2-D Numerical Simulation of the Ambipolar Filamentation of Turbulent Magnetic Fields

Magnetic fields play an important role in astrophysics and they often dominate the behavior of magnetized media. We simulate the mechanism (Tagger et al., 1995) by which turbulence in a weakly ionized plasma, as it cascades to the ambipolar scale (where the neutrals are imperfectly coupled to the ions) leads to a filamentation of the magnetic flux tubes: the turbulent velocity of the neutrals is higher in the more ionized regions, because they are better coupled to the ions. This results in a non-linear ponderomotive (<v.∇ v>) force driving them out of the ionized regions, so that the initial ionization inhomogeneities are strongly amplified. This effect causes the ions and magnetic field to condense and separate from the neutrals, resulting in a filamentary structure. We present the first results of a 2-D, 2-fluid (ions and neutrals) simulation, where a magnetized, weakly ionized plasma is submitted to turbulence in the ambipolar frequency range. We discuss the efficiency of this mechanism, the filamentary structure it should produce, and its relevance to the astrophysical context. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rayleigh–Taylor instability in an ionized medium

We study the linear theory of the magnetized Rayleigh–Taylor instability in a system consisting of ions and neutrals. Both components are affected by a uniform vertical gravitational field. We consider ions and neutrals as two separate fluid systems that can exchange momentum through collisions. However, ions have a direct interaction with the magnetic field lines but neutrals are not affected by the field directly. The equations of our two-fluid model are linearized and by applying a set of proper boundary conditions, a general dispersion relation is derived for our two superposed fluids separated by a horizontal boundary. We found two unstable modes for a range of wavenumbers. It seems that one of the unstable modes corresponds to the ions and the other one is for the neutrals. Both modes are reduced with increasing particle collision rate and ionization fraction. We show that if the two-fluid nature is considered, the RT instability would not be suppressed and we also show that the growth time of the perturbations increases. As an example, we apply our analysis to the Local Clouds which seem to have arisen because of the RT instability. Assuming that the clouds are partially ionized, we find that the growth rate of these clouds increases in comparison to the fully ionized case.     

Mean-field dynamo in partially ionized plasmas – I

There are several astrophysical situations where one needs to study the dynamics of magnetic flux in partially ionized turbulent plasmas. In a partially ionized plasma, the magnetic induction is subjected to the ambipolar diffusion and the Hall effect in addition to the usual resistive dissipation. In this paper, we initiate the study of the kinematic dynamo in a partially ionized turbulent plasma. The Hall effect arises from the treatment of the electrons and the ions as two separate fluids and the ambipolar diffusion due to the inclusion of neutrals as the third fluid. It is shown that these non-ideal effects modify the so-called α effect and the turbulent diffusion coefficient β in a rather substantial way. The Hall effect may enhance or quench the dynamo action altogether. The ambipolar diffusion brings in an α which depends on the mean magnetic field. The new correlations embodying the coupling of the charged fluids and the neutral fluid appear in a decisive manner. The turbulence is necessarily magnetohydrodynamic with new spatial and time-scales. The nature of the new correlations is demonstrated by taking the Alfvénic turbulence as an example.     

Element separation effects in the boundary region of a plasma surrounded by neutral gas

A one-dimensional model is being considered where a fully ionized plasma is separated from a neutral gas by a homogeneous magnetic field directed along the plasma boundary. The plasma and the neutral gas consist of two different types of ions and neutral particles. In a stationary state the outflux of plasma by diffusion across the magnetic field is compensated by an influx of neutrals which are ionized in a partially ionized boundary region. It is found that the ratio between the ion densities in the fully ionized region will in general differ from the density ratio of the two types of neutrals being present in the gas region. This provides a separation mechanism with applications both to cosmical and laboratory plasmas, such as in the following cases:

1. The abundance anomalies in magnetic variable stars and in the solar wind.
2. Separation processes of non-identical ions and neutral atoms in gas blanket systems.

     

Thermosolutal instability of a partially-ionized plasma

The thermosolutal instability of a partially-ionized plasma in the presence of a horizontal magnetic field is considered to include the frictional effect of collisions of ionized with neutrals. The sufficient conditions for non-existence of overstability are derived. The solute gradient and magnetic field introduce oscillatory modes in thermosolutal convection which were non-existent in their absence. The magnetic field and stable solute gradient are found to have stabilizing effects whereas collisional effect of ionized with neutrals is found to have destabilizing effect on thermosolutal instability of a partially ionized plasma.     

Kolmogorov dissipation scales in weakly ionized plasmas

In a weakly ionized plasma, the evolution of the magnetic field is described by a 'generalized Ohm's law' that includes the Hall effect and the ambipolar diffusion terms. These terms introduce additional spatial and time-scales which play a decisive role in the cascading and the dissipation mechanisms in magnetohydrodynamic turbulence. We determine the Kolmogorov dissipation scales for the viscous, the resistive and the ambipolar dissipation mechanisms. The plasma, depending on its properties and the energy injection rate, may preferentially select one of these dissipation scales, thus determining the shortest spatial scale of the supposedly self-similar spectral distribution of the magnetic field. The results are illustrated taking the partially ionized part of the solar atmosphere as an example. Thus, the shortest spatial scale of the supposedly self-similar spectral distribution of the solar magnetic field is determined by any of the four dissipation scales given by the viscosity, the Spitzer resistivity (electron–ion collisions), the resistivity due to electron–neutral collisions and the ambipolar diffusivity. It is found that the ambipolar diffusion dominates for reasonably large energy injection rate. The robustness of the magnetic helicity in the partially ionized solar atmosphere would facilitate the formation of self-organized vortical structures.     

Drag Instability

With the ionization rate of neutral particles caused by cosmic rays and balanced by the recombination rate of ions for a cold, weakly ionized fluid threaded by stressed magnetic fields, we show that a local perturbation can evolve to a traveling wave with its perturbed quantities growing with time so long as the drift velocity between neutrals and ions is comparable to the Alfven speed of the fluid. Since the large drift velocity is one of the key assumptions to drive this instability, we name it the “drag instability”. We suggest that the drag instability might occur in the regions where magnetic fields are highly stressed such as a C-shock front or a collapsing proto-stellar cloud.     

Investigating thermal evolution of the self-gravitating one dimensional molecular cloud by smoothed particle hydrodynamics

The heating of the ion-neutral (or ambipolar) diffusion may affect the thermal phases of the molecular clouds. We present an investigation on the effect of this heating mechanism in the thermal instability of the molecular clouds. A weakly ionized one-dimensional slab geometry, which is allowed for self-gravity and ambipolar diffusion, is chosen to study its thermal phases. We use the thermodynamic evolution of the slab to obtain the regions where slab cloud becomes thermally unstable. We investigate this evolution using the model of ambipolar diffusion with two-fluid smoothed particle hydrodynamics, as outlined by Hosking and Whitworth. Firstly, some parts of the technique are improved to test the pioneer works on behavior of the ambipolar diffusion in an isothermal self-gravitating slab. Afterwards, the improved two-fluid technique is used for thermal evolution of the slab. The results show that the thermal instability may persist inhomogeneities with a large density contrast at the intermediate parts of the cloud. We suggest that this feature may be responsible for the planet formation in the intermediate regions of a collapsing molecular cloud and/or may also be relevant to the formation of star forming dense cores in the clumps.     

Rayleigh-Taylor instability of ionized viscous fluids with FLR-corrections and surface-tension

The problem of Rayleigh-Taylor instability of superposed viscous magnetized fluids through porous medium is investigated in a partially-ionized medium. The fluid has ionized and neutralized particle components interacting with collisions. The effect of surface tension on R-T instability is also included in the present problem. The magnetohydrodynamic equations are modified for finite-Larmor radius corrections which is in the form of tensor. The equations of problem are linearized and using appropriate boundary condition, general dispersion relation is derived for two superposed fluids separated by horizontal boundary. The first part of the dispersion relation gives stable mode and condition is investigated using Hurwitz conditions. The second part of the dispersion relation shows that the growth rate of unstable system is reduced due to FLR corrections, viscosity, and collisional frequency of the neutrals. The role of surface tension on the system is also discussed.     

Collapse of weakly ionized rotating turbulent Cloud Cores

In view of the Turbulent Cooling Flows scenario we carry out several 3D axisymmetric calculations to follow the evolution of magnetically subcritical weakly ionized and rotating turbulent cloud cores. Turbulent Cooling Flows appear to pronounce the effects of ambipolar diffusion considerably, inducing thereby a runaway collapse of the core already on a diluted free-fall time scale. Ambipolar diffusion significantly weakens the efficiency of magnetic braking. This implies that most of the rotational energy is trapped into the dynamically collapsing core and that initiation of outflows is prevented at least in the early isothermal phases. The trapped rotational energy is found to enhance the formation of rings that may afterwards fragment. It is shown that the central region of a strongly ionized magnetically subcritical core is principally overdense, with central density up to one order of magnitude larger than the surroundings. These results confirm that large scale magnetic fields threading a cloud core relax the supersonic random motions on an Alfvén wave crossing time. Moreover, ambipolar diffusion enhances dissipation of supersonic turbulence even more.     

Modelling of magnetic interactions in partially-ionized gas: application to the FIP effect

We have adapted the ZEUS code to model magnetic interactions in partially ionized gas. When two regions of opposite polarity come into contact with each other, ions drifting in response to the Lorentz force fall into the minimum of the magnetic field, and then the drifting ions force the neutrals to take part in the flow. Because of the finite time required for ion-atom collisions to occur, the gas which emerges from the interaction site has an ion/atom ratio which may be altered relative to that in the ambient medium. In order to model this effect, we adapt the Zeus code to a two-step iterative process involving a cycle between the hydrodynamic (HD) and the magnetohydrodynamic (MHD) versions of the code. The ion and atom fluids are coupled by collisions. Our simulations show that in chromospheric conditions, outflowing gas exhibits enhancements in ion/atom ratios which may be as large as a factor of 10 or more. The magnitude of the enhancements is determined by two key ratios which enter into the problem: the degree of ionization (ni/na), and the plasma parameter. We show that, in the context of the mechanism we propose here, the amplitude of the ion/atom enhancements in the solar chromosphere is subject to a remarkable self-regulation because the ion density ni is almost invariant over the height range of interest to us. Our results are relevant in the context of the Sun, where the coronal abundances of elements with low first ionization potential (FIP) are systematically enhanced in certain magnetic structures. Although data for stars other than the Sun are sparse, we point out that our results are also useful for interpreting the available stellar data.     

Formation of fluctuations in a molecular slab via isobaric thermal instability

Frictional heating by the ion-neutral drift is calculated and its effect on the isobaric thermal instability is studied. Ambipolar drift heating of a one-dimensional self-gravitating magnetized molecular slab is used under the assumptions of quasi-magnetohydrostatic and local ionization equilibrium. We see that ambipolar drift heating is inversely proportional to density and its value in some regions of the slab can be significantly larger than the average heating rates of cosmic rays and turbulent motions. The results show that isobaric thermal instability can occur in some regions of the slab, and thus it may produce slab fragmentation and formation of astronomical unit scale condensations.     

Plasma environment of Jupiter family comets

As any comet nears the Sun, gas sublimes from the nucleus taking dust with it. Jupiter family comets are no exception. The neutral gas becomes ionized, and the interaction of a comet with the solar wind starts with ion pickup. This key process is also important in other solar system contexts wherever neutral particles become ionized and injected into a flowing plasma such as at Mars, Venus, Io, Titan and interstellar neutrals in the solar wind. At comets, ion pickup removes momentum and energy from the solar wind and puts it into cometary particles, which are then thermalised via plasma waves. Here we review what comets have shown us about how this process operates, and briefly look at how this can be applied in other contexts. We review the processes of pitch angle and energy scattering of the pickup ions, and the boundaries and regions in the comet-solar wind interaction. We use in-situ measurements from the four comets visited to date by spacecraft carrying plasma instrumentation: 21P/Giacobini-Zinner, 1P/Halley, 26P/Grigg-Skjellerup and 19P/Borrelly, to illustrate the process in action. While, of these, comet Halley is not a Jupiter class comet, it has told us the most about cometary plasma environments. The other comets, which are from the Jupiter family, give an interesting comparison as they have lower gas production rates and less-developed interactions. We examine the prospects for Rosetta at comet Churyumov-Gerasimenko, another Jupiter family comet where a wide range of gas production rates will be studied.     

Energy Flux of Alfvén Waves in Weakly Ionized Plasma and Coronal Heating of the Sun

The influence of collisions between neutrals and ions on the energy flux of Alfvén-type waves in partially ionized plasma based on the three-fluid equations is considered. It has been shown that amplitudes of Alfvén waves that are generated or propagating in the solar photosphere do not depend on the ionization ratio, if the wave periods are much larger than 10⁻⁴ s. This contradicts results of Vranjes et al. (Astron. Astrophys. 478, 553, 2008) and is explained by the strong coupling due to ion–neutral collisions. Alfvén waves can be effectively excited in the photosphere of the Sun by convective motions, providing the required energy for coronal heating.     

Solitons and double-layers of electron-acoustic waves in magnetized plasma; an application to auroral zone plasma

A theoretical investigation is carried out for understanding the properties of electron-acoustic potential structures (i.e., solitary waves and double-layers) in a magnetized plasma whose constituents are a cold magnetized electron fluid, hot electrons obeying a nonthermal distribution, and stationary ions. For this purpose, the hydrodynamic equations for the cold magnetized electron fluid, nonthermal electron density distribution, and the Poisson equation are used to derive the corresponding nonlinear evolution equation; modified Zakharov–Kuznetsov (MZK) equation, in the small amplitude regime. The MZK equation is analyzed to examine the existence regions of the solitary pulses and double-layers. It is found that rarefactive electron-acoustic solitary waves and double-layers strongly depend on the density and temperature ratios of the hot-to-cold electron species as well as the nonthermal electron parameter.     

Electron acceleration by electric fields near the footpoints of current-carrying coronal magnetic loops

We analyze the electric fields that arise at the footpoints of a coronal magnetic loop from the interaction between a convective flow of partially ionized plasma and the magnetic field of the loop. Such a situation can take place when the loop footpoints are at the nodes of several supergranulation cells. In this case, the neutral component of the converging convective flows entrain electrons and ions in different ways, because these are magnetized differently. As a result, a charge-separating electric field emerges at the loop footpoints, which can efficiently accelerate particles inside the magnetic loop under appropriate conditions. We consider two acceleration regimes: impulsive (as applied to simple loop flares) and pulsating (as applied to solar and stellar radio pulsations). We have calculated the fluxes of accelerated electrons and their characteristic energies. We discuss the role of the return current when dense beams of accelerated particles are injected into the corona. The results obtained are considered in light of the currently available data on the corpuscular radiation from solar flares.     

Charge transfer reactions at interfaces between neutral gas and plasma: Dynamical effects and X‐ray emission

Charge‐transfer is the main process linking neutrals and charged particles in the interaction regions of neutral (or partly ionized) gas with a plasma. In this paper we illustrate the importance of charge‐transfer with respect to the dynamics and the structure of neutral gas‐plasma interfaces. We consider the following phenomena: (1) the heliospheric interface ‐ region where the solar wind plasma interacts with the partly‐ionized local interstellar medium (LISM) and (2) neutral interstellar clouds embedded in a hot, tenuous plasma such as the million degree gas that fills the so‐called “Local Bubble”. In (1), we discuss several effects in the outer heliosphere caused by charge exchange of interstellar neutral atoms and plasma protons. In (2) we describe the role of charge exchange in the formation of a transition region between the cloud and the surrounding plasma based on a two‐component model of the cloud‐plasma interaction. In the model the cloud consists of relatively cold and dense atomic hydrogen gas, surrounded by hot, low density, fully ionized plasma. We discuss the structure of the cloud‐plasma interface and the effect of charge exchange on the lifetime of interstellar clouds. Charge transfer between neutral atoms and minor ions in the plasma produces X‐ray emission. Assuming standard abundances of minor ions in the hot gas surrounding the cold interstellar cloud, we estimate the X‐ray emissivity consecutive to the charge transfer reactions. Our model shows that the charge‐transfer X‐ray emission from the neutral cloud‐plasma interface may be comparable to the diffuse thermal X‐ray emission from the million degree gas cavity itself (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

GEOS-2 measurements of cold ions in the magnetosheath

The Suprathermal Plasma Analysers on GEOS-2 are able to make differential energy measurements of plasma particles down to sub-eV energies because the entire sensor package can be biased relative to the spacecraft. When the package is biased negatively with respect to space potential, low energy positive ions are sucked in and are more easily detected against the background. Large fluxes of ions with temperatures of the order of 1 eV or less were consistently detected at space potential when the spacecraft was in the magnetosheath though not when it was in the nearby magnetosphere. This apparent geophysical correlation, suggesting that the ions were part of the magnetosheath ion population, was contradicted by the fact that the ions showed no signs of the large drift velocity associated with the electric field in the magnetosheath. We conclude, after further investigation, that the observed ions were probably sputtered as neutrals from the spacecraft surface by the impact of solar wind ions and subsequently ionized by sunlight or electron impact. The effect of sputtering by solar wind ions has not been previously observed, although it could have consequences for the long-term stability of spacecraft surfaces.     

The evolution of charged particles in a model of contracting cloud

The evolution of the charged particles are followed during contraction of a model of an interstellar cloud, with initial density number of n = 10 cm^–3. The contraction is followed up to density increase by five orders of magnitude. Special care is given to the details of the negative ions. In addition, we have tested the ambipolar diffusion according to the results of the ion density.The results predict the importance of atomic ions in the diffuse regions. H⁺ and C⁺ are distinctly enhanced in the beginning of contraction but decrease as contraction proceeds. Molecular ions enhance as contraction proceeds and becomes important in dense regions. The most enhanced molecular ions are HCO⁺, O₂ ⁺, C₂H₃ ⁺, H₃O⁺ and SO⁺, H₃ ⁺ is less abundant. The atomic ions (except metalic ions) decrease noticeably as density increases. In general the negative ions are of negligible fractional abundances. It has also been found that the time of ambipolar diffusion is shorter than the dynamical time, hence the magnetic field should be weakened in the central core as the central density increases to n = 10⁴ cm^–3.