Propagation of plane relativistic shock waves

Similarity solutions for propagation of plane shock waves in a relativistic gas, where the nucleon number density varies linearly as distance from its edge at near vacuum is obtained. The shock front moves with constant speed and the solutions are applicable only to an isothermal medium or cold gas.     

Propagation of interplanetary shock waves by observations of type II solar radio bursts on IMP-6

A new interpretation of the low frequency type II solar radio bursts of 30 June 1971, and 7–8 August 1972 observed with IMP-6 satellite (Malitson et al., 1973a,b) is suggested. The analysis is carried out for two models of the electron density distribution in the interplanetary medium taking into account that N ~ 3.5 cm^?3 at a distance of 1 a.u. It is assumed that the frequency of the radio emission corresponds to the average electron density behind the shock front which exceeds the undisturbed electron density by the factor of 3. The radio data indicate essential deceleration of the shock waves during propagation from the Sun up to 1 a.u. The characteristics of the shock waves obtained from the type II bursts agree with the results of the in situ observations.     

Simulation of solar flare particle interaction with interplanetary shock waves

In order to study the propagation of solar cosmic rays in interplanetary space a computer program has been developed using a Monte-Carlo technique, which traces the histories of particles released impulsively at the Sun. The particle propagation model considers the adiabatic deceleration during the convective and diffusive transport of the particles, and the model of the interplanetary medium incorporates a radially expanding blast wave which exerts a sweeping action on the particles and accelerates them through the first-order Fermi process. It is shown that energetic storm particle events cannot be simulated by assuming a pure sweeping action of the interplanetary blast wave, but that energization of the particles while reflected at the shock can explain many observed features of such events.     

Propagation of plane relativistic shock waves in a slowly moving medium

Similarity solutions for the propagation of plane relativistic shock waves in a slowly moving medium, where the nucleon number density obeys an exponential law ofx/t, is obtained in this paper. 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.     

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.     

Flare-associated shock waves observed by interplanetary scintillation

Daily observations of a grid of scintillating sources during the period January–August 1971 indicate that enhancements in scintillation index which cannot be related to corotating structure, are related to interplanetary shock waves associated with solar flares. Only 3 enhancements in scintillation index associated with shock waves were observed during the eight months period of observations.     

Interaction of interplanetary MHD shock waves with the magnetopause

The interaction between a shock-wave and the magnetopause is formulated on the basis of one-dimensional magnetohydrodynamics. The magnetopause is assumed to be a tangential discontinuity, and the magnetic field is limited to the case of perpendicularity. Both the forward and reverse shocks' impact on the magnetopause are considered and analyzed separately. The forward shock-magnetopause interaction results in a transmitted shock, a tangential discontinuity, and a simple rarefaction wave. The reverse shock-magnetopause interaction creates a transmitted shock, a tangential discontinuity, and a reflected wave. The propagation of an SSC signal which is related to an interplanetary shock-induced geomagnetic storm's onset-time on Earth is discussed in general terms. It was found in earlier work (Shen and Dryer, 1972) that the propagation velocity of an inter-planetary shock is decreased by about 1015% following its impact with the earth's bow shock; the present study shows that its velocity is then suddenly increased by a factor of two to three after impact with the magnetopause. The fast propagating shock-wave inside the magnetosphere degenerates into a hydromagnetic wave as it advances into an increasing intensity of the distorted dipole geomagnetic field.     

Low-energy proton increases associated with interplanetary shock waves

Impulsive increases in the low energy proton flux observed by the Explorer 34 satellite, in very close time association with geomagnetic storm sudden commencements are described. It is shown that these events are of short duration (20–30 min) and occur only during the decay phase of a solar cosmic-ray flare event. The differential energy spectrum and the angular distribution of the direction of arrival of the particles are discussed. Two similar increases observed far away from the earth by the Pioneer 7 and 8 deep-space probes are also presented. These impulsive increases are compared with Energetic Storm Particle events and their similarities and differences are discussed. A model is suggested to explain these increases, based on the sweeping and trapping of low energy cosmic rays of solar origin by the advancing shock front responsible for the sudden commencement detected on the Earth.Part of this work was performed while the author was at the University of Texas at Dallas as a Visiting Professor.     

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)     

Homology of solar flare-associated radio events

The concept of homology, introduced by Ellison, Mc Kenna, and Rceid (1960) for optical flares, can be extended to flare-associated radio events. Successive flares within the same centre of activity sometimes produce radio events that are remarkably similar. The similarity amounts to the fact that they extend over about the same range(s) in frequency, producing at each frequency responses of comparable intensity and duration. On some occasions the intensity curves at individual frequencies show even detailed resemblance. The occurrence of homologous radio events is commonly restricted to periods of less than 48 hours.Without being homologous, radio events that occur in the same centre of activity may present a common characteristic that is typical for that centre. Two such characteristics are (1) the production of radio responses at centimetric, decimetric and metric frequencies, and (2) the impulsiveness of microwave outbursts. The distribution of time intervals during which such bursts occur is compared with the same distribution for homologous events (Figure 3).     

Propagation of cylindrical shock waves in magnetogasdynamics

Using a well-known similarity method, different aspects of cylindrical shock waves in magnetogasdynamics are investigated. Weak and strong shocks have been discussed in strong magnetic field. Combined effects of both the components of magnetic field on flow variables are studied.     

Propagation of exponential shock waves in magnetogasdynamics

Self-similar flows of a perfect gas behind the cylindrical shock wave propagating exponentially in an atmosphere whose density varies inversely as the fourth power of shock radius are investigated. The effects of radiation flux has also been taken into consideration. The total energy of the wave is constant.     

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.     

Propagation of axi-symmetric relativistic shock waves

Solutions in series for the propagation of relativistic shock waves with axial symmetry are obtained in this paper. We assume that the gaseous elements move almost radially and that the disturbance moves through a cold gas at rest wherein the nucleon number density and the energy density obey an exponential law of distance from a given plane. The motion is sustained by continuous explosions in the central region liberating energy varying as the cube of time. Also, we assume the equation of state of the moving elements as that of photonic gas.     

Propagation of spherical magnetogasdynamic shock waves

Magnetogasdynamic shock waves propagating in a medium of increasing density are discussed. The shock travels in a dense atmosphere. We have used the Runge-Kutta method to obtain a numerical solution of the problem. The distribution of flow variables behind the shock are shown by graphs.     

Propagation of magnetoacoustic shock waves in cylindrical geometry

Cylindrical Korteweg-de Vries-Burgers (cKdVB) equation for magnetoacoustic wave is derived for dissipative magneto plasmas. Two fluid collisionless electromagnetic model is considered and reductive perturbation method is employed to study the propagation of magnetoacoustic shock waves in cylindrical geometry. Two level finite difference method is employed by using Runge-Kutta method to solve cKdVB equation numerically. The effects of nonplanar geometry, plasma density, magnetic field strength, temperature dependence and kinematic viscosity on magnetoacoustic shocks are investigated. The numerical results are also presented for illustration.     

Propagation of magneto-radiative shock waves,II

Self-similar motion of a perfect gas behind a cylindrical shock wave with radiation heat flux in the presence of an azimuthal magnetic field have been discussed. The shock is assumed to be propagating in a medium at rest with non-uniform density. The conductivity of the gas is infinite and magnetic permeability is one everywhere. Also, the shock is assumed to be transparent and isothermal.     

Numerical modelling of shock waves in the solar wind

This review briefly surveys some recent progress in the numerical simulation study of magnetohydrodynamic (MHD) shock waves in the solar wind.     

Evidence for confinement of low-energy cosmic rays ahead of interplanetary shock waves

Short-lived ( 15 min), low-energy proton increases associated with the passage of interplanetary shock waves have been previously reported. In the present paper, we have examined in a fine time scale ( 1 min) the concurrent particle and magnetic field data, taken by detectors on Explorer 34, for four of these events which occurred on 30 May 1967, 5 June 1967, 29 November 1967, and 11 January 1968. Our results further support the view that these impulsive events are due to confinement of the solar cosmic-ray particles in the region just ahead ( 10⁶ km) of the advancing shock front. Data from the Pioneer 7 spacecraft for a similar event on 30 August 1966, when this spacecraft was 1.9 × 10⁶ km from the Earth, are shown to be consistent with this interpretation.