Gravitational Instability of a Rotating Viscous Thermally Conducting Plasma

This paper deals with the gravitational instability of an infinite homogeneous viscous rotating plasma of finite electrical conductivity in the combined presence of effects of Hall currents, finite Larmor radius (FLR) and thermal conductivity. The ambient magnetic field is assumed to be uniform and acting along the vertical direction. Both longitudinal and transverse modes of wave propagation have been studied. It is shown that Jean's criterion determines the gravitational instability even in the presence of the effects of thermal conductivity, viscosity, finite electrical conductivity, FLR, rotation and Hall currents. Further it is found that while FLR, viscosity and rotation have a stabilizing influence, both the thermal and the electrical conductivities have a destabilizing influence on the gravitational instability of a plasma.     

Magnetogravitational Instability of a Thermally Conducting Rotating Plasma through a Porous Medium

Magnetogravitational instability of an infinite homogeneous, viscous, thermally conducting, rotating plasma flowing through a porous medium has been studied with the help of relevant linearized perturbation equations, using the method of normal mode analysis. Rotation is taken parallel and perpendicular to the magnetic field for both, the longitudinal and the transverse modes of propagation. The joint influence of the various parameters do not, essentially, change the Jeans' criterion but modifies the same. The adiabatic velocity of sound is being replaced by the isothermal one due to the thermal conductivity. Porosity reduces the effects of both, the magnetic field and the rotation, in the transverse mode of propagation, whereas the rotation is effective only along the magnetic field for an inviscid plasma. The viscosity removes the effect of rotation in the transverse mode of propagation.     

Wave propagation in a rarefied plasma with finite Larmor radius

Wave propagation in a rarefied two-component plasma immersed in a uniform constant magnetic field has been discussed wherein the plasma pressure is assumed to be anisotropic owing to finite Larmor radius effect. It is shown that, for propagation along the external magnetic field, there exist two modes of wave propagation, namely, the gravitational mode and the hydromagnetic mode. The former is found to be independent of the magnetic field and hence of the Larmor radius, while the latter is appreciably influenced by the finite Larmor radius. On the other hand, for transverse propagation, there are three modes of wave propagation viz. the ion-sound mode, the electron-sound mode and the electromagnetic mode. It is shown that only the lowfrequency ion-sound mode is affected by the finite Larmor radius.     

Finite Larmor radius and Hall effects on thermal instability of a compressible plasma

The effects of compressibility, finite Larmor radius (FLR) and Hall currents are considered on the thermal instability of a plasma in the presence of a uniform horizontal magnetic field. For stationary convection, the compressibility has a stabilizing effect whereas FLR and Hall currents have stabilizing as well as destabilizing effects. For (C _pβ/g)<1, the system is stable. The magnetic field, FLR and Hall currents introduce oscillatory modes in the system for (C _pβ/g)>1.     

On the Gravitational Instability of an Ionized Magnetized Rotating Plasma Flowing Through a Porous Medium with other Transport Processes and the Suspended Particles

The effects of suspended particles and the finite thermal and electrical conductivities on the magnetogravitational instability of an ionized rotating plasma through a porous medium have been investigated, under varying assumptions of the rotational axis and the modes of propagation. In all the cases it is observed that the Jeans' criterion determines the condition of instability with some modifications due to various parameters. The effects of rotation, the medium porosity, and the mass concentration of the suspended particles on instability condition have been removed by (1) magnetic field for longitudinal mode of propagation with perpendicular rotational axis, and (2) viscosity for transverse propagation with rotational axis parallel to the magnetic field. The mass concentration reduces the effects of rotation. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one, whereas the effect of the finite electrical conductivity is to delink the alignment between the magnetic field and the plasma. Porosity reduces the effects of both the magnetic field and the rotation, on Jeans' criterion.     

Gravitational Instability of a Rotating Viscous Finitely Conducting Plasma

The gravitational instability of infinite homogeneous plasma has been studied to include simultaneously the effects of rotations, Hall currents, viscosity, finite electrical conductivity and the finite Larmor radius (FLR). Both the longitudinal, and transverse modes of wave propagation have been studied. It is found that the gravitational instability is determined by Jeans' criterion even in the presence of effects of rotation, Hall currents, FLR, viscosity and finite conductivity whether included separately or jointly.     

Finite Larmor radius effect on thermosolutal instability of a plasma in porous medium

The thermosolutal instability of a plasma in porous medium is considered in the presence of finite Larmor radius effect. The finite Larmor radius, stable solute gradient and magnetic field introduce oscillatory modes in the systems which were nonexistent in their absence. For stationary convection, the finite Larmor radius and stable solute gradient have stabilizing effects on the thermosolutal instability in porous medium. In presence of finite Larmor radius effect, the medium permeability has a destabilizing (or stabilizing) effect and the magnetic field has a stabilizing (or destabilizing) effect under certain condition whereas in the absence of finite Larmor radius effect, the medium permeability and the magnetic field have destabilizing and stabilizing effects, respectively, on thermosolutal instability of a plasma in porous medium. The sufficient conditions for nonexistence of overstability are obtained.The financial assistance to Mr. Sunil in the form of Senior Research Fellowship of the Council of Scientific and Industrial Research (CSIR), New Delhi is gratefully acknowledged.     

Thermosolutal Instability of a Rotating Plasma

The thermosolutal instability of a plasma is studied to include the effects of coriolis forces and the finiteness of ion Larmor Radius in the presence of transverse magnetic field. It is observed that the effect of rotation is destabilizing only in a typical case. However, the F. L. R. and stable solute gradient have stabilizing effects on stationary convection irrespective of the presence of coriolis forces.     

Cyclotron mechanism of electron acceleration in subpicosecond laser plasma

The effect of ultrastrong magnetic fields generated in a relativistic-intensity subpicosecond laser plasma on the acceleration of fast electrons was studied. It is shown that resonance electrons can continuously accumulate energy from the circularly polarized laser field in the presence of a longitudinal magnetic field. For the linear polarization and a transverse magnetic field, energy accumulation has a pulse-periodic character, and the electron trajectories correspond to electron rotation in the Larmor orbit in a quasi-stationary magnetic field, while the energy strongly oscillates. In both cases, electron energy may attain values higher than 100 MeV for intensities of 10²⁰ W/cm².     

Hydromagnetic Stability of a Self-Gravitating Composite Plasma in the Presence of Finite Larmor Radius

The hydromagnetic stability of a self-gravitating composite plasma has been studied to include the effects of ion viscosity and the finiteness of the ion Larmor radius. The whole medium is embedded in a uniform horizontal magnetic field. The F. L. R. effects have been included through the stress tensor. An explicit solution for a semi-infinite plasma of finite depth and with an exponential density variation along the vertical is obtained by means of a variational principle characterizing the problem. Numerical calculations show that the influence of the effects of ion viscosity and F. L. R. is to reduce the growth rate of unstable perturbations. On the other hand the effects of neutral gas collisions have been found to be both stabilizing as well as destabilizing.     

The Gravitational Instability of a Finitely Conducting Rotating Plasma Through a Porous Medium

The magneto-gravitational instability of an infinite homogeneous, finitely conducting, viscous rotating plasma through porous medium is investigated in view of its relevance to certain stellar atmospheres. The dispersion relation has been obtained from the relevant linearized perturbation equations of the problem and it has been discussed in the case of rotation parallel and perpendicular to the direction of magnetic field separately. The longitudinal and transverse modes of wave propagation are discussed in each case of rotation. It is found that the combined effect of viscosity, finite conductivity, rotation and the medium porosity does not essentially change the Jeans' criterion of gravitational instability. It is also shown that for the propagation transverse to the direction of magnetic field. the finite conductivity destabilizes the wave number band which is stable in the limit of infinite conductivity when the medium is considered inviscid.     

Magnetogravitational Instability of Anisotropic Plasma with Finite Ion Larmor and Generalized Polytrope Law

The effect of finite ion Larmor radius corrections on the propagation of small perturbations through self gravitating, anisotropic system with generalized polytrope law is investigated. The polytrope laws are considered for the pressure components in parallel and perpendicular directions to the magnetic field. The polytrope model proposed by Abraham-Shranuer can be reduced to CGL equations with double adiabatic equations of state and MHD set of equations with isothermal equation of state. The effects of FLR and polytrope indices are discussed on the gravitational, firehose and mirror instability. The critical Jeans wave numbers are found to depend on polytropic indices and derived for CGL and MHD cases. The FLR corrections are found effective in shorter wave length region and produce stabilizing influence. The condition of mirror instability is uninfluenced by FLR but dependent on polytropic indices.     

Hydromagnetic transverse instability of two highly viscous fluid-particle flows with finite ion Larmor radius corrections

A linear analysis of the combined effect of viscosity, finite ion Larmor radius and suspended particles on Kelvin-Helmholtz instability of two superposed incompressible fluids in the presence of a uniform magnetic field is carried out. The magnetic field is assumed to be transverse to the direction of streaming. A general dispersion relation for such a configuration has been obtained using appropriate boundary conditions. The stability analysis is discussed analytically, and the obtained results are numerically confirmed. Some special cases are recovered and corrected. The limiting cases of absence of suspended particles (or fluid velocities) and finite Larmor radius, absence of suspended particles are discussed in detail. In both cases, all other physical parameters are found to have stabilizing as well as destabilizing effects on the considered system. In the former case, the kinematic viscosity is found to has a stabilizing effect, while in the later case, the finite Larmor radius is found to has a stabilizing influence for a vortex sheet. It is shown also that both finite Larmor radius and kinematic viscosity stabilizations for interchange perturbations are similar to the stabilization effect due to a magnetic field for non-interchange perturbations. Received 13 January 2003 Published online 24 April 2003 RID="a" ID="a"Also at: Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt. e-mail: m.elsayed@uaeu.ac.ae     

Effect of Conductivity on Magneto-Gravitational Instability of a Medium with Finite Larmor Radius and Suspended Particles

The self-gravitational instability of an infinite homogeneous magnetised and finitely conducting gas-particle medium is considered to include the finite Larmor radius effect in the presence of suspended particles. The equations of the problem are linearized and from linearized equations a general dispersion relation for dusty-gas is obtained. The dispersion relations are also obtained for propagation, parallel and perpendicular to the direction of uniform magnetic field. The Jeans, criterion is discussed for these two different directions of wave propagation. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans' criterion for a self gravitating, finitely conducting, magnetized gas-particle medium.     

Magnetogravitational instability of a rotating homogeneous gas cloud with radiation

Magnetogravitational instability of an infinite, homogeneous rotating hot plasma cloud associated with radiative processes has been studied with the help of relevant MHD equations using normal mode analysis. Rotation is taken parallel and perpendicular to the magnetic field for both, the longitudinal and transverse modes of propagation. The Jeans espression of instability is modified to give the stabilizing effect of radiation pressure. The stabilizing effect of magnetic field is observed only for transverse mode of propagation whereas rotation stabilizes only along the magnetic field for transverse mode. The stabilizing effect of rotation is comparatively more effective.D. S. Vaghela gratefully acknowledges the financial assistance for his minor research project given by University Grants Commission of India.     

Finite Larmor radius effect on thermal instability of a compressible plasma

The thermal instability of a compressible plasma in the presence of a uniform vertical magnetic field is studied to include the effects of finiteness of the ion Larmor radius. When the instability sets in as stationary convection, both the compressibility and the finite Larmor radius are found to have stabilizing effect. The sufficient conditions for the nonexistence of overstability are investigated.     

Effects of Hall Currents and Gyroviscosity on the Instability of a Self-Gravitating Stratified Plasma

The instability in a horizontal layer of a partially ionized self gravitating plasma has been studied to include simultaneously the effects of Hall currents, viscosity and finiteness of Larmor radius (FLR). The ambient magnetic field is assumed to be uniform and vertical. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of unstable perturbations decreases with the effects of viscosity, neutral gas friction and FLR. The influence of effects of viscosity, neutral gas friction and FLR are consequently stabilizing. It is found that the Hall currents have a destabilizing influence as the growth rate is found to increase with this effect.     

Coaxial Discharge and Transverse Magnetic Field

The study deals with the effect of an applied transverse magnetic field on the dynamics and parameters of the focused and expanded plasma in a coaxial discharge. The experimental results were found with a 3 kJ Plasma focus device of a Mather geometry. The discharge takes place in hydrogen gas with base pressure of 0.5 Torr. The experiments are conducted with a 10 kV bank voltage, which corresponds to 100 kA peak discharge current with rise time 8 μs. Helmholtz magnetic coils are placed outside the expansions chamber to produce a transverse magnetic field with intensity 280 G perpendicular to the plasma expanded from the coaxial electrodes. The investigations have shown that the plasma flow along the expansion chamber axis is restricted when applying the externally transverse magnetic field and the maximum axial velocity of the expanded plasma is decreased by 33%. X-ray probe has been used to measure the focused plasma electron temperature (T_e). The experimental results and the calculations showed that T_e is decreased from 2.2 keV to 800 eV with the application of a transverse magnetic field. The expanded plasma electron temperature and density have been measured by an electric double probe, the results cleared that the expanded plasma electron temperature is decreased by 2.6 times while its density is increased by 9 times, when a transverse magnetic field is applied.     

Gravitational Instability of a Two-Component Viscous Plasma with Finite Conductivity Flowing Through a Porous Medium with Fir Corrections

The gravitational instability of a two component plasma is studied to include the simultaneous effects of collisions, gyroviscosity, finite conductivity, viscosity and porosity of the medium within the framework of two-fluid theory. From linearized equations of the system, using normal mode analysis, the dispersion relations for parallel and perpendicular directions to the magnetic field are derived and discussed. For longitudinal wave propagation it is found that the value of critical JEANS' wave number increases with increasing density and decreasing temperature of the neutral component. For transverse wave propagation the value of critical JEANS' wave number depends on gyroviscosity, ALFVÉN number, ratio of sonic speeds and densities of the two component and porosity of the medium. It is observed that the effect of magnetic field and porosity is suppressed by finite condutivity of the plasma and similarly the effect of gyroviscosity is removed by viscosity from JEANS' expression of instability. For both the directions instability is produced when the velocity perturbations are considered parallel to wave vector. The damping effect is produced due to collisional frequency, permeability of the porous medium and viscosity. The density of the neutral component and porosity of the medium tends to destabilize the system while an increased value of FLR corrections leads the system towards stabilization.     

Magnetogravitational Stability of Resistive Plasma through Porous Medium with Thermal Conduction and FLR Corrections

The problem of stability of self gravitating magnetized plasma in porous medium is studied incorporating electrical resistivity, thermal conduction and FLR corrections. Normal mode analysis is applied to derive the dispersion relation. Wave propagation is discussed for parallel and perpendicular directions to the magnetic field. Applying Routh Hurwitz Criterion the stability of the medium is discussed and it is found that Jeans' criterion determines the stability of the medium. Magnetic field, porosity and resistivity of the medium have no effect on Jeans' Criterion in longitudinal direction. For perpendicular direction, in case of resistive medium Jeans' expression remains unaffected by magnetic field but for perfectly conducting medium magnetic field modifies the Jeans' expression to show the stabilizing effect. Thermal conducitivity affects the sonic mode by making the process isothermal instead of adiabatic. Porosity of the medium is effective only in case of perpendicular direction to magnetic field for perfectly conducting plasma as it reduces the stabilizing effect of magnetic field. For longitudinal wave propagation, though FLR corrections have no effect on sonic mode but it changes the growth rate for Alfvén mode. For transverse wave propagation FLR corrections and porosity affect the Jeans' expression in case of nonviscous medium but viscosity of the medium removes the effect of FLR and porosity on Jeans' condition.