Growth and decay of sonic waves in thermally radiative magnetogasdynamics

The propagation of weak discontinuities headed by a wavefront and their formation into shock waves are investigated in a thermally-radiative ideal plasma. It is found that all compressive waves grow without bound only if the magnitude of initial discontinuity associated with the wave exceeds a critical value. In particular, the grow and decay of weak discontinuities in plane, cylindrical, and spherical geometries have been discussed and the shock formation distance and time in all these cases have been derived in presence of magnetic field and radiation, separately.     

Weak MHD discontinuities in a radiation-induced flow field

The growth of weak MHD discontinuities have been studied in a radiation induced flow field at very high temperature. Growth and decay properties of weak MHD discontinuities have been discussed under the influences of time-dependent gasdynamic field, the radiation field and the magnetic field with finite electrical conductivity. The effects of thermal radiation and conduction of the global behaviour of weak MHD discontinuities have been studied under a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat transfer equation. It is shown that the existence of the time-dependent radiation field gives rise to a radiation induced wave which has a negligibly small effect on the non-relativistic flow properties of the gasdynamic field. It is also shown that the radiation stresses resist the steepening tendency of a compressive weak wave and help in stabilizing it whereas the thermal conduction effects counteracts to destabilize it. It is found that under radiation effects the shock formation is either disallowed or delayed. The two cases of diverging waves and converging waves have been studied separately to answer a particular question as to when a shock discontinuity or a coustic will be formed or disallowed under curvature effects.     

Weak waves in radiating gases

The propagation of weak waves has been studied by taking into account the influence of thermal radiative field. The singular surface theory is used to determine the modes of wave propagation and to evaluate the behaviour at the wave head. The effects of thermal radiation, conduction and the initial wave front curvature on the nonlinear breaking of weak waves are discussed. It is concluded that, under the thermal radiation effects, the shock wave formation is either disallowed or delayed. On the other hand, the thermal conduction effects destabilize the waves.     

The onset of shock wave in an electrically conducting and radiating gas

The present work applies the method of characteristics to study the behaviour of planar and cylindrical wave-heads propagating through a perfectly electrically conducting and thermally radiating inviscid gas under the optically thin limit in the presence of a transverse magnetic field. The true nonlinear progress of the flow variable gradients at the wavefront is predicted and the critical distance at which the characteristics pile up at the wavefront to form a shock wave is obtained. It is investigated as to how the effects of radiative flux, the magnetic field strength and the specific heat ratio influence the process of steepening or flattening of the characteristic wavefront.     

Propagation of sonic waves in an optically thick medium in the presence of magnetic field

This paper studies sonic waves in an optically thick medium under the influence of a magnetic field. The conductivity of the medium has been taken to be infinite. The effects of radiation, radiation energy density, radiative heat transfer and magnetic field have been taken into account. It has been obtained that the magnetic field has significant effect on sonic velocity. The fundamental differential equations governing the growth and decay of sonic waves are determined and solved.     

Effects of nonlinear Alfvén wave interaction on particle diffusive shock acceleration. The Earth’s bow shock

We investigate the role of nonlinear Alfvén-wave interaction in the diffusive shock acceleration of solar-wind ions at the Earth’s bow shock. Allowance for the nonlinear wave interaction through induced scattering and two-quanta absorption at plasma parameters β≲0.1 is shown to limit the Alfvén-wave amplitude δB to δB≲B, whereas the quasi-linear approach predicts the generation of waves with amplitudes much larger than the diffusive shock magnetic field strength B. The nonlinear interaction results in spectral wave energy transfer to lower frequencies, which yields a significant increase in the particle acceleration rate.     

Non-Linear Amplification of a Magnetic Field Driven by Cosmic Ray Streaming

One dimensional numerical results of the non-linear interaction between cosmic rays and a magnetic field are presented. These show that cosmic ray streaming drives large amplitude Alfvénic waves. The cosmic ray streaming energy is very efficiently transfered to the perturbed magnetic field of the Alfvén waves. Thus a magnetic field of interstellar values, assumed in models of supernova remnant blast wave acceleration, would not be appropriate in the region of the shock. The increased magnetic field reduces the acceleration time and so increases the maximum cosmic ray energy, which may provide a simple and elegant resolution to the highest energy galactic cosmic ray problem were the cosmic rays themselves provide the fields necessary for their acceleration. This revised version was published online in July 2006 with corrections to the Cover Date.     

Laboratory Observation of Secondary Shock Formation Ahead of a Strongly Radiative Blast Wave

We have previously reported the experimental discovery of a second shock forming ahead of a radiative shock propagating in Xe. The initial shock is spherical, radiative, with a high Mach number, and it sends a supersonic radiative heat wave far ahead of itself. The heat wave rapidly slows to a transonic regime and when its Mach number drops to two with respect to the downstream plasma, the heat wave drives a second shock ahead of itself to satisfy mass and momentum conservation in the heat wave reference frame. We now show experimental data from a range of mixtures of Xe and N₂, gradually changing the properties of the initial shock and the environment into which the shock moves and radiates (the radiative conductivity and the heat capacity). We have successfully observed second shock formation over the entire range from 100% Xe mass fraction to 100% N₂. The formation radius of the second shock as a function of Xe mass fraction is consistent with an analytical estimate.     

Oscillations of magnetohydrodynamic shock waves on the surfaces of T Tauri stars

This work treats the matter deceleration in a magnetohydrodynamic radiative shock wave at the surface of a star. The problem is relevant to classical T Tauri stars where infalling matter is channelled along the star's magnetic field and stopped in the dense layers of photosphere. A significant new aspect of this work is that the magnetic field has an arbitrary angle with respect to the normal to the star's surface. We consider the limit where the magnetic field at the surface of the star is not very strong in the sense that the inflow is super-Alfvénic. In this limit, the initial deceleration and heating of plasma (at the entrance to the cooling zone) occurs in a fast magnetohydrodynamic shock wave. To calculate the intensity of radiative losses we use 'real' and 'power-law' radiative functions. We determine the stability/instability of the radiative shock wave as a function of parameters of the incoming flow: velocity, strength of the magnetic field, and its inclination to the surface of the star. In a number of simulation runs with the 'real' radiative function, we find a simple criterion for stability of the radiative shock wave. For a wide range of parameters, the periods of oscillation of the shock wave are of the order of  0.02–0.2 s  .     

The emergence of a spherical magnetogasdynamic shock wave at the surface of a star

The propagation of a magnetogasdynamic shock wave originating in a stellar interior, is ocnsidered when it approaches the surfaces of the star. The flow behind the shock wave is assumed isothermal rather than adiabatic to stimulate the conditions of large radiative transfer near the stellar surface. The product solution of McVittie has been used to obtain exact solution of the problem. It has been obtained that velocity, density, pressure and magnetic field increases as we move from shock surface towards the nucleus of the star.     

Strong cylindrical magnetogasdynamic shock waves in a rotating interplanetary medium

Strong cylindrical magnetogasdynamic shock waves in rotating interplanetary medium has been studied and an analytic solution for their propagation has been obtained. Using characteristic method and considering the effect of Coriolis force, we have shown that magnetic field has significant effect on the velocity of the shock wave.     

First phase acceleration mechanisms and implications for hard X-ray burst models in solar flares

Requirements for the number of nonthermal electrons which must be accelerated in the impulsive phase of a flare are reviewed. These are uncertain by two orders of magnitude depending on whether hard X-rays above 25 keV are produced primarily by hot thermal electrons which contain a small fraction of the flare energy or by nonthermal streaming electrons which contain > 50% of the flare energy. Possible acceleration mechanisms are considered to see to what extent either X-ray production scenario can be considered viable. Direct electric field acceleration is shown to involve significant heating. In addition, candidate primary energy release mechanisms to convert stored magnetic energy into flare energy, steady reconnection and the tearing mode instability, transfer at least half of the stored energy into heat and most of the remaining energy to ions. Acceleration by electron plasma waves requires that the waves be driven to large amplitude by electrons with large streaming velocities or by anisotropic ion-acoustic waves which also require streaming electrons for their production. These in turn can only come from direct electric field acceleration since it is shown that ion-acoustic waves excited by the primary current cannot amplify electron plasma waves. Thus, wave acceleration is subject to the same limitations as direct electric field acceleration. It is concluded that at most 0.1% of the flare energy can be deposited into nonthermal streaming electrons with the energy conversion mechanisms as they have been proposed and known acceleration mechanisms. Thus, hard X-ray production above 10 keV primarily by hot thermal electrons is the only choice compatible with models for the primary energy release as they presently exist.     

The structure of the turbulent shock wave propagating in the solar atmosphere across the magnetic field

A consistent account of plasma turbulence in magnetohydrodynamics equations describing transport processes across the magnetic field is presented. The structure of the perpendicular shock wave generated in the solar atmosphere, as a result of either local disturbance of the magnetic field or dense plasma cloud motion with a frozen-in magnetic field, has been investigated. The region of parameters in the solar atmosphere at which the electron-ion relative drift velocity u exceeds the electron thermal velocity V _eand generation of radio emission becomes possible, has been determined. The plasma turbulence inside the front has been shown, under conditions of solar corona, not to cause the oscillation structure of shock front to break down. Under chromospheric conditions, the shock profile is aperiodical. Then, the condition u > V_ecan be satisfied and shock waves having an Alfvén Mach number M which exceeds the critical value M _c 3.3 for aperiodical shock waves can exist (Eselevich et al., 1971a). Arguments are given in favour of the fact that perpendicular shock waves are generated in the Sun's atmosphere when dense plasma clouds, with a frozen-in magnetic field, are expanded.     

Dispersive shock waves in the solar wind

Compressional waves in the solar wind propagating over large distances are likely to steepen into shock waves where the increase in the amplitude is balanced by dissipation. Dispersive effects caused by, e.g. Hall currents perpendicular to the ambient magnetic field can influence the generation and propagation of shock waves. In the present study the dispersion is considered weak but in time its importance can grow. When the effect of dispersion is strong enough, it can balance the nonlinear steepening of waves leading to the formation of solitons. The obtained results show that the weak dispersion will alter the amplitude and propagation speed of the shock wave. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-linear amplification of a magnetic field driven by cosmic ray streaming

One-, two- and three-dimensional numerical results of the non-linear interaction between cosmic rays and a magnetic field are presented. These show that cosmic ray streaming drives large-amplitude Alfvénic waves. The cosmic ray streaming energy is very efficiently transferred to the perturbed magnetic field of the Alfvén waves, and the non-linear time-scale of the growth of the waves is found to be very rapid, of the order of the gyro-period of the cosmic ray. Thus, a magnetic field of interstellar values, assumed in models of supernova remnant blast wave acceleration, would not be appropriate in the region of the shock. The increased magnetic field reduces the cosmic ray acceleration time and so increases the maximum cosmic ray energy, which may provide a simple and elegant resolution to the highest energy Galactic cosmic ray problem, where the cosmic rays themselves provide the fields necessary for their acceleration.     

Fully nonlinear ion-acoustic solitary waves in a warm magnetized plasma with electron inertia

Ion-acoustic solitary waves in a warm, magnetized plasma with electron inertia have been investigated through Sagdeev pseudopotential method. It has been established the existence of both compressive supersonic solitons, and rarefactive subsonic and supersonic solitons within the parametric domains. The effect of the external magnetic field for generation of the supersonic compressive solitons of constant amplitudes appears to be passive after some critical direction of propagation of the wave. However, up to the critical direction of propagation, the magnetic resistance is found to be quite active to drastically reduce the soliton amplitudes. The generation of rarefactive solitons in this warm magnetized plasma is rather more feasible to be supersonic without electron inertia.     

MHD free-convection flow of an elasto-viscous fluid past an infinite vertical plate

A theoretical model of shock wave propagation in a self-gravitating radiative magneto-hydrodynamic medium has been studied. The effects of the magnetic field, radiation, and gravitation have been discussed separately. The results discussed depend upon the numerical variations of flow variables behind the shock.     

Nonlinear magnetosonic waves propagating perpendicular to a magnetic neutral sheet

Nonlinear magnetosonic waves propagating in a magnetic neutral sheet are investigated within the framework of a fluid model. It is shown that the behavior of the magnetosonic waves is governed by a ‘modified Burgers equation’ with an additional termc(η)? due to the relevant slowly varying background plasma parameter (density or magnetic field), $$\frac{{\partial \phi }}{{\partial \eta }}$$ where ?(ξ, η) is the amplitude of the wave, \(\xi = \int {k_x } {\text{d}}x + k_y y - \omega t\) , and η=εx is the coordinate stretched by a smallness parameter ε. When we consider fast magnetosonic waves propagating toward the neutral region across the magnetic field, they grow and undergo rapid steepening after passing through the neutral region; i.e., shock formation is promoted by the background inhomogeneity. By the numerical computation of the above equation, the time evolution is examined for two initial disturbances, the pulse type (gaussian) and the wave train type (sinusoidal wave). The relevance of the interactions between the magnetosonic shock waves and the neutral sheet plasma to a triggering mechanism of sympathetic flares is also suggested.     

Acceleration of a spherical neutral shell produced by an ionization-shock front in an inhomogeneous interstellar medium

We numerically model the formation and acceleration of a neutral gas shell as an ionization-shock front propagates in a spherical cloud by taking into account the photoionization and radiative heating of the gas, the spectral radiative transfer. We suggest and implement an approximation of the cooling function that allows calculations to be performed in a wide range of gas ionization fractions and temperatures. The total mass, average velocity, and thickness of the shell have been determined. The results are compared with approximate formulas known in the literature. Based on the parameters of the shell found, we estimate its acceleration, characteristic scales, and the growth times of unstable perturbations. We analyze the influence of the cloud particle density, cloud radius, stellar temperature, and radiation spectrum on the integrated characteristics of the neutral gas in the layer between the ionization and shock fronts. The distribution of matter in the shell and its thickness are shown to differ significantly from those used in approximate models.