Isothermal shock waves in uniform atmospheres

Similarity solutions describing the isothermal flow of a perfect gas behind shock waves are investigated for spherical symmetry. The flow is caused by a propelling contact surface (or expanding piston) and its total energy increases as a power of the time. The shock is propagating in a medium at rest with a uniform density.     

Strong plane shock waves in exponential and optically-thin atmospheres,II

Non-similarity solutions for the propagation of strong plane shock waves in optically-thin grey atmosphere are investigated. The density increases exponentially under low pressure. The shock moves with variable velocity and the total energy of the wave is not constant. Planck's diffusion approximation has been taken into account in the present problem.     

Electro-hydromagnetic waves in a fully ionized gas-II

The propagation of hydromagnetic and low frequency radio waves in all directions in a fully ionized gas containing a magnetic field is examined. For longitudinal and transverse propagation the addition of one extra term in the magneto-ionic formulae (without collisions) accounts for the presence of heavy ions.

The partition of energy of disturbance between kinetic (K) and magnetic (M) for longitudinal propagation of all frequencies is given by

where V is the Alfvén speed. Thus approximate equipartition may exist for some audio- and radio-frequencies in the Earth's exosphere.

Some errors in Paper I of this series are corrected.     

Dissipating waves in a hot,compressible, magnetic,structured atmosphere

The damping of ducted, fast, magnetohydrodynamic (MHD) waves by ion viscosity and electron heat conduction in a radiating, optically thin, warm, structured atmosphere has been evaluated. Dissipation is more effective in a warm plasma than in a cold one but, for waves ducted by solar coronal loops, dissipation is only efficient if the periods of the waves are shorter than a few tens of seconds and only if the background magnetic field is less than about 15 G. It appears that MHD waves of longer periods and in stronger magnetic fields will survive the dissipative mechanisms considered here and may be manifest as observable coronal oscillations.     

Spherical shock waves in viscous magnetogasdynamics

The point-source, spherical magnetogasdynamics shock wave moving into a constant density -law gas is considered in the limit of infinite shock strength, from the point of view of the Richtmyer-Von Neumann viscosity technique. Numerical solutions of this problem has been obtained in viscous and non-viscous regions. A similarity solution of this problem is shown to exist. We have shown that field variables change rapidly when the magnetic field is imposed in both the viscous and the non-viscous regions.Supported by CSIR, New DeIhi under the grant No. 7157/287/81-DMR-I.     

Strong-plane shock waves in optically-thin atmospheres in magnetogasdynamics

In this paper, similarity solutions for the propagation of strong-plane shock waves in optically-thin grey atmospheres are obtained in the presence of a magnetic field. Density and magnetic field are constant in the undisturbed gaseous medium in front of the shock. Planck's diffusion approximation has been taken into account in this problem and a comparative study has been made between the results of ordinary gasdynamics and magnetogasdynamics.     

Rayleigh-Taylor instability of ionized viscous fluids with FLR-corrections and surface-tension

The problem of Rayleigh-Taylor instability of superposed viscous magnetized fluids through porous medium is investigated in a partially-ionized medium. The fluid has ionized and neutralized particle components interacting with collisions. The effect of surface tension on R-T instability is also included in the present problem. The magnetohydrodynamic equations are modified for finite-Larmor radius corrections which is in the form of tensor. The equations of problem are linearized and using appropriate boundary condition, general dispersion relation is derived for two superposed fluids separated by horizontal boundary. The first part of the dispersion relation gives stable mode and condition is investigated using Hurwitz conditions. The second part of the dispersion relation shows that the growth rate of unstable system is reduced due to FLR corrections, viscosity, and collisional frequency of the neutrals. The role of surface tension on the system is also discussed.     

Magnetosonic waves in structured atmospheres with steady flows

The magnetosonic modes of magnetic plasma structures in the solar atmosphere are considered taking into account steady flows of plasma in the internal and external media and using a slab geometry. The investigation brings nearer the theory of magnetosonic waveguides, in such structures as coronal loops and photospheric flux tubes, to realistic conditions of the solar atmosphere. The general dispersion relation for the magnetosonic modes of a magnetic slab in magnetic surroundings is derived, allowing for field-aligned steady flows in either region. It is shown that flows change both qualitatively and quantitatively the characteristics of magnetosonic modes. The flow may lead to the appearance of a new type of trapped mode, namelybackward waves. These waves are the usual slab modes propagating in the direction opposite to the internal flow, but advected with the flow. The disappearance of some modes due to the flow is also demonstrated.The results are applied to coronal and photospheric magnetic structures. In coronal loops, the appearance of backward slow body waves or the disappearance of slow body waves, depending upon the direction of propagation, is possible if the flow speed exceeds the internal sound speed ( 300 km s^–1). In photospheric tubes, the disappearance of fast surface and slow body waves may be caused by an external downdraught of about 3 km s^–1.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The Hohlov-Zabolotskaja equation with an additional boundary condition is shown to describe long nonlinear small-amplitude fast sausage surface waves in a magnetic slab embedded in magnetic environment. It is proved that the obtained boundary problem has no solutions in the form of solitary waves. Approximate solution in the form of nonlinear stationary wave is found with the use of expansion in the power series of small amplitude. Second harmonic generation by a sinusoidal wave is studied. The law of energy conservation is obtained. Results of numerical computations are presented. They show that a sinusoidal disturbance does not overturn. The possibility of transmission of wave energy into corona along a magnetic slab is discussed in connection with these results.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The propagation of nonlinear slow sausage small-amplitude waves in a magnetic slab in a magnetic environment is considered. The equation for surface waves that is allied form of the Benjamin-Ono equation and the equation for body waves that is allied form of the equation for body waves in the slab are derived with the use of the method of stretching variables. The solutions of the equation for surface waves in the form of solitary waves are obtained numerically.     

Long nonlinear waves in a compressible magnetically structured atmosphere

The Benjamin-Ono equation is derived for long slow sausage waves propagating in a vertical magnetic slab embedded into a stratified atmosphere, provided that the slab thickness is much smaller than the scale height of the atmosphere. The soliton propagation in a nonstratified atmosphere is discussed. The approximate formulas describing the slow evolution of the amplitude and the length of a soliton propagating in a very weakly stratified atmosphere are obtained. The exact soliton-like solution for an atmosphere with a linearly growing temperature is found.     

Electro-hydromagnetic waves in a fully ionized gas—I

Transport equations are used to determine coefficients which are generalizations for any frequency of electric field of the parallel, Pedersen and Hall conductivities in a fully ionized gas.

These coefficients are used in an investigation of the propagation of weak electromagnetic and hydromagnetic waves of all frequencies across a homogeneous and constant magnetic field in a rarefied fully ionized gas. For propagation perpendicular to the magnetic field it is found for all frequencies

(i)

(ii)

where V² = H²/4π and v, h are the perturbations of the velocity, magnetic field. Similar relationships are deduced for propagation at any angle to the field for frequencies greater than about 10 times the gyrofrequency of electrons.

The theory is applied to discuss transmission of disturbance across the interplanetary medium, the temperature of the solar corona and the earth's outer atmosphere, the emission of non-thermal solar radio noise, cosmic radio noise and the anomalous emission of light from shock fronts.     

Excitation of plasma waves by bodies moving in ionized atmosphere

A body moving in an ionized atmosphere acquires an electric charge through the processes of accretion of charged particles and emission of electrons by high energy photons. The moving charged body may then interact with the charged particles of the atmosphere and any pervading magnetic field to excite plasma waves. Of particular interest is the situation in which the body collects an ionized cloud in front of it. The motion of this ionized cloud in the atmosphere induces an electrostatic instability and causes a column of ionized gas to move ahead of the body. The electrostatic instability is conducive to the excitation of electrostatic oscillations which if already present are further enhanced. A magnetic field along the direction of motion assists in the formation of the ionized cloud. If the pervading magnetic field is of suitable weak strength, it may excite extraordinary electromagnetic waves. A pervading transverse magnetic field of suitable strength may cause the excitation of magnetohydrodynamic waves.     

Stability of magneto-acoustic waves in a thermally conducting compressible fluid

The stability of magneto-acoustic waves in an inviscid, perfectly conducting isothermal fluid, stratified under constant gravity and subjected to a horizontal magnetic field is investigated in the presence of thermal dissipation.     

Isothermal shock waves in uniform and non-uniform atmospheres with an idealized magnetic field

Similarity solutions of an isothermal flow of a perfect gas behind spherical shock waves are studied in the presence of magnetic field. The flow is caused by a propelling contact surface (or expanding piston) and its total energy increases with time. The shock is propagating in a medium at rest with uniform and non-uniform density. The two important models have been also considered here in which the magnetic field is proportional to ^–1 and ^–3/2.     

On thermal waves in stars,II

The regularities of strong thermal waves moving in non-uniform media are considered in some detail. The application of thermal wave theory to Nova outburst interpretation is discussed.     

Comets, meteorites and atmospheres

The relatively low value of Xe/Kr in the atmospheres of Earth and Mars seems to rule out meteorites as the major carriers of noble gases to the inner planets. Laboratory experiments on the trapping of gases in ice forming at low temperatures suggest that comets may be a better choice. It is then possible to develop a model for the origin of inner planet atmospheres based on volatiles delivered by comets added to volatiles originally trapped in planetary rocks. The model will be tested by results from the Galileo Entry Probe.     

Comets, meteorites and atmospheres

The relatively low value of Xe/Kr in the atmospheres of Earth and Mars seems to rule out meteorites as the major carriers of noble gases to the inner planets. Laboratory experiments on the trapping of gases in ice forming at low temperatures suggest that comets may be a better choice. It is then possible to develop a model for the origin of inner planet atmospheres based on volatiles delivered by comets added to volatiles originally trapped in planetary rocks. The model will be tested by results from the Galileo Entry Probe.