Magnetogravitational instability of a finitely-conducting medium with variable streaming motion

A discussion of gravitational instability of a finitely conducting medium with streams of variable velocity distribution is made in the presence of a uniform magnetic field. It is found that the variable streaming motion shows a destabilizing effect and affects the instability criterion only in the case of general wave propagation. For purely parallel propagation to the direction of the magnetic field and the streaming motion, the criterion is independent of the variation in the streaming motion and further the Jeans's criterion is found to remain unaffected in this case. For purely transverse propagation, the criterion is independent of any streaming motion and the Jeans's criterion remains unaffected. The criterion is further independent of the magnetic field and the finite conductivity except in the case of transverse propagation where the magnetic field exhibits a stabilizing influence in case of an infinitely conducting medium.     

Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids

The Kelvin-Helmholtz discontinuity in two superposed viscous conducting fluids has been investigated in the presence of a two-dimensional horizontal uniform magnetic field. The streaming motion is also assumed to be two-dimensional. The stability analysis has been carried out for two highly viscous fluids of uniform densities. It is found that the streaming motion has dual influence on the unstable system, destabilizing for low values of streaming velocity and stabilizing for high values of streaming velocity. The effect of viscosity is, however, found to be stabilizing as the growth rate of the unstable configuration decreases on increasing the viscosity.     

Nonaxisymmetric magnetogravitational instability of a streaming fluid cylinder ambient with a tenuous medium pervaded by transverse varying fields

The stability of a self-gravitating streaming fluid cylinder acting upon the electromagnetic force ambient with a tenuous medium of negligible inertia but pervaded by a transverse varying fields, has been developed. The stability criterion is derived, discussed analytically and the results are verified numerically. The cylinder is purely self-gravitating unstable in small axisymmetric domain and stable in all the rest states. modes while the transverse field exterior the cylinder is stabilizing or destabilizing according to restrictions in the asymmetric modes and purely destabilizing in the symmetric one. The streaming has a strong destabilizing influence and that influence is independent of the kind of the perturbation and wavelengths. Both the streaming and the electromagnetic influences increase the gravitational axisymmetric unstable domain and shrink those of stability in the axisymmetric and non-axisymmetric perturbations. Moreover, the stabilizing character of the Lorentz force of some states, is physicaly interpreted, will not be able to suppress the gravitational instability because the gravitational instability of sufficiently long waves will persist.     

On the gravitational instability of a medium in non-uniform rotation and magnetic field

The effect of a non-uniform magnetic field on the gravitational instability for a non-uniformly rotating, infinitely extending axisymmetric cylinder in a homogeneous medium has been studied. The Bel and Schatzman criterion of gravitational instability for a non-uniformly rotating medium is modified under the effect of a non-uniform/uniform magnetic field acting along the tangential and axial directions. As a consequence the stabilizing and destabilizing effect of the non-uniform magnetic field is obtained, a new criterion for the magneto-gravitational instability is deduced in terms of Alfven’s wave velocity; and it is also found that the Jeans criterion determines the gravitational instability in the absence of rotation and when the non-uniform/uniform magnetic field acts along the axis of the cylinder.     

Stability of a compressible fluid cylinder ambient with a bounded conducting medium under general varying magnetic fields

The stability of a compressible fluid cylinder pervaded by a longitudinal uniform magnetic field-ambient with a bounded conducting medium of negligible inertia penetrated with general varying vacuum magnetic fields has been developed. The stability criterion describing the stability characteristics of that model is derived and discussed analytically in general terms. The axial fields have always stabilizing influences. The azimuthal vacuum field has a destabilizing effect, however, it becomes minimal if the perturbed and the unperturbed vacuum fields are not orthogonal. The magnetodynamic instability of the fluid jet is modified in the presence of the fluid compressibility. The stabilizing influence due to the latter may be realized more clearly on utilizing the numerical methods for investigating the eigenvalue relation.Several reported works can be recovered as limiting cases with appropriate simplifications.     

Magnetodynamic stability of a fluid cylinder under the lundquist force-free magnetic field

The magnetodynamic (in)stability of a conducting fluid cylinder subject to the capillarity and electromagnetic forces has been developed. The cylinder is pervaded by a uniform magnetic field but embedded in the Lundquist force-free varying field that allows for flowing a current surrounding the fluid. A general eigenvalue relation is derived based on a study of the equilibrium and perturbed states. The stability criterion is discussed analytically in general terms. The surface tension is destabilizing for small axisymmetric mode and stable for all others. The principle of the exchange of stability is allowed for the present problem due to the non-uniform behaviour of the force-free field. Each of the axial and transverse force-free fields separately exerts a stabilizing influence in the most dangerous mode but the combined contribution of them is strongly destabilizing. Whether the model is acted upon the electromagnetic force (with the Lundquist field) the stability restrictions or/and the capillarity force are identified.Several reported works can be recovered as limiting cases with appropriate simplifications.     

A numerical study of the unsteady MHD free convection with hall current

Effect of Hall current on the hydromagnetic free-convection flow of an electrically-conducting viscous incompressible fluid past an impulsively accelerated vertical porous plate in the presence of a uniform transverse magnetic field subjected to a constant transpiration velocity is analyzed for the case of small magnetic Reynolds number. Numberical solutions are obtained for the axial and transverse components of the velocity as well as the skin-friction by employing the Crank-Nicolson implicit finite-difference method for all probable values of the Prandtl number. The results are discussed with the effects of the Grashof number Gr, the transpiration velocity parameter , the Hall current parameterm, and the magnetic field parameterM for the Prandtl number Pr=0.71 which represents air at 20° C.     

Kelvin-Helmholtz instability of two viscous superposed rotating and conducting fluids

Kelvin-Helmholtz instability of the interface separating two viscous rotating-conducting fluids has been studied in the presence of finite ion-Larmor radius (FLR) effects. Emloying the normal mode technique, the solutions have been obtained when the fluids are assumed to be permeated by a uniform horizontal magnetic field. For the case of two highly viscous fluids, the dispersion relation has been derived and solved numerically. It is found that the streaming velocity has a stabilizing influence on the potentially unstable arrangement of the fluids. The viscosity and FLR effects are also found to have a stabilizing influence while the Coriolis forces have a destabilizing influence on the system.     

Interstellar turbulent magnetic field generation by plasma instabilities

The maximum magnetic field strength generated by Weibel-type plasma instabilities is estimated for typical conditions in the interstellar medium. The relevant kinetic dispersion relations are evaluated by conducting a parameter study both for Maxwellian and for suprathermal particle distributions showing that micro Gauss magnetic fields can be generated. It is shown that, depending on the streaming velocity and the plasma temperatures, either the longitudinal or a transverse instability will be dominant. In the presence of an ambient magnetic field, the filamentation instability is typically suppressed while the two-stream and the classic Weibel instability are retained.     

Studies on some properties of coronal mass ejections based on angular width

The paper investigates the effects of thermal conductivity and non-uniform magnetic field on the gravitational instability of a non-uniformly rotating infinitely extending axisymmetric cylinder in a homogeneous heat conducting medium. The non-uniform rotation and magnetic field are supposed to act along θ and z directions of the cylinder. It is found that the gravitational instability of this general problem is determined by the same criterion as obtained by Dhiman and Dadwal (Astrophys. Space Sci. 325(2):195–200, 2010) for the self-gravitating isothermal medium in the presence of non-uniform rotation and magnetic field with the only difference that adiabatic sound velocity is now replaced by the isothermal sound velocity. It is found that the thermal conductivity has stabilizing effect on the onset of gravitational instability. Further, the stabilizing/destabilizing effect of the non-uniform magnetic field on the gravitational instability of heat conducting medium has been discussed and is illustrated by considering some special forms of the basic magnetic fields.     

Magnetohydrodynamic oscillation of a gas jet of zero inertia dispersed in a resistive liquid with energy conservation

The dynamical oscillation and instability of a gas cylinder of zero inertia immersed in a resistive liquid has been developed for symmetric perturbations. In the absence of the magnetic field we have used the conservation of energy to study such problem for all symmetric and asymmetric perturbations. In the latter it is found that the temporal amplification is much lower than that of the full fluid jet. The model is capillary stable for all short and long wavelengths in the asymmetric perturbation while in the symmetric disturbances it is stabilizing or not according the perturbed wavelength is shorter than the gas cylinder circumference or not. The resistivity is stabilizing or destabilizing according to restrictions. The electromagnetic body force is stabilizing for all wavelengths in the rotationally-symmetric disturbances. The Lorentz body force, for high magnetic field intensity, could be suppressing the destabilizing character of the present model. This may be due to the fact that the acting magnetic field is uniform and that the fluid is considered to be incompressible.     

Magnetogravitational instability of an infinite homogeneous rotating plasma through a porous medium with finite electrical and thermal conductivities

The gravitational instability of an infinite homogenous rotating plasma through a porous medium in the presence of a uniform magnetic field with finite electrical and thermal conductivities has been studied. With the help of relevant linearized perturbation equations of the problem, a general dispersion relation is obtained, which is further reduced for the special cases of rotation, parallel and perpendicular to the megnetic field acting in the vertical direction. Longitudinal and transverse modes of propagation are discussed separately. It is found that the joint effect of various parameters is simply to modify the Jeans's condition of instability. The effect of finite electrical conductivity is to remove the effect of magnetic field where as the effect of thermal conductivity is to replace the adiabatic velocity of sound by the isothermal one. Rotation has its effect only along the magnetic field in the transverse mode of propagation for an inviscid plasma, thereby stabilizing the system. Porosity reduces the effect of both, the magnetic field and the rotation, in the transverse mode of propagation in both the cases of rotation. The effect of viscosity is to remove the rotational effects parallel to the magnetic field in the transverse mode of propagation.     

Hydromagnetic stability of some non-dissipative flows subject to non-axisymmetric disturbances

We study the linear stability of nondissipative flow of an electrically conducting fluid subject to non-axisymmetric disturbances in the following cases: (i) the radial flow of an incompressible fluid between two concentric porous circular cylinders in the presence of a radial magnetic field and (ii) axial flow of a compressible fluid between two concentric circular cylinders permeated by a helical magnetic field (0,B ₀(r),B _0z) in a cylindrical coordinate system. It is shown that in case (i), the flow is stable if the Alfvén velocity based on the undisturbed radial magnetic field exceeds the radial velocity due to suction or injection at the cylinder surfaces. In case (ii), it is found that under certain conditions the complex wave speed for an unstable mode lies within a circle of diameterW _max-W _min, whereW _max andW _min are the maximum and minimum values of the axial velocity in the flow region. In the presence of a purely axial magnetic field, however, the complex wave speed for an unstable mode always lies within the above circle.     

The influence of momentum addition on the acceleration of the solar and stellar winds

The influence of the momentum addition, which may be associated with the average or fluctuation transverse component of the magnetic field or others, on the acceleration the solar wind or stellar wind is studied in a local streamtube. The results show that the larger the momentum addition the stronger the acceleration of the wind. For example, if the typical transverse magnetic field is about 0.1 of the longitudinal field, the velocity of the solar wind at 1 AU may be increased by 40%. The coronal hole may be considered as a streamtube, the presence of a high stream from the coronal hole may be explained by the existence of an average or fluctuation transverse magnetic field in the streamtube. A similar conclusion may be applied to the polar region, where the velocity of the solar wind will be larger than elsewhere as if there is a transverse component of magnetic field, as well as to the stellar wind. The influence of other parameters on the acceleration of the solar wind is also discussed. From the viewpoint of the solar wind mechanism, the present paper shows that the momentum addition in the subsonic flow region can increase the velocity of the solar wind at 1 AU.     

VLF emissions and substorm activity

The resonant interaction between the whistler mode waves and the energetic electrons near the plasmapause boundary has been studied in the presence of field aligned currents which seem to exist during substorm activity. It is shown that the electrons which carry the current along the direction of the magnetic field enhance the whistler mode growth considerably if the streaming velocity is small compared to the phase velocity of the wave. It is likely that this is one of the mechanisms explaining the intense VLF emissions observed near the plasmapause during substorm activity.     

Larmor radius effects on the instability of a rotating layer of a self-gravitating plasma

The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.     

Evolution of filamentary molecular clouds in the presence of magnetic fields

The purpose of this paper is to explore the effect of magnetic fields on the dynamics of magnetized filamentary molecular clouds.We suppose there is a filament with cylindrical symmetry and two components of axial and toroidal magnetic fields.In comparison to previous works,the novelty in the present work involves a similarity solution that does not define a function of the magnetic fields or density.We consider the effect of the magnetic field on the collapse of the filament in both axial and toroidal directions and show that the magnetic field has a braking effect,which means that the increasing intensity of the magnetic field reduces the velocity of collapse.This is consistent with other studies.We find that the magnetic field in the central region tends to be aligned with the filament axis.Also,the magnitude and the direction of the magnetic field depend on the magnitude and direction of the initial magnetic field in the outer region.Moreover,we show that more energy dissipation from the filament causes a rise in the infall velocity.     

Nonlinear simulations of magnetic Taylor‐Couette flow with currentfree helical magnetic fields

Themagnetorotational instability (MRI) in cylindrical Taylor‐Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (10⁶) (axial field only) to O (10³) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ∼50 Gauss and axial current ∼4 kA for the toroidal field. It is sufficient that the vertical velocity u_z of the flow can be measured with a precision of 0.1 mm/s.We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hall effects on MHD free-convection flow in the Stokes problem for a vertical porous plate

Hall effects on the MHD flow of an incompressible, electrically-conducting viscous fluid past an impulsively started infinite vertical porous plate has been analysed for the case of small magnetic Reynolds number. Exact solutions have been obtained for the axial and the transverse components of the velocity and the skin-friction by defining a complex velocity with the help of the Laplace transform technique. The velocity profiles are shown graphically and the numerical values of axial and transverse components of skin-friction are tabulated for different values of the dimensionless parameters occurring into the problem.     

Rayleigh-Taylor instability of a two-fluid layer under a general rotation field and a horizontal magnetic field

In this paper the Rayleigh-Taylor instability (RTI) of a two-fluid layer system under the simultaneous action of a general rotation field and a horizontal magnetic field is presented. An approximate and an exact solution of the eigenvalue equation are calculated. These solutions are important not only to understand more deeply the physical problem but also to determine the correct numerical solutions. Numerical calculations are done for an unstable density stratification in the cases of horizontal magnetic field parallel and perpendicular to the horizontal component of the angular velocity. For an adverse density stratification, it is shown that in comparison to previous works, the horizontal magnetic field creates new angular areas (of the angle of propagation of the perturbation) at which the perturbation is stable and propagates as traveling waves. It is also shown that the vertical component of the angular velocity has a destabilizing effect because it works to eliminate the stable angular areas.