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.     

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.     

Modeling the onset of thermosolutal convective instability in a non-Newtonian nanofluid-saturated porous medium layer

The onset of double-diffusive (thermosolutal) convection in horizontal porous layer saturated with an incompressible couple stress nanofluid saturated is studied with thermal conductivity and viscosity dependent on the nanoparticle volume fraction. To represent the momentum equation for porous media, a modified Darcy-Maxwell nanofluid model incorporating the effects of Brownian motion and thermophoresis has been used. The thermal energy equation includes regular diffusion and cross diffusion (Soret thermo-diffusion and Dufour diffuso-thermal) terms. A linear stability analysis depends on the normal mode technique and the onset criterion for stationary and oscillatory convection is derived analytically. The nonlinear theory based on the representation of the Fourier series method is applied to capture the behavior of heat and mass transfer. It is found that the couple stress parameter enhances the stability of the system in both the stationary and oscillatory convection modes. The viscosity ratio and conductivity ratio both enhance heat and mass transfer. Transient Nusselt number is found to be oscillatory when time is small. However, when time becomes very large, all the three transient Nusselt number values approach to their steady state values.     

Hall effects on thermosolutal instability of a rotating plasma

Summary The thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of Hall current. When the instability sets in as stationary convection for the case of no rotation, the Hall effects are found to be destabilizing. The stable solute gradient and rotation are found to have stabilizing effects. In the presence of rotation the Hall currents are found to be stabilizing forT ₁>M(1+x)². the case of overstability is also considered and it is shown that such solutions exist. The variation of the frequency with respect to the wave number at the neutral state is graphically shown. The authors of this paper have agreed to not receive the proofs for correction.     

Thermosolutal instability in porous medium in a partially ionized plasma

The thermosolutal instability in porous medium in a partially ionized plasma in the presence of a uniform vertical magnetic field is considered. The presence of each, magnetic field and stable solute gradient, brings oscillatory modes which were nonexistent in their absence. The collisional effects may also bring in oscillatory modes. The stable solute gradient and magnetic field are found to have stabilizing effect whereas the medium permeability and collisional frequency have destabilizing effect on the thermosolutal instability in porous medium.     

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.     

The ion Larmor radius effects on the interchange instability in a sheared magnetic field

The localized interchange instability in a low β collisionless plasma is studied as an eigenvalue problem in the presence of magnetic shear. It is found that while shear is always stabilizing, the ion Larmor radius effects become destabilizing if the shear exceeds a certain value.     

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.     

The instability of fronts in a porous medium

We use a random choice numerical method to analyze the instability of a front separating two fluids in a porous medium. We observe a linear instability and a catastrophic finite amplitude instability. A qualitative analogy with problems involving a transition to turbulence is pointed out.     

Mikhailovsky's finite Larmor radius effects and gravitational instability of plasma,treated by method of moments of Boltzmann-Vlasov equation

The effect of the stabilization of the gravitational instability of a hot rarefied plasma by the finite Larmor radius, established by Rosenbluth, Krall and Rostocker with the aid of the collisionless Boltzmann-Vlasov equation, was later derived by several authors from the magnetohydrodynamic equations modified by terms describing the magnetic viscosity of the plasma. It is shown in this paper that even the effect of the disappearance of this stabilization at very low plasma density, as found by Mikhailovsky, may be derived from the two-fluid macroscopic equations (the method of moments of the Boltzmann-Vlasov equation) using a very simple iterative procedure in which directly figures the so-called effective electric field of perturbation employed by some authors for physical interpretation of the effects of the finite Larmor radius.     

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     

Hydromagnetic instability of streaming fluids in porous medium

The instability of the plane interface between two uniform, superposed, electrically conducting and counter-streaming fluids through a porous medium is considered in the presence of a horizontal magnetic field. In the absence of surface tension, perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming if perturbations in the direction of streaming are ignored. For perturbations in all other directions there exists instability for a certain wavenumber range. The instability of this system is postponed by the presence of magnetic field. The magnetic field and surface tension are able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations and the medium porosity reduces the stability range given in terms of a difference between the streaming velocities and the Alfvén velocity.This research forms a part of the research project awarded to the first author (R.C.S.) by the University Grants Commission.     

Effects of finite larmor radius and variable gravitational field on thermal instability of fluid layer under rotation in porous medium

The effect of finite Larmor radius, magnetic field, rotation and variable gravitational field on thermal instability of fluid layer in porous medium is investigated. It is found that the principle of exchange of stability is valid in the absence of magnetic field and rotation. The system is stable/unstable depending upon certain conditions in the presence of rotation, magnetic field and medium permeability. The system is stable in presence of finite Larmor radius. The above work has been carried out under research project financed by University Grants Commission New Delhi (India) and the authors are grateful to University Grants Commission for their financial support.     

The onset of Darcy-Brinkman thermosolutal convection in a horizontal porous media

On the basis of Brinkman model, the onset of double-diffusive (thermosolutal) convection with a reaction term in a horizontal sparsely packed porous media is studied using the normal mode analysis. The effects of Brinkman term, the reaction term, the normalized porosity ε and Lewis number Le on the Rayleigh number for stationary and oscillatory case are presented graphically. The Darcy number destabilize the system in case of both stationary and oscillatory mode. The effects of Lewis number and reaction term depend on the value of the values of solutal Rayleigh number. Furthermore, some results of Darcy model can be recovered in limit cases.     

Computation of the dielectric tensor of a magnetized maxwellian plasma in the case of large Larmor radius effects

Summary It is shown how to deduce an asymptotic form of the Gordeev dispersion function of a Maxwellian plasma in a magnetic field, in the limit in which the Larmor radius parameter approaches infinity on the complex plane. This asymptotic form is necessary in the numerical computation of the elements of the plasma dielectric tensor in all physical circumstances characterized by large Larmor radius effects.     

Influences of finite Larmor radius on wake effects and stopping power for proton moving in magnetized two-component plasma

Considering finite Larmor radius (FLR) effects, wake effects and stopping power induced by proton projectile in two-component magnetized plasma are investigated within a linear response framework. Numerical results show that, FLR lessens wake effects and stopping power, essentially through excitation of collective plasma electron modes.