Oscillations of a polytrope with a toroidal magnetic field

The radial and the non-radial (l=2) modes of oscillation of a gaseous polytrope with a toroidal magnetic field are examined using a variational principle. It is found that the frequencies of oscillation of the radial mode and the Kelvin mode (l=2) decrease due to the presence of the magnetic field. The shift in the frequency of the Kelvin mode may be split up into two parts, viz. the shift in frequency due to the magnetic field on the unperturbed sphere [(1²)m, say] and the shift in frequency due to the distortion of the structure by the magnetic field [(1²)s, say]. In the first order calculations using one parameter trial function, it is found that (1²)m is indeed positive but is overweighed by a negative (1²)s. In the second order calculations using a trial function with two variational parameters, we find that the general behaviour of (1²)m and (1²)s is unchanged but that (1²)m becomes negative for polytropic indicesn1.5.In Appendix I we study the effect of a small rotation and toroidal magnetic field on the structure of a polytrope. It is found that the resulting configuration is a prolate spheroid, a sphere or an oblate spheroid according as respectively. Here denotes the magnetic energy andT the kinetic energy due to rotation andq is a constant which depends on the polytropic indexn. The values ofq are given in Table I.     

Oscillations of a self-gravitating fluid spheroid with prevalent magnetic field

The Kelvin modes of oscillation of a selfgravitating, homogeneous fluid spheroid in hydrostatic equilibrium with a poloidal magnetic field inside and a dipole type field outside, are studied, using a variational principle. On the assumption that the eccentricitye of the spheroid is small, the frequencies of oscillation are calculated to the first order ine ².     

Pair production in a strong time-depending magnetic field: The effect of a strong gravitational field

We present the calculation of the probability production of an electron–positron pair in the presence of a strong magnetic field with time-varying strength. The calculation takes into account the presence of a strong, constant and uniform gravitational field in the same direction of the magnetic field. The results show that the presence of the gravitational field in general enhances very much the production of pairs. In particular, high-energy pairs are more likely produced in the presence of the gravitational field than in Minkowski spacetime.     

Freezing-in condition a magnetic field and current sheets in plasma

In the ideal magnetohydrodynamic approximation it is shown that for physically permissible boundary conditions there may exist some lines on which freezing-in condition is not valid. Such singular lines are closed magnetic lines of force and lines with both ends on the boundary surface. By analogy with the singular lines of a potential magnetic field the conclusion is made that X-type singular lines are the place where current sheets (sheet pinches) appear in plasma, whereas on O-type singular lines quasi-cylindrical pinches of a usual type appear.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Stability of thermally conducting plasma in a variable magnetic field

The flow of an infinitely extending homogenous thermally conducting plasma permeated by a variable magnetic field is considered. The combined effect of several physical parameters, namely Hall currents, finite conductivity, ion viscosity and thermal conductivity on plasma instability is studied in the framework of Tsallis statistics. A new Jeans Criterion is derived, which depends explicitly on the nonextensive parameter q. The standard values are obtained in the limiting case q=1.     

Rayleigh instability of compressible plasma in a vertical magnetic field

A study of the Rayleigh instability of a compressible plasma of density stratified in horizontal planes and subjected to a vertical magnetic field is made. The special case of a plane interface separating two superposed uniform plasmas of different densities and speeds of sound is treated as an example to illustrate the compressibility effects on the hydromagnetic Rayleigh instability. It is found that the hydromagneticcompressibility effects act toward reducing the growth rate in a hydrodynamically unstable situation.     

Nonlinear waves in a low-density plasma with a strong magnetic field

The nonlinear evolution of waves in a low-density plasma in a strong magnetic field is investigated on the basis of the Chew-Goldberger-Low approximation. The nonlinear effects are found to be essentially different for the magneto-acoustic and Alfvén modes. For the magnetic-acoustic mode, waveform distortion occurs at order ² (where is a measure of the linear wave amplitude) and shock formation occurs over a time-scale of order ^–1. For the Alfvén wave, modulation occurs at order ³ and shock formation over a time-scale of order ^–2. The nature of the waveform distortion is qualitatively different for the two modes.     

The gravitational field of a disk

This note gives the gravitational potential of the disk {(x, y, z):x ² +y ² p ² , z=0} and the gravitational field at the point (x, y, z). Formulas for a ring can be obtained as the difference of our results for two different values ofp. Results are obtained in terms of elliptic integrals and we indicate how these functions can be computed efficiently. Formulas necessary for the computation of partial derivatives are also given.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS7-100, sponsored by the National Aeronautics and Space Administration.     

Propagation of light in a Maxwell-like gravitational field

We propose a coupling between the gravitational and electromagnetic fields so that we consider the electrodynamical Maxwell's equations as the basic ones and add the four-vector of gravitational potential to the differential operators occurring in it. It is shown that by means of this coupling all well-known tests of Einstein's theory of gravitation connected with the propagation of light in gravitational field can be correctly calculated.     

Acceleration of particles by electron plasma waves in a moderate magnetic field

A general scheme is established to examine any magnetohydrodynamic (MHD) configuration for its acceleration potential including the effects of various types of plasma waves. The analysis is restricted to plasma waves in a magnetic field with electron cyclotron frequency less than, but comparable to, the electron plasma frequency (moderate field). The general role of electron plasma waves is examined in this paper independent of a specific MHD configuration or generating mechanism in the weak turbulence limit. The evolution of arbitrary wave spectra in a non-relativistic plasma is examined, and it is shown that the nonlinear, process of induced scattering on the polarization clouds of ions leads to the collapse of the waves to an almost one-dimensional spectrum directed along the magnetic field. The subsequent acceleration of non-relativistic and relativistic particles is considered. It is shown for non-relativistic particles that when the wave distribution has a negative slope the acceleration is retarded for lower velocities and enhanced for higher velocities compared to acceleration by an isotropic distribution of electron plasma waves in a magnetic field. This change in behavior is expected to affect the development of wave spectra and the subsequent acceleration spectrum.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Two-dimensional equilibrium of a neutral sheet in a gravitational field

We solve the two-dimensional MHD-equations to find the equilibrium structure of a neutral sheet having its axis parallel to the gravitational field in an atmosphere. The evolution of an initially plane sheet which is a self-consistent, non-equilibrium solution of the MHD-equations, is followed until static equilibrium of forces is obtained. The effect of field line anchoring in a cool dense layer at the bottom of the sheet is taken into account.Presently at The Auroral Observatory, Boks 953, 9001 Tromsø, Norway.     

Thermal-convective instability of a composite plasma in a stellar atmosphere with rotation and magnetic field

Thermal-convective instability of a composite plasma in a stellar atmosphere, when the effects of a uniform rotation and a uniform magnetic field are included simultaneously, is discussed. It is found that the criterion for monotonic instability is the same as in the absence or presence (separately) of these two effects.     

Energization of plasma in a weak magnetic field and structure of the geomagnetic tail

A two-fluid plasma is described as a single continuum characterised by the generalised tensor of mechanical pressure and generalised vector of flow of mechanical energy. Plasma energization due to the transfer of mechanical energy inside the plasma body is emphasised and the energization of plasma by conversion of the electromagnetic energy into the mechanical energy is discussed. Two kinds of conversion associated with the convection electric field –(1/c)V×B and with the deviationE ^* of the total electric field from –(1/c)V×B are distinguished. TheV×B-field is related to the work done upon the plasma, while theE ^*-field is related to the plasma heating.Plasma motions with scale length larger than the Debye distance, taking place in the central part of the Earth-plasma sheet, are considered. The change of energy of any element of plasma is due mainly to the transfer of mechanical energy across the element's boundary; the EM-field is not strong enough to make a significant contribution. The work done by the internal loads is the main source of mechanical energy in the configurations in which the physical quantities do not vary along the current lines. The rates of change of the kinetic and internal energies are comparable. The transfer of mechanical energy is the principal source of the kinetic energy also in the general case when the physical quantities vary along the current lines. Conversion of the EM energy into mechanical energy is the main source of the internal energy in this case. In the tail plasma located outside the central part of the plasma sheet, conversion of the EM-energy into mechanical energy, which is due to the work done by the EM-force, takes place. The tail plasma is likely to undergo a two-phase energization process: first, it is accelerated and later, when it approaches the neutral sheet, it is heated.     

Numerical computer simulation of cross-field propagation of a plasma stream in a magnetic field

A one-dimensional electrostatic particle simulation of plasma streaming perpendicular to a magnetic field with nonperiodic boundary condition has been carried out. When a bulk of plasma in injected across an ambient magnetic field, a stream of neutral plasma, consisting of equal numbers of ions and electrons, polarizes, and the resulting polarization electric field gives rise to the penetration of plasma across the magnetic field so that the integrity of plasma maintains. Computer simulation demonstrates the properties of cross-field propagation of plasma stream in a magnetic field with different plasma parameters.     

Equilibria in the gravitational field of a triangular body

The existence, stability and bifurcation analysis is performed for equilibria of a material point in the gravitational field of three homogeneous penetrable balls fixed in absolute frame. The radii of the balls are assumed finite. In the case when the mass distribution admits a symmetry axis, analytic expressions are written out, allowing one to investigate the properties of equilibrium positions located both on the symmetry axis and outside it. The stability of solutions is studied; domains with different instability degree are described.