Propagation of cylindrical relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of cylindrical relativistic shock waves in the presence of a constant azimuthal magnetic field or in its absence for the medium, where the nucleon number density is uniform. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Propagation of plane relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of plane relativistic shock waves in the presence of a transverse magnetic field for the medium, where the nucleon number density obeys a power law of distance from the plane of explosion. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Nonlinear stability of an infinite cylinder in the presence of a uniform axial magnetic field

The effect of a uniform axial magenetic field on the nonlinear instability of a self-gravitating infinite cylinder is examined. Using the method of multiple scales, it is found that while the nonlinear (modulational) instability cannot be completely suppressed, the presence of a magnetic field does increase the range of stable wave numbers. The evolution of the amplitude is governed by a non-linear Schrödinger equation which gives the criterion for modulational instability.Department of Chemical Engineering and Technology.Department of Mathematics.     

Nonlinear break up of an infinite cylinder in the presence of a uniform axial magnetic field

A third-order theory has been developed to study the instability of an infinite cylinder in the presence of a uniform axial magnetic field. By use of strained coordinates, the growth of the surface waves is calculated for wave numbers less than the critical wave number. It is observed that the perturbed surface of an infinite cylinder assumes a non-sinusoidal shape resulting in secondary waves due to energy transfer between the harmonics of different orders.Department of Chemical Engineering and Technology.Department of Mathematics.     

Reverse shock wave in relativistic explosions

The dynamical evolution of a relativistic explosion in a homogeneous medium is studied by means of a time-dependent, hydrodynamic code. When the expanding velocity of the shock front reduces to the sound velocity in the relativistic fluid, the reverse shock wave propagating inward through the expanding material is generated. The radius of the turning point of the reverse shock wave is proportional to the explosion energy and hardly depends on the mass of the explosion products. In the case of the non-relativistic explosion, the reverse shock wave is generated just after the free expansion stage. The radius of the turning point of the reverse shock wave is proportional to the mass of the explosion products and little depends on the explosion energy. In both cases of the non-relativistic and relativistic explosion, the reverse shock wave is strong in a spherical explosion and weak in a cylindrical one. The plane symmetric explosion does not generate the reverse shock wave.     

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.     

Dynamo action in the presence of an imposed magnetic field

Dynamo action within the cores of Ap stars may offer intriguing possibilities for understanding the persistent magnetic fields observed on the surfaces of these stars. Deep within the cores of Ap stars, the coupling of convection with rotation likely yields magnetic dynamo action, generating strong magnetic fields. However, the surface fields of the magnetic Ap stars are generally thought to be of primordial origin. Recent numerical models suggest that a primordial field in the radiative envelope may possess a highly twisted toroidal shape. We have used detailed 3-D simulations to study the interaction of such a twisted magnetic field in the radiative envelope with the core-dynamo operating in the interior of a 2 solar mass A-type star. The resulting dynamo action is much more vigorous than in the absence of such a fossil field, yielding magnetic field strengths (of order 100 kG) much higher than their equipartition values relative to the convective velocities. We examine the generation of these fields, as well as the growth of large-scale magnetic structure that results from imposing a fossil magnetic field. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gnetic wave instability in a plasma ith relativistic particles in a random magnetic field

A new mechanism, which accounts for the direct excitation of electromagnetic waves by relativistic particles moving in random magnetic fields, is considered. We are then able to study maser-type wave excitations by slightly anisotropic particle distribution functions as well as electromagnetic wave emissions in beam-plasma interactions     

The stability of a velocity shear in the presence of an inhomogeneous magnetic field

The stability of a velocity shear in the presence of a parallel but non-uniform magnetic field is considered in general terms. Two special cases are then investigated; (i) the well known case of a plane interface at which a discontinuity in the magnetic field coincides with the velocity shear; (ii) an axially symmetric flow in which discontinuities in the magnetic and velocity fields occur at a cylindrical surface whose axis is parallel to the flow. In the first case the flow is stabilized if the rms Alfvén velocity of the magnetic field exceeds the shear velocity; a result consistent with that obtained by other writers. In the second case it is shown that the discontinuity in the magnetic field increases the stability of the system. The significance of this result for the stability of the flux ropes associated with sunspots in the solar convection zone is considered.     

Matter infall in collapsing molecular cloud cores with an axial magnetic field

The magnetic fields affect collapse of molecular cloud cores. Here, we consider a collapsing core with an axial magnetic field and investigate its effect on infall of matter and formation of accretion disk. For this purpose, the equations of motion of ions and neutral infalling particles are numerically solved to obtain the streamlines of trajectories. The results show that in a non-steady state of ionization and ion–neutral coupling, which is not unexpected in the case of infall, the radius of accretion disk will be larger as a consequence of axial magnetic field.     

Relation between classical and relativistic shock wave theories by means of shock tube tests

The author proposes a laboratory simulation of cosmic shock waves by means of the mathematical correlations between the shock equations in the classical and the relativistic fluid dynamics, respectively. In the present note only the normal shock is treated.     

Global wave patterns in the Sun's magnetic field

When the observed pattern of solar magnetic fields is decomposed in its spherical-harmonic components and a time series analysis is performed, a resonant global wave pattern is revealed. The power spectrum indicates modes with discrete frequencies, obeying a strict parity selection rule in the case of the zonal, rotationally-symmetric modes (with spherical-harmonic orderm=0). For instance, the 22 yr resonance that dominates for the anti-symmetric modes (with odd values of the spherical-harmonic degreel) is completely absent for the symmetric modes, which instead exhibit a number of resonances having frequencies increasing withl.A more traditional way of looking at the evolution of the zonal magnetic pattern is in the form of isocontours in latitude-time space (as in the butterfly diagram of sunspots). We show how this pattern can to a good approximation be represented as a superposition of 14 discrete modes, each with a purely sinusoidal time variation, one mode for each value ofl (=1,2, ..., 14). This corresponds to the assumption that the true, fully resolved and noise-free power spectrum consists of -function peaks, one for eachl value.This approach allows us to analyse the roles of the individual discrete modes in generating the well-known features in the traditional btterfly diagrams, e.g., the drift of the sunspot zones towards the equator and the prominence zones towards the poles during the course of the 11 yr cycle. It is shown that these features are accounted for entirely by the odd parity modes with the single, sinusoidal period of 22 yr. The drifts (and thus the arrow of time) are caused by the systematic phase relations between the 22 yr modes. The even modes exhibit an entirely different pattern. Since they have considerably shorter periods, they cause an undulation of the odd-mode contour lines when superposed on the anti-symmetric pattern.The dispersion, amplitude, and phase relations of the discrete modes are given. It is indicated how they can be used in combination with spectral inversion techniques to determine the depth variation of the parameters in the governing global wave equation.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Two-stream instability in the presence of longitudinal magnetic field

A multiple sclaes perturbation theory has been applied to investigate the nonlinear behaviour of beam-plasma system near a marginally stable state in the presence of longitudinal magnetic field. The perturbation method leads to a nonlinear Schrödinger equation for the finite amplitude. The coefficients of this equation show that only if the beam is compressed isothermally can there exist a range of wavenumbers for which stabilization might occur. The stable region increases with the applied magnetic field.     

Distribution function of relativistic electrons in a strong magnetic field

The motion and radiation of relativistic particles with radiation reaction in a strong magnetic field has been considered. The kinetic equation determining the relaxation of the distribution function with radiation reaction has been investigated. The universal one-dimensional distribution function is found to which any isotropic ultrarelativistic distribution in a strong magnetic field is relaxed. It is of power type ^–3 for ultrarelativistic energies mc ². Estimations are made which indicate that under the pulsar conditions the one-dimensional electron distribution function is likely formed due to radiation losses while for ions the one-dimensionalization is associated with the conservation of the adiabatic invariant.     

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.     

Vertically self-gravitating ADAFs in the presence of toroidal magnetic field

Force due to the self-gravity of the disc in the vertical direction is considered to study its possible effects on the structure of a magnetized advection-dominated accretion disc. We present steady-sate self similar solutions for the dynamical structure of such a type of the accretion flows. Our solutions imply reduced thickness of the disc because of the self-gravity. It also imply that the thickness of the disc will increase by adding the magnetic field strength.     

Umbral oscillations in the presence of a spreading magnetic field

Résumé Des onze observatoires qui, depuis 1947, ont à des degrés divers participé à l'obtention de données coronales au coronographe, six seulement sont encore en service. Rendues homogènes à partir d'un traitement statistique, ces données permettraient de couvrir trente cinq années d'activité solaire, soit près de quatre cycles complets. Une exploitation intéressante de ces mesures est la recherche des trous coronaux (autre que polaires), sources du vent solaire à haute vitesse dont les retombées en matière d'accroissement de nos connaissances sur la physique de la haute atmosphère et relations avec le climat terrestre sont primordiales. De nombreuses résolutions récentes de symposium ont conclu en ce sens et il serait bon que les commissions spécialisées concernées de l'UAI se prononcent sur ce problème au cours de l'une de ses prochaines réunions.

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Thirty-five years of patrol measurements of the intensity of the solar corona outside eclipses

A review of the various observatories having done daily measurements of the activity of the solar corona and having regularly published their results is being given hereby. Out of eleven observatories having taken out to the observation campaign since 1947, only six are still working in this field. Due to the fact that the scales, the focus and photometric systems are not always the same, the measurements are not homogeneous and directly comparable. However, astronomers can find there a great lot of statistical data covering thirty five years of coronal activity, that is more than three solar cycles. Some of these data, such as those of the Pic-du-Midi observatory, are readily available on magnetic tapes and may be asked from the authors. One of the most interesting exploitations of these data is the search of coronal holes (other than polar holes which are simply the signature of the periodic activity of corona) and it is shown here that such features are easily detectable. So, it will be vital for future research in solar physics, and especially in solar weather and climate relationships (bearing in mind that coronal holes are the sources of high speed streamers of the solar wind which interacts with the Earth magnetosphere), to ensure continuity and quality of patrol ground-based corona intensities outside eclipses. A number of recent conclusions of symposia in this field have led to such recommendations, and it would be suitable if next specialized commissions of IAU meetings were to think about that matter.