Thermal instability in a weakly ionized plasma

We revisit the problem of clump formation due to thermal instabilities in a weakly ionized plasma with the help of a linear perturbation analysis, as discussed by Nejad-Asghar & Ghanbari. In the absence of a magnetic field and ambipolar diffusion the characteristic equation reduces to the thermal instability described by Field. We derive the critical wavelengths, which separate the spatial ranges of stability and instability. Contrary to the original analysis of Nejad-Asghar & Ghanbari, perturbations with a wavelength larger than the critical wavelength destabilize the cloud. Moreover, the instability regime of isentropic perturbations is drastically reduced. Isobaric modes with real values of the critical wavelength appear only if the density dependence of the cooling rate is more pronounced than the temperature dependence. Isentropic modes arise only if the power of the density in the cooling rate is smaller than 1/2, which is not fulfilled for CO cooling. We find that ambipolar diffusion is not a dominating heating process in molecular gas.     

Magnetorotational instability in stratified, weakly ionized accretion discs

We present a linear analysis of the vertical structure and growth of the magnetorotational instability in stratified, weakly ionized accretion discs, such as protostellar and quiescent dwarf novae systems. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and is assumed to be constant with height.
We obtained solutions for the structure and growth rate of global unstable modes for different conductivity regimes, strengths of the initial magnetic field and coupling between ionized and neutral components of the fluid. The envelopes of short-wavelength perturbations are determined by the action of competing local growth rates at different heights, driven by the vertical stratification of the disc. Ambipolar diffusion perturbations peak consistently higher above the midplane than modes including Hall conductivity. For weak coupling, perturbations including the Hall effect grow faster and act over a more extended cross-section of the disc than those obtained using the ambipolar diffusion approximation.
Finally, we derived an approximate criterion for when Hall diffusion determines the growth of the magnetorotational instability. This is satisfied over a wide range of radii in protostellar discs, reducing the extent of the magnetic 'dead zone'. Even if the magnetic coupling is weak, significant accretion may occur close to the midplane, rather than in the surface regions of weakly ionized discs.     

The Balbus–Hawley instability in weakly ionized discs

MHD in protostellar discs is modified by the Hall current when the ambipolar diffusion approximation breaks down. Here I examine the Balbus–Hawley (magnetorotational) instability of a weak, vertical magnetic field within a weakly ionized disc. Vertical stratification is neglected, and a linear analysis is undertaken for the case in which the wavevector of the perturbation is parallel to the magnetic field.
The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel case if the Hall current is dominated by negative (positive) species. The less-unstable orientation is stable for χ ≲0.5, where χ is the ratio of a generalized neutral–ion collision frequency to the Keplerian frequency. The other orientation has a formal growth rate of the order of the Keplerian angular frequency even in the limit χ →0! In this limit the wavelength of the fastest-growing mode tends to infinity, so the minimum level of ionization for instability is determined by the requirement that a wavelength fit within a disc scaleheight. In the ambipolar diffusion case, this requires χ > v _A c _s; in the Hall case this imposes a potentially much weaker limit,         

Kelvin–Helmholtz instability in a weakly ionized layer

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.     

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.     

Whistler instability in anti-loss-cone plasma

Whistler mode can become unstable above electron cyclotron frequency, Ω in anti-loss-cone plasma observed beyond the plasmapause. The growth rate can be as high as 0.1 Ω.     

Hall effects on thermal hydromagnetic instability of a partially ionized medium

Thermal instability of a finitely conducting hydromagnetic composite medium is considered including the effects of Hall currents and the collisions with neutrals. The equilibrium magnetic field is assumed to be uniform and vertical. For stationary convection, the collissions have no effect, while the Hall currents are found to have a destabilizing effect on the thermal instability. It is further shown that whenM is finite andQ the asymptotic behaviours of the critical Rayleigh number, the critical wave number and the critical temperature gradient remain the same as those obtained by Chandrasekhar whereM is a nondimensional number which includes the Hall current effects andQ stands for the Chandrasekhar number.     

The role of Kelvin–Helmholtz instability in dusty and partially ionized outflows

We investigate the linear theory of Kelvin–Helmholtz instability at the interface between a partially ionized dusty outflow and the ambient material analytically. We model the interaction as a multifluid system in a planar geometry. The unstable modes are independent from the charge polarity of the dust particles. Although our results show a stabilizing effect for charged dust particles, the growth time-scale of the growing modes gradually becomes independent of the mass or charge of the dust particles when the magnetic-field strength increases. We show that growth time-scale decreases with increasing the magnetic field. Also, as the mass of the dust particles increases, the growth time-scale of the unstable mode increases.     

Two-stream instability in a collisionless plasma

This paper discusses the development of two-stream instability in a collisionless plasma. The plasma is described by velocity moments of Vlasov equation where heat flow tensor has been neglected. A dispersion relation for arbitrary propagation is derived for a collisionless electron fluid. Special cases of propagation parallel and perpendicular to the field lines are discussed. Growth rate is computed for parameters representative of the shear layers of solar wind at one AU. It is found that the shear layers are likely to be overstable.     

Thermal instability and transport effects in comets

The localized ion density depletion region observed at comet Halley can be understood in terms of a thermal instability of the cometary plasma due to the excitation of rotational and vibrational levels of water molecules. The electron energy losses due to these processes peak near 4000 K and at higher temperatures a localized cooling leads to the thermal instability due to the increased radiation loss. The resulting increase in recombination leads to the ion density depletion and the estimates for this depletion at comet Halley agree with the observations. The transport effects at the density depletion region due to the diffusion and thermal conductivity are found have time scales larger than the instability time scale and does not affect the formation of the depletion region.     

Thermal effects in the ultrarelativistic two-stream instability

The dispersion relation for longitudinal waves in a one-dimensional ultrarelativistic plasma is calculated. Analytical and numerical results for the growth rate and frequency of the two-stream instability are presented as a function of the energy spread in the denser stream when the dilute stream is cold. The case of energy spreads in both beams is investigated numerically: it is found that relatively small energy spreads in both streams can lead to suppression of the instability.     

Unstable kinetic Alfvén wave in partially ionized plasma

The stability of kinetic Alfven waves is discussed for a partially ionized plasma with a flux of ionizing electrons which balance the plasma particle losses. Accidental electromagnetic perturbations are shown to be unstable due to the energy change of ionizing electrons.     

Elemental diffusion and segregation processes in partially ionized solar plasma

Although diffusion is usually associated with equalizing of the chemical composition, the pressure and temperature gradients inside the Sun cause elemental diffusion segregation. While light hydrogen is flowing up to the solar envelope, helium and heavier elements are settling down to the core. The target of our simulation is an accurate estimation of the settling rate in solar plasma during the course of solar evolution. The rate of helium depletion in the envelope is a key parameter of the solar evolution and depends on position and conditions around the base of the convective mixing zone. The rate of heavy element settling is sensitive to the degree of ionization and interaction with the radiation flux. We estimate the effect of ion ionization on the settling rate for several heavy elements up to iron in the framework of the LTE assumption and the thermodynamic calculation according to SAHA-S EOS.     

Excitation of plasma waves by bodies moving in ionized atmosphere

A body moving in an ionized atmosphere acquires an electric charge through the processes of accretion of charged particles and emission of electrons by high energy photons. The moving charged body may then interact with the charged particles of the atmosphere and any pervading magnetic field to excite plasma waves. Of particular interest is the situation in which the body collects an ionized cloud in front of it. The motion of this ionized cloud in the atmosphere induces an electrostatic instability and causes a column of ionized gas to move ahead of the body. The electrostatic instability is conducive to the excitation of electrostatic oscillations which if already present are further enhanced. A magnetic field along the direction of motion assists in the formation of the ionized cloud. If the pervading magnetic field is of suitable weak strength, it may excite extraordinary electromagnetic waves. A pervading transverse magnetic field of suitable strength may cause the excitation of magnetohydrodynamic waves.     

The instability of two non-parallel plasma shells in quantum plasma

The instability of two non-relativistic non-parallel electron-proton plasma shells in quantum plasma is investigated when the perturbation wave propagates perpendicular to the direction of one of the shells. It is assumed that the ions are not affected by the perturbation. The full three-dimensional dispersion tensor is derived by the fluid-Maxwell equations and the dispersion equation has been solved numerically. It is shown that two kinds of instability, the two-stream instability and the filamentation instability, may occur in the system. The effects of the angle between two plasma shells on the growth rate of instabilities and the cut-off wave number have been illustrated.     

Current-driven dust-acoustic instability in a collisional plasma

The excitation of the dust-acoustic instability in a collisional dusty plasma is investigated. For conditions similar to those of recent laboratory experiments with neutral gas pressures of 100mTorr, it is found that zero-order electric fields E₀ 10 Vm⁻¹ are sufficient for the growth of perturbations with centimeter wavelengths. Much larger wavelengths generally require larger values of E₀. Free electrons in the dusty plasma have a stabilizing effect, which can be very pronounced at the longest wavelengths.