The overshooting convective motions in the solar photosphere are frequently proposed as the source for the excitation of Alfvén waves. However, the photosphere is a) very weakly ionized, and, b) the dynamics of the plasma particles in this region is heavily influenced by the plasma-neutral collisions. The purpose of this work is to check the consequences of these two facts on the above scenario and their effects on the electromagnetic waves. It is shown that the ions and electrons in the photosphere are both un-magnetized; their collision frequency with neutrals is much larger than the gyro-frequency. This implies that eventual Alfvén-type electromagnetic perturbations must involve the neutrals as well. This has the following serious consequences: i) in the presence of perturbations, the whole fluid (plasma + neutrals) moves; ii) the Alfvén velocity includes the total (plasma + neutrals) density and is thus considerably smaller compared to the collision-less case; iii) the perturbed velocity of a unit volume, which now includes both plasma and neutrals, becomes much smaller compared to the ideal (collision-less) case; and iv) the corresponding wave energy flux for the given parameters becomes much smaller compared to the ideal case.
The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identically to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse gradients efficiently generate transversely propagating fast magnetoacoustic waves. However, high resolution full MHD numerical simulations of the developed stage of the pulse evolution show that the gene…
We present a self-consistent mean field theory of the dynamo in 3D and turbulent diffusion in 2D in weakly ionized gas. We find that in 3D, the backreaction does not alter the beta effect while it suppresses the alpha effect when the strength of a mean magnetic field exceeds a critical value. These results suggest that a mean field dynamo operates much more efficiently in weakly ionized gas compared to the fully ionized gas. Furthermore, we show that in 2D, the turbulent diffusion is suppressed by back reaction when a mean magnetic field reaches the same critical strength, with the upper bound…
We show that the Hall scale in a weakly ionized plasma depends on the fractional ionization of the medium and, Hall MHD description becomes important whenever the ion-neutral collision frequency is comparable to the ion-gyration frequency, or, the ion-neutral collisional mean free path is smaller than the ion gyro-radius. Wave properties of a weakly-ionized plasma also depends on the fractional ionization and plasma Hall parameters, and whistler mode is the most dominant mode in such a medium. Thus Hall MHD description will be important in astrophysical disks, dark molecular clouds, neutron st…
Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall-MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toro…
In this Letter, weak turbulence theory is used to investigate interactions among Alfven waves and fast and slow magnetosonic waves in collisionless low-beta plasmas. The wave kinetic equations are derived from the equations of magnetohydrodynamics, and extra terms are then added to model collisionless damping. These equations are used to provide a quantitative description of a variety of nonlinear processes, including "parallel" and "perpendicular" energy cascade, energy transfer between wave types, "phase mixing," and the generation of back-scattered Alfven waves.
The turnover of interstellar gas on $\sim 10^9$yr timescales argues for the continuous operation of a galactic dynamo. The conductivity of interstellar gas is so high that the dynamo must be "fast" - i.e. the magnetic field must be amplified at a rate nearly independent of the magnetic diffusivity. Yet, all the fast dynamos so far known - and all direct numerical simulations of interstellar dynamos - yield magnetic power spectra that peak at the resistive scale, while galactic magnetic fields have substantial power on large scales. In this paper we show that in weakly ionized gas the limiting …
The magnetorotational instability (MRI) of a weakly ionized, differentially rotating, magnetized plasma disk is investigated in the multi-fluid framework. The disk is threaded by a uniform vertical magnetic field and charge is carried by electrons and ions only. The inclusion of ion dynamics causes significant modification to the conductivity tensor in a weakly ionized disk. The parallel, Pedersen and Hall component of conductivity tensor become time dependent quantities resulting in the AC and DC part of the conductivity. The conductivity may change sign leading to the significant modificatio…
Ambient interstellar material may become entrained in outflows from massive stars as a result of shear flow instabilities. We study the linear theory of the Kelvin - Helmholtz instability, the simplest example of shear flow instability, in a partially ionized medium. We model the interaction as a two fluid system (charged and neutral) in a planar geometry. Our principal result is that for much of the relevant parameter space, neutrals and ions are sufficiently decoupled that the neutrals are unstable while the ions are held in place by the magnetic field. Thus, we predict that there should be …
We study the linear theory of Kelvin-Helmholtz instability in a layer of ions and neutrals with finite thickness. In the short wavelength limit the thickness of the layer has a negligible effect on the growing modes. However, perturbations with wavelength comparable to layer's thickness are significantly affected by the thickness of the layer. We show that the thickness of the layer has a stabilizing effect on the two dominant growing modes. Transition between the modes not only depends on the magnetic strength, but also on the thickness of the layer.
We investigate the effects of ambipolar diffusion and the Hall effect on the stability of weakly-ionized, magnetized planar shear flows. Employing a local approach similar to the shearing-sheet approximation, we solve for the evolution of linear perturbations in both streamwise-symmetric and non-streamwise-symmetric geometries using WKB techniques and/or numerical methods. We find that instability arises from the combination of shear and non-ideal magnetohydrodynamic processes, and is a result of the ability of these processes to influence the free energy path between the perturbations and the…
The stratification-driven Hall instability in a weakly ionized polytropic plasma is investigated in the local approximation within an equilibrium Keplerian disk of a small aspect ratio. The leading order of the asymptotic expansions in the aspect ratio is applied to both equilibrium as well as the perturbation problems. The equilibrium disk with an embedded purely toroidal magnetic field is found to be stable to radial, and unstable to vertical short-wave perturbations. The marginal stability surface is found in the space of the local Hall and inverse plasma beta parameters, as well as the fre…
The diffusion of uni-directional magnetic fields by two dimensional turbulent flows in a weakly ionized gas is studied. The fields here are orthogonal to the plane of fluid motion. This simple model arises in the context of the decay of the mean magnetic flux to mass ratio in the interstellar medium. When ions are strongly coupled to neutrals, the transport of a large--scale magnetic field is driven by both turbulent mixing and nonlinear, ambipolar drift. Using a standard homogeneous and Gaussian statistical model for turbulence, we show rigorously that a large-scale magnetic field can decay o…
Understanding the mechanism that drives accretion has been the primary challenge in accretion disk theory. Turbulence provides a natural means of dissipation and the removal of angular momentum, but firmly establishing its presence in disks proved for many years to be difficult. The realization in the 1990s that a weak magnetic field will destabilize a disk and result in a vigorous turbulent transport of angular momentum has revolutionized the field. Much of accretion disk research now focuses on understanding the implications of this mechanism for astrophysical observations. At the same time,…
Cool weakly ionized gaseous rotating disk, are considered by many models as the origin of the evolution of protoplanetary clouds. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Thus, a hierarchy of successive fragmentations into smaller and smaller pieces as a part of the Kant-Laplace theory of formation of the planetary system remains valid also for contemporary cosmogony. Traditionally, axisymmetric magnetohydrodynamic (MHD), and recently Hall-MHD instabilities have been thoroughly studied as providers of an effic…
Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and proto-stellar accretion discs for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics. Diffusive processes are known to restrict the stabili…
We calculate the proton distribution function due to heating by subsonic (Alfvenic) turbulence in a weakly magnetized collisionless plasma. The distribution function is nonthermal. For non-relativistic energies, it is an exponential of the magnitude of the proton velocity. For ultra-relativistic energies, it can be characterized as a power law with a momentum-dependent slope.
The Hall effect arises in a plasma when electrons are able to drift with the magnetic field but ions cannot. In a fully-ionized plasma this occurs for frequencies between the ion and electron cyclotron frequencies because of the larger ion inertia. Typically this frequency range lies well above the frequencies of interest (such as the dynamical frequency of the system under consideration) and can be ignored. In a weakly-ionized medium, however, the Hall effect arises through a different mechanism -- neutral collisions preferentially decouple ions from the magnetic field. This typically occurs …
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 n…
This Letter presents a calculation of the power spectra of weakly turbulent Alfven waves and fast magnetosonic waves ("fast waves") in low-beta plasmas. It is shown that three-wave interactions transfer energy to high-frequency fast waves and, to a lesser extent, high-frequency Alfven waves. MHD turbulence is thus a promising mechanism for producing the high-frequency waves needed to explain the anisotropic heating of minor ions in the solar corona.
(Shortened) Thermal instability of partially ionized plasma is investigated by linear perturbation analysis. According to the previous studies under the one fluid approach, the thermal instability is suppressed due to the magnetic pressure. However, the previous studies did not precisely consider the effect of the ion-neutral friction, since they did not treat the flow as two fluid which is composed of ions and neutrals. Then, we revisit the effect of the ion-neutral friction of the two fluid to the growth of the thermal instability. According to our study, (1) The instability which is charact…
Interaction of impulsively generated MHD waves with a one-dimensional plasma inhomogeneity, transverse to the magnetic field, is considered in the three-dimensional regime. Because of the transverse inhomogeneity, MHD fluctuations, even if they do not include initially any density perturbation, evolve toward states where the compressible components tend to become predominant. The propagating MHD pulse asymptotically reaches a quasi-steady state with the final levels of density perturbation weakly depending on the degree of non-planeness of the pulse in the homogeneous transverse direction and …
The self-sustained turbulence which develops in magnetized accretion disks is suppressed in the weakly-ionized, quiescent disks of close binary stars. Because accretion still proceeds during quiescence, another viscosity mechanism operates in these systems. An anticorrelation of the recurrence times of SU UMa dwarf novae with their mass ratio supports spiral waves or shock-waves tidally induced by the companion star as the main process responsible for accretion in the quiescent disks. Other weakly-ionized gaseous disks in systems lacking a massive companion have to rely on yet another transpor…
Under ideal MHD conditions the magnetic field strength should be correlated with density in the interstellar medium (ISM). However, observations indicate that this correlation is weak. Ambipolar diffusion can decrease the flux-to-mass ratio in weakly ionized media; however, it is generally thought to be too slow to play a significant role in the ISM except in the densest molecular clouds. Turbulence is often invoked in astrophysical problems to increase transport rates above the (very slow) laminar values predicted by kinetic theory. We describe a series of numerical experiments addressing the…
We investigate the interaction of magnetohydrodynamic waves with plasma density inhomogeneities. Our numerical study of the full MHD equations shows that: (A) Plasma density inhomogeneities are a source of non-linear generation of transverse compressive waves by a plane Alfven wave, and substantially enhance (by about a factor of 2) the generation of the longitudinal compressive waves. (B) Attained maximal values of the generated transverse compressive waves are insensitive to the strength of the plasma density inhomogeneity and the initial amplitude of the Alfven wave. (C) Efficiency of the g…
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field, and the coupling to compressional Alfvén waves. The gravitational waves are considered in the high frequency limit and the plasma is modelled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and el…
Radio-wave scintillation observations reveal a nearly Kolmogorov spectrum of density fluctuations in the ionized interstellar medium. Although this density spectrum is suggestive of turbulence, no theory relevant to its interpretation exists. We calculate the density spectrum in turbulent magnetized plasmas by extending the theory of incompressible MHD turbulence given by Goldreich & Sridhar to include the effects of compressibility and particle transport. Our most important results are as follows. (1) Density fluctuations are due to the slow mode and the entropy mode. Both modes are passively…
Two cases of weakly and strongly stressed X-point collapse were considered. Here descriptors weakly and strongly refer to 20 % and 124 % unidirectional spatial compression of the X-point, respectively. In the weakly stressed case, the reconnection rate, defined as the out-of-plane electric field in the X-point (the magnetic null) normalised by the product of external magnetic field and Alfvén speeds, peaks at 0.11, with its average over 1.25 Alfvén times being 0.04. Electron energy distribution in the current sheet, at the high energy end of the spectrum, shows a power law distribution with th…
We examine the effect of weak, small scale magnetic field structure on the rate of reconnection in a strongly magnetized plasma. This affects the rate of reconnection by reducing the transverse scale for reconnection flows, and by allowing many independent flux reconnection events to occur simultaneously. Allowing only for the first effect and using Goldreich and Sridhar's model of strong turbulence in a magnetized plasma with negligible intermittency, we find that the lower limit for the reconnection speed is the Alfven speed times the Lundquist number to the power (-3/16). The upper limit on…
The saturation mechanism of the Weibel instability is investigated theoretically by considering the evolution of currents in numerous cylindrical beams that are generated in the initial stage of the instability. Based on a physical model of the beams, it is shown that the magnetic field strength attains a maximum value when the currents in the beams evolve into the Alfven current and that there exist two saturation regimes. The theoretical prediction of the magnetic field strength at saturation is in good agreement with the results of two-dimensional particle-in-cell simulations for a wide ran…
We present a theoretical framework for plasma turbulence in astrophysical plasmas (solar wind, interstellar medium, galaxy clusters, accretion disks). The key assumptions are that the turbulence is anisotropic with respect to the mean magnetic field and frequencies are low compared to the ion cyclotron frequency. The energy injected at the outer scale scale has to be converted into heat, which ultimately cannot be done without collisions. A KINETIC CASCADE develops that brings the energy to collisional scales both in space and velocity. Its nature depends on the physics of plasma fluctuations.…
