Effect of Hall Current on the Magnetogravitational Instability of Anisotropic Plasma with Generalized Polytrope Law

The effect of Hall current on the propagation of small perturbations through self gravitating anisotropic collisionless pressure plasma with generalized polytrope law is investigated. The poly-trope law for pressure components parallel and perpendicular to the direction of magnetic field is utilized in the analysis. The effect of Hall current and finite conductivity is introduced in the generalized Ohm's law. Using the polytrope law and Ohm's law dispersion relations are obtained from linearized perturbation equations for wave propagation along and perpendicular to the direction of magnetic field. The dispersion relations incorporating polytrope indices are able to represent the Chew, Goldberger and Low approximation with double adiabatic equation of state for the anisotropic pressure and the magnetohydrodynamic set of equations with isothermal equation of state for the isotropic pressure. The effect of Hall current, finite conductivity and polytrope indices is discussed on the well known hose and gravitational instability. It is found that Jeans' criterion depends on polytrope indices and the condition of gravitational instability is determined for different special cases of interest.     

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.     

Influence of Finite Larmor Radius with Finite Electrical and Thermal Conductivities on the Gravitational Instability of a Magnetized Rotating Plasma Through a Porous Medium

An infinitely extending homogeneous, self-gravitating rotating magnetized plasma flowing through a porous medium has been considered under the influence of Finite Larmor Radius (FLR) and other transport phenomena. A general dispersion relation has been derived through the linearized perturbation equations. Longitudinal and transverse modes of propagation have been discussed for the rotation with axis parallel and perpendicular to the magnetic field. The joint influence, of the aforesaid parameters, does not essentially change the Jeans' criterion of instability but modifies the same. The adiabatic sonic speed has been replaced by the isothermal one due to the thermal conductivity. It is further observed that the FLR corrections have stabilizing effect for an inviscid, non-rotating plasma, in case of transverse propagation. Rotation decreases the Larmor radius, whereas the porosity reduces the effects of rotation, FLR, and the magnetic field. Viscosity removes the effects of both, the roation, and the FLR corrections.     

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.     

Assembling Stabilization of the R-T Instability by the Effects of Finite Larmor Radius and Sheared Axial Flow

In the present paper, based on the incomepressible finite Larmor radius （FLR） magnetohydrodynamic （ MHD ） equations, we consider the stabilizing effect of the finite Larmor radius on the Rayleigh-Taylor （ RT ） instability in implosions of annular Z-pinch plasma. Here, the FLR is considered as a type of viscositytll, independent of any collisions （i.e., collisionless viscosity, or gyrouiscosity ）. Since we are introducing a sheared velocity,     

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.     

Cathode Sheath Instability at Frequencies Near the Ion Plasma Frequency

We consider steady-state and nonstationary processes in a near-cathode region. Equations describing the plasma dynamics near a cathode at frequencies close to the ion plasma frequency are derived, and solutions of these equations for various zones of a discharge gap are found. A piecewise-uniform model of a cathode sheath is developed, which points out the possibility of an instability at a frequency slightly less than the near-cathode ion plasma frequency. The gas pressure effect on the instability threshold with respect to the discharge current is considered. The obtained results are in good agreement with the data of experimental studies of the cathode sheath in a hollow-cathode discharge.     

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.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion accoustic waves in a dust plasma with ion-dust collision effects is studied.Using the perturbation method,a modified nonlinear Schroedinger equation contains a damping term that comes from the effect of the ion-dust collision is derived.It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

Modulational Instability of Dust Ion Acoustic Waves in a Collisional Dusty Plasma

The modulational instability of dust ion acoustic waves in a dust plasma with ion-dust collision effects is studied. Using the perturbation method, a modified nonlinear Schrodinger equation contains a damping term that comes from the effect of the ion-dust collision is derived. It is found that the inclusion of the ion-dust collision would modify the modulational instability of the wave packet and could not admit any stationary envelope solitary waves.     

The Effect of Finite Larmor Radius on Gravitational Instability of a Finitely Conducting Magnetised Hall Medium in Presence of Suspended Particles

The problem of stability of a self-gravitating, infinite homogeneous gas in the presence of suspended particles is investigated. The medium is assumed conducting and effect of external magnetic field, Hall current and finite Larmor radius corrections are also considered. The equations of the problem are linearized and from linearized equations a general dispersion relation for a dusty gas-particle medium is obtained. The dispersion relation is reduced for two special cases of wave propagations: Parallel and perpendicular to the direction of uniform magnetic field. The effect of suspended particles on the medium is investigated in both the cases. It is found that in the presence of finite Larmor radius corrections and suspended particles the condition of instability is determined by Jeans's criterion for a self gravitating finitely conducting magnetised Hall medium.     

Short Wavelength Ion Temperature Gradient Driven Instability in Noncircular Flux Surface Plasmas with Finite Aspect Ratio

By employing the local equilibrium of shaped tokamak plasmas, a gyrokinetic model with integral eigenmode equations is developed to investigate effects of the finite aspect ratio and noncircular flux surface on short wavelength ion temperature gradient （SWITG） driven modes. It is found that when nonadiabatic electron and trapped particle effects are not considered, the SWITG mode can be stabilized by finite aspect ratio A, elongation and triangularity δ, and can be destabilized by the Shafranov shift gradient θRo/θr.     

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.     

Finite Larmor radius magnetohydrodynamic analysis of the ballooning modes in tokamaks

In this paper,the effect of finite Larmor radius (FLR) on high n ballooning modes is studied on the basis of FLR magnetohydrodynamic (FLR-MHD) theory.A linear FLR ballooning mode equation is derived in an ’s α’ type equilibrium of circular-flux-surfaces,which is reduced to the ideal ballooning mode equation when the FLR effect is neglected.The present model reproduces some basic features of FLR effects on ballooning mode obtained previously by kinetic ballooning mode theories.That is,the FLR introduces a real frequency into ballooning mode and has a stabilising effect on ballooning modes (e.g.,in the case of high magnetic shear s ≥ 0.8).In particular,some new properties of FLR effects on ballooning mode are discovered in the present research.Here it is found that in a high magnetic shear region (s ≥ 0.8) the critical pressure gradient (α c,FLR) of ballooning mode is larger than the ideal one (α c,IMHD) and becomes larger and larger with the increase of FLR parameter b 0.However,in a low magnetic shear region,the FLR ballooning mode is more unstable than the ideal one,and the α c,FLR is much lower than the α c,IMHD.Moreover,the present results indicate that there exist some new weaker instabilities near the second stability boundary (obtained from ideal MHD theory),which means that the second stable region becomes narrow.     

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.     

Numerical Simulation of Anisotropic Preheating Ablative Rayleigh-Taylor Instability

The linear growth rate of the anisotropic preheating ablative Rayleigh-Taylor instability （ARTI） is studied by numerical simulations. The preheating model κ （T）=κSH [1＋f（T）] is applied, where f（T） is the preheating function interpreting the preheating tongue effect in the cold plasma ahead of the ablative front. An arbitrary coefficient D is introduced in the energy equation to study the influence of transverse thermal conductivity on the growth of the ARTI. We find that enhancing diffusion in a plane transverse to the mean longitudinal flow can strongly reduce the growth of the instability. Numerical simulations exhibit a significant stabilization of the ablation front by improving the transverse thermal conduction. Our results are in general agreement with the theory analysis and numerical simulations by Masse [Phys. Rev. Lett. 98 （2007） 245001].     

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.     

Effects of Energetic Electrons on Collector and Source Potentials in a Finite Ion Temperature Plasma

Formation of the potential in a two-electron-temperature plasma region facing a floating collector was studied theoretically with a kinetic plasma-sheath model and by electrostatic particle simulation. The electrons were described by truncated full Maxwellian velocity distribution functions and the ions by an accelerated half-Maxwellian velocity distribution function. The collector potential and the plasma source sheath or presheath potential drop were evaluated as functions of the hot to cool electron temperature ratio and the hot electron density ratio using Vlasov and Poison equations. The results showed that the presheath potential drop varied continuously with electron composition ratio for lower values of the electron temperature ratio, while for higher values in a narrow composition ratio range, triple values of the potential were found. Of the two physically acceptable values, the lower was characterized by the cool electrons and the higher by the hot electrons. It is anticipated that a current-free double layer structure is formed in the plasma system between these two potential regions. The collector floating potential, as a function of electron composition ratio, is mainly dominated by the hot electrons, since already a small value of hot electron current is sufficient to compensate the ion saturation current. In order to complete the theoretical investigation we also study the hydrogen plasma system with the XPDP1 particule-in-cell simulation code composed at Berkeley. At certain plasma parameter values formation of a double layer structure was observed. The potential Values on the upper and lower side of the double layer, as well as that of the collector floating potential, corresponded very well to the calculated values. On the upper side the plasma was composed of ions, accelerated through the source sheath potential drop, and electrons consisting of cool full Maxwellian and hot truncated full Maxwellian populations. On the lower side only hot electrons and ions additionally accelerated through the double layer were found.     

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.