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.     

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 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 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.     

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.     

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     

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.     

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.     

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.     

Jeans' gravitational instability of a thermally conducting plasma

The gravitational instability of an infinitely extending homogenous plasma endowed with several physical mechanisms, namely Hall currents, finite conductivity, ion viscosity and thermal conductivity is considered. The main result is that the various parameters play different physical roles in the perturbed problem. Jeans' criterion is analyzed in the framework of Tsallis' statistics for possible modifications due to the presence of nonextensive effects. A simple generalization of the Jeans' criterion is obtained and the standard values are obtained in the limiting case q=1, q being the nonextensive parameter.     

Some moments method of solving the Boltzmann equation

An approximate method to obtain time dependent solutions of the Boltzmann equation (BE) is proposed. Here we restrict our consideration to the homogeneous BE only. Approximate evolution equations for mean values are formulated.The work was supported by the Polish Ministry of Science, Higher Education and Technology, Project M.R.I.7     

Nuclear charge radius,spin and nuclear moments of45Ca by laserspectroscopy

The mean square charge radius, the spin, the magnetic moment and the quadrupole moment of the⁴⁵Ca nucleus have been determined from the isotope shift in the Ca- intercombination line and from the hyperfine structure splitting of the 4s4p³P₁. state. A highly sensitive laserspectroscopic technique in combination with an atomic beam was used in the experiment.     

The RMS charge radius of the proton and Zemach moments

On the basis of recent precise measurements of the electric form factor of the proton, the Zemach moments, needed as input parameters for the determination of the proton rms radius from the measurement of the Lamb shift in muonic hydrogen, are calculated. It turns out that the new moments give an uncertainty as large as the presently stated error of the recent Lamb shift measurement of Pohl et al. De Rújula's idea of a large Zemach moment in order to reconcile the five standard deviation discrepancy between the muonic Lamb shift determination and the result of electronic experiments is shown to be in clear contradiction with experiment. Alternative explanations are touched upon.     

Direct quadrature method of moments solution of the Fokker–Planck equation

The direct quadrature method of moments is presented as an efficient and accurate means of numerically computing solutions of the Fokker–Planck equation corresponding to stochastic nonlinear dynamical systems. The theoretical details of the solution procedure are first presented. The method is then used to solve Fokker–Planck equations for both 1D and 2D (noisy van der Pol oscillator) processes which possess nonlinear stochastic differential equations. Higher-order moments of the stationary solutions are computed and prove to be very accurate when compared to analytic (1D process) and Monte Carlo (2D process) solutions.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.     

Unified boundary integral equation for the scattering of elastic and acoustic waves: solution by the method of moments

A unified boundary integral equation (BIE) is developed for the scattering of elastic and acoustic waves. Traditionally, the elastic and acoustic wave problems are solved separately with different BIEs. The elastic wave case is represented in a vector BIE with the traction and displacement vectors as unknowns whereas the acoustic wave case is governed by a scalar BIE with velocity potential or pressure as unknowns. Although these two waves can be unified in the form of a partial differential equation, the unified form in its BIE counterpart has not been reported. In this work, we derive the unified BIE for these two waves and then show that the acoustic wave case can be derived from this BIE by introducing a shielding loss for small shear modulus approximation; hence only one code needs to be maintained for both elastic and acoustic wave scattering. We also derive the asymptotic Green's tensor for zero shear modulus and solve the corresponding vector equation. We employ the method of moments, which has been widely used in electromagnetics, as a numerical tool to solve the BIEs involved. Our numerical experiments show that it can also be used robustly in elastodynamics and acoustics.