect, and the Biermann battery effect. From the point of view of the numerical solution of the single-fluid equations, when ambipolar diffusion or Hall effects dominate can introduce severe restrictions on the integration time step and can compromise the stability of the numerical scheme. In this paper we introduce two numerical schemes to overcome those limitations. The first of them is known as super time-stepping (STS) and it is designed to overcome the limitations imposed when the ambipolar diffusion term is dominant. The second scheme is called the Hall diffusion scheme (HDS) and it is used when the Hall term becomes dominant. These two numerical techniques can be used together by applying Strang operator splitting. This paper describes the implementation of the STS and HDS schemes in the single-fluid codeMANCHA3D. The validation for each of these schemes is provided by comparing the analytical solution with the numerical one for a suite of numerical tests.

Rayleigh-Taylor instabilities with sheared magnetic fields in partially ionised plasmas

Aims. In the present study we investigate the nature of the magnetic Rayleigh-Taylor instability appearing at a tangential discontinuity in a partially ionised plasma when the effect of magnetic shear is taken into account. Methods. The partially ionised character of the plasma is described by the ambipolar diffusion in the induction equation. The dynamics of the plasma is investigated in a single-fluid approximation. After matching the solutions on both sides of the interface we derive a dispersion equation and calculate the instability increment using analytical methods for particular cases of parameters, and numerical investigation for a wide range of parameters. Results. We calculated the dependence of the instability increment on the perturbation wavenumber. We also calculated the dependence of the maximum instability increment on the shear angle of the magnetic field for various values of the ionisation degree. Conclusions. Our results show that the Rayleigh-Taylor instability becomes sensitive to the degree of plasma ionisation only for plasmas with small values of plasma beta and in a very weakly ionised state. Perturbations are unstable only for those wavenumbers that are below a cut-off value.

Influence of the magnetic field on the density distribution of solar wind protons and cometary ions in the shock layer ahead of cometary ionospheres

The “mass loading” of the solar wind by cometary ions produced by the photoionization of neutral molecules outflowing from the cometary nucleus plays a major role in the interaction of the solar wind with cometary atmospheres. In particular, this process leads to a decrease in the solar wind velocity with a transition from supersonic velocities to subsonic ones through the bow shock. The so-called single-fluid approximation, in which the interacting plasma flows are considered as a single fluid, is commonly used in modeling such an interaction. However, it is occasionally necessary to know the distribution of parameters for the components of the interacting plasma flows. For example, when the flow of the cometary dust component in the interplanetary magnetic field is considered, the dust particle charge, which depends significantly on the composition of the surrounding plasma, needs to be known. In this paper, within the framework of a three-dimensional magnetohydrodynamic model of the solar wind flow around cometary ionospheres, we have managed to separately obtain the density distributions of solar wind protons and cometary ions between the bow shock and the cometary ionopause (in the shock layer). The influence of the interplanetary magnetic field on the position of the point of intersection between the densities with the formation of a region near the ionopause where the proton density is essentially negligible compared to the density of cometary ions is investigated. Such a region was experimentally detected by the Vega-2 spacecraft when investigating Comet Halley in March 1986. The results of the model considered below are compared with some experimental data obtained by the Giotto spacecraft under the conditions of flow around Comets Halley and Grigg–Skjellerup in 1986 and 1992, respectively. Unfortunately, our results of calculations on Comet Churyumov–Gerasimenko are only predictive in character, because the trajectory of the Rosetta spacecraft, which manoeuvred near its surface for several months, is complex.

ON THE SPATIAL SCALES OF WAVE HEATING IN THE SOLAR CHROMOSPHERE

Dissipation of magnetohydrodynamic (MHD) wave energy has been proposed as a viable heating mechanism in the solar chromospheric plasma. Here, we use a simplified one-dimensional model of the chromosphere to theoretically investigate the physical processes and the spatial scales that are required for the efficient dissipation of Alfv\'en waves and slow magnetoacoustic waves. We consider the governing equations for a partially ionized hydrogen-helium plasma in the single-fluid MHD approximation and include realistic wave damping mechanisms that may operate in the chromosphere, namely Ohmic and ambipolar magnetic diffusion, viscosity, thermal conduction, and radiative losses. We perform an analytic local study in the limit of small amplitudes to approximately derive the lengthscales for critical damping and efficient dissipation of MHD wave energy. We find that the critical dissipation lengthscale for Alfv\'en waves depends strongly on the magnetic field strength and ranges from 10~m to 1~km for realistic field strengths. The damping of Alfv\'en waves is dominated by Ohmic diffusion for weak magnetic field and low heights in the chromosphere, and by ambipolar diffusion for strong magnetic field and medium/large heights in the chromosphere. Conversely, the damping of slow magnetoacoustic waves is less efficient, and spatial scales shorter than 10~m are required for critical damping. Thermal conduction and viscosity govern the damping of slow magnetoacoustic waves and play an equally important role at all heights. These results indicate that the spatial scales at which strong wave heating may work in the chromosphere are currently unresolved by observations.

Three-dimensional magnetohydrodynamic model of the interaction between the solar wind and cometary atmospheres

A magnetohydrodynamic (MHD) model of the interaction between the solar wind and an expanding gas flow issuing from a comet nucleus is presented. The processes of photoionization of the neutral component of the comet matter and the resonance charge exchange between charged and neutral particles are taken into account, together with the interplanetary magnetic field effect. The adequacy of the single-fluid MHD approximation in describing the plasma flow with different temperatures of the components is shown. The model is numerically realized on the basis of the higher-order Godunov method using an approximate solution of the arbitrary MHD discontinuity breakdown problem. The results of a numerical investigation of the plasma and magnetic field parameters in the vicinity of a comet are presented for the conditions corresponding to the flyby of several spacecraft near comet Halley in March 1986 and the expected fly-round of comet Churyumov-Gerasimenko by the Rosetta spacecraft in 2015.

Investigation of the surface layer of dimethyl ether/triethylene glycol solutions

Method for calculating density and concentrations profiles of dimethyl ether (DME) solutions in triethylene glycol (TEG) was proposed in the paper. The thickness values of the surface layer of solutions were determined, and its structure was studied. The method for determining the effective surface concentration of the solution was proposed. The studies were performed in the framework of the gradient theory using the Peng-Robinson equation of state in single-fluid approximation with a modified procedure for determining the SE coefficients. The studies were conducted in order to determine the effective composition of the surface layer of the solution. It is this solution composition rather than of the bulk liquid phase composition that must be taken into account when interpreting the experimental data on the saturated vapor pressure and surface tension of solutions. As a result, it was found that the effective thickness of the surface layer of the solution increases with a decrease in the DME amount in solution, and as approaching the critical temperature tends to infinity. Herewith, surface layer of the studied solutions is composed of two sublayers. DME partial molar density profiles have a maximum. This means that the surface layer of the solution is enriched with this component. Analysis of the results has shown that the difference between the component concentrations in the surface layer and in the bulk liquid phase of the solution increases with temperature. The results are of fundamental importance in both the experimental investigation of the solution properties, and thermodynamic modeling of phase equilibria of solutions and forecasting their surface tension.