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Showing papers on "Shock wave published in 1984"


Journal ArticleDOI
TL;DR: In this article, a steady state, spherically symmetric, magnetohydrodynamic model of the Crab nebula is constructed, where a highly relativistic positronic positronic pulsar wind is terminated by a strong MHD shock that decelerates the flow and increases its pressure to match boundary conditions imposed by the recently discovered supernova remnant that surrounds the nebula.
Abstract: A steady state, spherically symmetric, magnetohydrodynamic model of the Crab nebula is constructed. A highly relativistic positronic pulsar wind is terminated by a strong MHD shock that decelerates the flow and increases its pressure to match boundary conditions imposed by the recently discovered supernova remnant that surrounds the nebula. If the magnetic luminosity of the pulsar wind upstream of the shock is about 0.3 percent of its particle luminosity, the pressure and velocity boundary conditions imposed by the remnant place the shock where it is inferred to be: near the outer boundary of an underluminous region observed to surround the pulsar. It is necessary to include the weak magnetization of the wind to satisfy the boundary conditions and to calculate the regular synchrotron radiation self-consistently.

927 citations


Journal ArticleDOI
TL;DR: In this article, two-dimensional hydrodynamic codes are used to simulate the growth of perturbations at an interface between two fluids of different density due to Rayleigh-Taylor instability.

612 citations


Journal ArticleDOI
TL;DR: In this article, the problem of nonstationary, nonlinear perturbations in one-dimensional granular media is stated on the basis of the wellknown interaction between neighboring granules.
Abstract: The study of mechanics of a granular medium is of substantial interest, both scientifically and for the solution of applied problems. Such materials are, for example, good buffers for shock loads. Their, study is important for the development of processes of the pulse deformation of several porous materials. A review of studies of small deformations and elastic wave propagation in these media was carried out in [i] on the basis of discrete models. The structure of a stationary shock wave was analyzed in [2] as a function of its amplitude. i. Statement of the Problem. The problem of nonstationary, nonlinear perturbations in one-dimensional granular media is stated in the present paper on the basis of the wellknown interaction between neighboring granules. As an interaction law we choose the Hertz law [3]

389 citations


Journal ArticleDOI
TL;DR: In this article, the evolution of the electromagnetic ion beam instability driven by the reflected ion component backstreaming away from the earth's bow shock into the foreshock region is studied by means of computer simulation.
Abstract: The evolution of the electromagnetic ion beam instability driven by the reflected ion component backstreaming away from the earth's bow shock into the foreshock region is studied by means of computer simulation. The linear and quasi-linear stages of the instability are found to be in good agreement with known results for the resonant mode propagating parallel to the beam along the magnetic field and with theory developed in this paper for the nonresonant mode, which propagates antiparallel to the beam direction. The quasi-linear stage, which produces large amplitude delta B approximately B, sinusoidal transverse waves and 'intermediate' ion distributions, is terminated by a nonlinear phase in which strongly nonlinear, compressive waves and 'diffuse' ion distributions are produced. Additional processes by which the diffuse ions are accelerated to observed high energies are not addressed. The results are discussed in terms of the ion distributions and hydromagnetic waves observed in the foreshock of the earth's bow shock and of interplanetary shocks.

248 citations


Journal ArticleDOI
TL;DR: In this paper, the adiabatic energy gain of electrons in the stationary electric and magnetic field structure of collisionless shock waves was examined analytically in reference to conditions of the earth's bow shock.
Abstract: The adiabatic energy gain of electrons in the stationary electric and magnetic field structure of collisionless shock waves was examined analytically in reference to conditions of the earth's bow shock. The study was performed to characterize the behavior of electrons interacting with the cross-shock potential. A normal incidence frame (NIF) was adopted in order to calculate the reversible energy change across a time stationary shock, and comparisons were made with predictions made by the de Hoffman-Teller (HT) model (1950). The electron energy gain, about 20-50 eV, is demonstrated to be consistent with a 200-500 eV potential jump in the bow shock quasi-perpendicular geometry. The electrons lose energy working against the solar wind motional electric field. The reversible energy process is close to that modeled by HT, which predicts that the motional electric field vanishes and the electron energy gain from the electric potential is equated to the ion energy loss to the potential.

228 citations


Journal ArticleDOI
TL;DR: In this article, the first critical fast Mach number is defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed, i.e., it is the moment when the superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the critical Mach number.
Abstract: The first critical fast Mach number is rigorously defined to be the one at which the downstream flow speed in the shock frame equals the ordinary downstream sound speed. Above the first critical Mach number, resistivity alone is unable to provide all the dissipation needed for the required Rankine-Hugoniot shock jump. A survey of the dependence of the first critical Mach number upon upstream plasma parameters is needed to guide studies of the structure of collisionless shocks in space. We vary the upstream plasma beta, the upstream shock normal angle, and the ratio of specific heats for the plasma. The first critical Mach number depends sensitively upon upstream plasma parameters, and is between 1 and 2 for typical solar wind parameters, rather than the often quoted value of 2·7, which is valid for perpendicular shocks propagating into a cold plasma. We introduce the suggestion that the flux of superthermal and energetic ions upstream at quasi-parallel shocks might increase suddenly at the first critical Mach number. Our parametric survey indicates that this hypothesis might be most conveniently tested using interplanetary shocks.

181 citations


Journal ArticleDOI
TL;DR: In this paper, the results of Monte Carlo simulations of steady state shocks generated by a collision operator that isotropizes the particles by means of elastic scattering in some locally defined frame of reference are presented.
Abstract: The results of Monte Carlo simulations of steady state shocks generated by a collision operator that isotropizes the particles by means of elastic scattering in some locally defined frame of reference are presented. The simulations include both the back reaction of accelerated particles on the inflowing plasma and the free escape of high-energy particles from finite shocks. Energetic particles are found to be naturally extracted out of the background plasma by the shock process with an efficiency in good quantitative agreement with an earlier analytic approximation (Eichler, 1983 and 1984) and observations (Gosling et al., 1981) of the entire particle spectrum at a quasi-parallel interplanetary shock. The analytic approximation, which allows a self-consistent determination of the effective adiabatic index of the shocked gas, is used to calculate the overall acceleration efficiency and particle spectrum for cases where ultrarelativistic energies are obtained. It is found that shocks of the strength necessary to produce galactic cosmic rays put approximately 15 percent of the shock energy into relativistic particles.

161 citations


Journal ArticleDOI
TL;DR: The hydromagnetic flow configurations associated with cosmic ray modulation in 1977 to 1980 were determined using solar wind plasma and magnetic field data from Voyagers 1 and 2 and Helios 1.
Abstract: The hydromagnetic flow configurations associated with cosmic ray modulation in 1977 to 1980 were determined using solar wind plasma and magnetic field data from Voyagers 1 and 2 and Helios 1. The modulation was related to two types of large scale systems of flows: one containing a number of transients such as shocks, post shock flows and magnetic clouds; the other consisting primarily of a series of quasi-stationary flows following interaction regions containing a stream interface and often bounded by a forward reverse shock pair. Each of the three major episodes of cosmic ray modulation was characterized by the passage of the system of transient flows. Plateaus in the cosmic ray intensity time profile were associated with the passage of systems of corotating streams.

153 citations


Journal ArticleDOI
TL;DR: In this paper, the fluid dynamics of violent volcanic eruptions by laboratory experiment is described, and the important fluid-dynamic processes that can be examined in laboratory models are discussed in detail.
Abstract: The study of the fluid dynamics of violent volcanic eruptions by laboratory experiment is described, and the important fluid-dynamic processes that can be examined in laboratory models are discussed in detail. In preliminary experiments, pure gases are erupted from small reservoirs. The gases used are Freon 12 and Freon 22, two gases of high molecular weight and high density that are good analogs of heavy and particulate-laden volcanic gases; nitrogen, a moderate molecular weight, moderate density gas for which the thermodynamic properties are well known; and helium, a low molecular weight, lowdensity gas that is used as a basis for comparison with the behavior of the heavier gases and as an analog of steam, the gas that dominates many volcanic eruptions. Transient jets erupt from the reservoir into the laboratory upon rupture of a thin diaphragm at the exit of a convergent nozzle. The gas accelerates from rest in the reservoir to high velocity in the jet. Reservoir pressures and geometries are such that the fluid velocity in the jets is initially supersonic and later decays to subsonic. The measured reservoir pressure decreases as the fluid expands through repetitively reflecting rarefaction waves, but for the conditions of these experiments, a simple steady-discharge model is sufficient to explain the pressure decay and to predict the duration of the flow. Density variations in the flow field have been visualized with schlieren and shadowgraph photography. The observed structure of the jet is correlated with the measured pressure history. The starting vortex generated when the diaphragm ruptures becomes the head of the jet. Though the exit velocity is sonic, the flow head in the helium jet decelerates to about one-third of sonic velocity in the first few nozzle diameters, the nitrogen head decelerates to about three-fourths of sonic velocity, while Freon maintains nearly sonic velocity. The impulsive acceleration of reservoir fluid into the surrounding atmosphere produces a compression wave. The strength of this wave depends primarily on the sound speed of the fluid in the reservoir but also, secondarily with opposite effect, on the density: helium produces a relatively strong atmospheric shock while the Freons do not produce any optically observable wave front. Well-formed N waves are detected with a microphone far from the reservoir. Barrel shocks, Mach disks, and other familiar features of steady underexpanded supersonic jets form inside the jet almost immediately after passage of the flow head. These features are maintained until the pressure in the reservoir decays to sonic conditions. At low pressures the jets are relatively structureless. Gas-particle jets from volcanic eruptions may behave as pseudogases if particle concentrations and mass and momentum exchange between the components are sufficiently small. The sound speed of volcanic pseudogases can be as large as 1000 m s^(−1) or as small as a few tens of meters per second depending on the mass loading and initial temperature. Fluids of high sound speed produce stronger atmospheric shock waves than do those of low sound speed. Therefore eruption of a hot gas lightly laden with particulates should produce a stronger shock than eruption of a cooler or heavily laden fluid. An empirical expression suggests that the initial velocity of the head of supersonic volcanic jets is controlled by the sound speed and the ratio of the density of the erupting fluid to that of the atmosphere. The duration of gas or pseudogas eruptions is controlled by the sound speed of the fluid and the ratio of reservoir volume to vent area.

146 citations


Journal ArticleDOI
TL;DR: In this paper, a weak shock theory is developed to treat inviscid motions, and the method of multiple scales is used to derive the nonlinear parabolic equation governing the evolution of weakly dissipative waves.
Abstract: One-dimensional small-amplitude waves in which the local value of the fundamental derivative changes sign are examined. The undisturbed medium is taken to be a Navier–Stokes fluid which is at rest and uniform with a pressure and density such that the fundamental derivative is small. A weak shock theory is developed to treat inviscid motions, and the method of multiple scales is used to derive the nonlinear parabolic equation governing the evolution of weakly dissipative waves. The latter is used to compute the viscous shock structure. New phenomena of interest include shock waves having an entropy jump of the fourth order in the shock strength, shock waves having sonic conditions either upstream or downstream of the shock, and collisions between expansion and compression shocks. When the fundamental derivative of the undisturbed media is identically zero it is shown that the ultimate decay of a one-signed pulse is proportional to the negative 1/3-power of the propagation time.

138 citations


Journal ArticleDOI
TL;DR: In this article, a statistical study on the proton energy spectra in the range of 35-1600 keV during the one-hour interval centered on the time of arrival of the shock front at the spacecraft of 75 interplanetary shocks that cover the period from August 1978 until December 1980, using the low-energy proton experiment on ISEE 3.
Abstract: We present the results of a statistical study on the proton energy spectra in the range of 35–1600 keV during the one-hour interval centered on the time of arrival of the shock front at the spacecraft of 75 interplanetary shocks that cover the period from August 1978 until December 1980, using the low-energy proton experiment on ISEE 3. The strength of the shocks was determined by calculating the ratio of the downstream to upstream plasma density by using the ion data obtained by the Los Alamos solar wind instrument. The shock events were sub-divided into four different classes based on the behavior of their low-energy (35–238 keV) spectral index. The signatures of the shock events and their spectral index-time profiles in the different classes are (1) smooth profiles associated with oblique, strong, and fast shocks, which roughly corresponds with predictions following from diffusive shock acceleration theory; (2) irregular profiles mainly associated with quasi-perpendicular shocks and (3) spikelike profiles associated with quasi-perpendicular shock spike events, where the properties within both classes point at predominant shock drift acceleration; (4) flat profiles, mainly associated with weak shocks accompanied by little or no shock-accelerated particles. Strong and fast oblique shocks are found to be the most effective particle accelerators. The spectrum at the shock can generally be described by two power laws with a breakpoint energy near 250 keV. For only 15% of the events the spectrum followed a power law over the full energy range. We found that the low-energy spectral index, measured immediately downstream of shocks associated with clear flux enhancements, is related to the shock strength according to predictions from first-order Fermi acceleration, irrespective of the assigned diffusive or drift character of the event.

Journal ArticleDOI
TL;DR: In this paper, microscopic dissipation processes in quasi-perpendicular shocks are studied by two-dimensional plasma simulations in which electrons and ions are treated as particles moving in self-consistent electric and magnetic fields.
Abstract: Microscopic dissipation processes in quasi-perpendicular shocks are studied by two-dimensional plasma simulations in which electrons and ions are treated as particles moving in self-consistent electric and magnetic fields. Cross-field currents induce substantial turbulence at the shock front reducing the reflected ion fraction, increasing the bulk ion temperature behind the shock, doubling the average magnetic ramp thickness, and enhancing the upstream field aligned electron heat flow. The short scale length magnetic fluctuations observed in the bow shock are probably associated with this turbulence.

Journal ArticleDOI
TL;DR: In this paper, a new statistical mechanical theory of multiphase, multicomponent systems is presented based on Ross's modification of the Mansoori-Canfield-Rasaiah-Stell hard-sphere variational theory and the improved one-fluid van der Waals mixture model.
Abstract: We present a new statistical mechanical theory of multiphase, multicomponent systems. It is based on Ross’s modification of the Mansoori–Canfield–Rasaiah–Stell hard‐sphere variational theory and the improved one‐fluid van der Waals mixture model. Next, the new theory and exponential‐6 potentials that accurately reproduce shock wave data of major detonation‐product species are used to compute the detonation properties of PETN (pentaerythritol tetranitrate). The results show satisfactory agreement with the experimental Chapman–Jouguet (CJ) data at initial densities ( ρ0) between 0.25 and 1.77 g/cm3. Small (≂9%) deviations which occur between the experimental and the theoretical CJ pressures at high ρ0 (>1.55 g/cm3) are attributed to time‐dependent processes associated with formation of solid carbon which is theoretically present in detonation products. We suggest that some CJ pressure experiments might have finished too soon to experimentally observe late‐time reactions involved in formation of solid carbon...

Journal ArticleDOI
TL;DR: In this article, a model for the shock consolidation of powders is developed which predicts, for a given powder density, the regimes of shock pressure P and shock duration t_d expected to yield fully densified compacts of near optimum strength.

Journal ArticleDOI
TL;DR: In this paper, the authors used ISEE 1 and 2 spacecraft magnetic field data to determine the scale lengths of various elements of shock structure, as well as wavelengths and wave polarizations, in a study of structural elements which include shock ramps and precursor wave trains over a series of oblique, low Mach number terrestrial bow shocks.
Abstract: ISEE 1 and 2 spacecraft magnetic field data are used to determine the scale lengths of various elements of shock structure, as well as wavelengths and wave polarizations, in a study of structural elements which include shock ramps and precursor wave trains over a series of oblique, low Mach number terrestrial bow shocks. Dissipative processes are reflected in the damping of the precursors, and dissipative scale lengths are of 200-800 km, or several times greater than shock thicknesses. The source of dissipation in the shocks does not appear to be the wave-wave decay of the whistlers, for which no evidence is found. The interaction of the whistler itself with upstream electrons is suggested as a simple and self-consistent explanation for the observed wave train damping.

Journal ArticleDOI
TL;DR: In this article, the authors compare results from a two-dimensional numerical eruption simulation (KACHINA) to calculations based upon a shock tube analog, and conclude that the hydrodynamics during the initial minutes of large caldera-forming ash flow eruptions may be dominated by blast wave phenomena.
Abstract: Comparison of results from a two-dimensional numerical eruption simulation (KACHINA) to calculations based upon a shock tube analog supports the conclusion that the hydrodynamics during the initial minutes of large caldera-forming ash flow eruptions may be dominated by blast wave phenomena. Field evidence for this phenomenology is pyroclastic surge deposits commonly occurring both directly below caldera-related ash flow sheets, on top of a preceding Plinian fall deposit (ground surge), and separating individual ash flow units. We model the eruption of the Tshirege member of the Bandelier Tuff (1.1 Ma B.P.) from the Valles caldera, New Mexico. In the model a magma chamber at 100 MPa (1 kbar) and 800°C is volatile rich, with an average H2O abundance above saturation greater than 8.7 wt % increasing to nearly 100 wt % near the very top of the chamber. Using a shock tube analogy, decompression of the chamber through a wide-open dikelike vent 0.1 km wide and 1 to 5 km long forms a shock wave of 3 MPa (≃3O atm) with a velocity greater than 1.0 km s−1. Steady flow of material erupted from the vent begins after 20 to 100 s based upon a 7-km depth from the ground surface to a reflective (density) boundary in the chamber and a rarefaction wave velocity of 100 to 600 m s−1. The velocity of the ash front behind the shock wave is 300 to 500 m s−1. The shock tube model serves as a basis to evaluate the consistency of the KACHINA code results which are similar to a one-dimensional problem along the symmetry axis. The results of the KACHINA simulation show in some detail the effect of multiple reservoir rarefaction reflections and possibly Prandtl-Meyer expansion in generating compressive wave fronts following the initial shock. The rarefaction resonance not only prolongs unsteady flow in the vent but tends to promote surging flow of ash behind the leading shock. Furthermore, these results are consistent with a blast wave characterized as a shock front followed by one or more pulses of entrained ash. The blast wave shocks ambient air to higher pressures and temperatures, the magnitudes of which depend strongly on the initial chamber overpressure, distance, and direction from the vent. In consideration of volcanic hazards our numerical model shows that a shock wave compressed the atmosphere to pressures of ≃0.2 to 0.7 MPa (2–7 atm) and temperatures of ≃200° to 300°C for distances to 10 km from the Bandelier vent(s).

Journal ArticleDOI
TL;DR: In this paper, the shape of diffracting waves is calculated by modifying Whitham's theory for the calculation of the shape and the flow pattern of diffracted waves in gases.

Journal ArticleDOI
TL;DR: In this paper, a model for the deposition of energy at powder particle surfaces during dynamic consolidation is presented, where the average energy flux incident on the surface of a powder particle is estimated to be E/τA where E is the specific energy deposited by the shock, τ is the shock rise time, and A the measured powder specific surface area.
Abstract: A model is presented for the deposition of energy at powder particle surfaces during dynamic consolidation. The average energy flux incident on the surface of a powder particle is estimated to be E/τA where E is the specific energy deposited by the shock, τ is the shock rise time, and A the measured powder specific surface area. This flux is assumed to be constant over the rise time of the shock, falling abruptly to zero for times longer than τ. Solution of the thermal transport equation subject to this boundary condition yields the thermal history within a powder particle having the area‐equivalent diameter D=6/ρ0A, where ρ0 is the solid density. The magnitude of the temperatures and the heating and cooling rates indicate likely material transformations. The penetration of a given isotherm provides an estimate of the volume fraction of material transformed. Good agreement is found between model calculations and measurements of the extent of local martensite formation in consolidated 4330V steel powder an...

Patent
24 Jul 1984
TL;DR: In this article, an essentially planar shock wave is generated with the assistance of a shock wave tube via a magnetic dynamic effect, which is focussed by an acoustic convergent lens, whereby the calculus to be pulverized is placed at the focal point (F) of the convergence lens.
Abstract: The utilization of the apparatus fundamentally lies in the medical sector. An essentially planar shock wave is generated with the assistance of a shock wave tube via a magnetic dynamic effect. This shock wave is focussed by an acoustic convergent lens, whereby the calculus to be pulverized is placed at the focal point (F) of the convergent lens. In order to couple the shock wave to the patient, the space that the shock wave traverses is filled with a coupling agent, for example water. The shock wave tube, the convergent lens and a fine adjustment for the displacement of the convergent lens relative to the shock wave tube are attached to a mounting stand so as to be pivotable in all directions. This disintegration facility comprising a shock wave tube has high operating reliability with respect to high voltage, requires low maintenance, and has only negligible imaging or focussing errors resulting from the shock wave producing membrane and the convergent lens.

Journal ArticleDOI
D. A. Kleinman1, D. Auston2
TL;DR: In this paper, a general theory for electrooptic shock (Cerenkov) radiation in transparent crystals having a linear electro-optic effect is presented, which obtains expressions for the radiated electric field, power spectrum, and total energy both 2D and 3D geometries are discussed as well as the proper focusing conditions.
Abstract: A general theory is presented for electrooptic shock (Cerenkov) radiation in transparent crystals having a linear electrooptic effect Significant amounts of shock radiation require subpicosecond pulses of suitably focused laser radiation to produce a moving pulse of polarization in the medium The theory obtains expressions for the radiated electric field, power spectrum, and total energy Both 2D and 3D geometries are discussed as well as the proper focusing conditions Numerical examples are given based on the nonlinear material LiTaO 3

Journal ArticleDOI
TL;DR: In this article, the experimental results from a detailed investigation of the turbulent flowfields in supersonic shockwave/boundary-layer interactions at Af=2.25 were reported.
Abstract: This paper reports the experimental results from a detailed investigation of the turbulent flowfields in supersonic shock-wave/boundary-layer interactions at Af=2.25. The interactions were produced by twodimensional compression corners having angles of 8, 13, and 18 deg, the flows being respectively attached, incipiently separated, and separated. Turbulence data from a laser velocimeter and a constant-temperature, hotwire anemometer are presented along with a mean flow survey from wall and pitot-static pressures. Qualitative aspects of the turbulence deduced from spectral analysis and high-speed schlieren pictures are also discussed. It is shown that a large amount of the turbulent energy is contained in large-scale structures that are still observed downstream of the interacting region, despite the severe pressure gradient. The lateral extent of these structures is of the order of one boundary-layer thickness and is roughly half of their longitudinal scale. A low-frequency unsteadiness is associated with the existence of a separation bubble, but does not affect the rest of the flow. The Reynolds shear stress is reduced in the vicinity of the separation bubble where the spatial derivatives of the normal stresses become significant.

Journal ArticleDOI
TL;DR: In this article, ISEE 1, 2 and 3 data from 1978 on interplanetary magnetic fields, shock waves and particle energetics are examined to characterize a quasi-parallel shock.
Abstract: ISEE 1, 2 and 3 data from 1978 on interplanetary magnetic fields, shock waves and particle energetics are examined to characterize a quasi-parallel shock. The intense shock studied exhibited a 640 km/sec velocity. The data covered 1-147 keV protons and electrons and ions with energies exceeding 30 keV in regions both upstream and downstream of the shock, and also the magnitudes of ion-acoustic and MHD waves. The energetic particles and MHD waves began being detected 5 hr before the shock. Intense halo electron fluxes appeared ahead of the shock. A closed magnetic field structure was produced with a front end 700 earth radii from the shock. The energetic protons were cut off from the interior of the magnetic bubble, which contained a markedly increased density of 2-6 keV protons as well as the shock itself.

Journal ArticleDOI
TL;DR: In this article, a near-field microphone array and a single-sensor wedge-shaped hot-film probe were used to investigate shock noise associated with unheated supersonic jets.
Abstract: Shock noise associated with unheated supersonic jets was investigated using a near-field microphone array and a single-sensor wedge-shaped hot-film probe. Both over- and underexpanded cases were investigated using Mach 1.45 and 1.99 convergent-divergent nozzles. Correlation measurements through each shock cell of a single underexpanded case with the Mach 1.45 nozzle were obtained between the hot-film probe and the microphone array. The results of the hot-film/near-field microphone correlations show general agreement with certain theoretical models as to the location for shock noise production, and provide evidence for the existence of some large-scale flow structure that collectively interacts and phases the motion of the downstream shocks. The nearfield microphone correlations demonstrate that downstream shocks dominate shock noise production and suggest the existence of a Doppler effect in the near field of the sources. In addition, broadband shock noise is found to propagate at small angles to the jet axis.

Journal ArticleDOI
TL;DR: In this article, high-resolution magnetic field measurements adjacent to the boundary of the distant magnetotail plasma sheet have been analyzed, and the nature of the changes in the field between the lobe and the plasma sheet is consistent with the boundary being a slow mode shock.
Abstract: High time-resolution magnetic field measurements adjacent to the boundary of the distant magnetotail plasma sheet have been analyzed. The nature of the changes in the field between the lobe and the plasma sheet is consistent with the boundary being a slow mode shock. The crossing times are relatively long (about 30 sec), implying a shock thickness estimated to be approximately 2000 km. An increase in the entropy of the electrons is consistent with dissipation at the shock. Reasonable shock-normal directions are derived, and may be used to determine the location of the spacecraft relative to the reconnection or merging region. It is suggested that a foreshock exists in which upstream wave and particle phenomena are occurring.

Journal ArticleDOI
TL;DR: In this paper, an iterative method is presented for modelling reactive gas flows within shock tunnels, which overcomes both the problem of the stiffness of the chemical rate equations, which arises due to the greatly varying reaction' rates, and the throat singularity in the velocity equation for subsonicsupersonic flow within a Laval nozzle.
Abstract: An iterative method is presented for modelling reactive gas flows within shock tunnels. The method overcomes both the problem of the stiffness of the chemical rate equations, which arises due to the greatly varying reaction' rates, and the throat singularity in the velocity equation for subsonicsupersonic flow within a Laval nozzle. The effects of Coulomb interactions which depress the ionization potential of the ionic species can also be included because of the iterative nature of the method. The method computes the state of the gas both along the flow and within the reservoir or stagnation region. Sample computations are given for air, carbon dioxide and nitrogen for reservoir-nozzle gas flows and for flows behind normal shocks.

Journal ArticleDOI
TL;DR: In this article, the authors present evidence for two types of relatively large amplitude MHD waves upstream and downstream of quasi-parallel forward and reverse interplanetary shocks, which propagate along the magnetic field.
Abstract: Evidence for two types of relatively large amplitude MHD waves upstream and downstream of quasi-parallel forward and reverse interplanetary shocks is presented. The first mode is an Alfven wave with frequencies (in the spacecraft frame) in the range of 0.025 to 0.07 Hz. This is a left-hand polarized mode and propagates within a few degrees of the ambient magnetic field. The second is a fast MHD mode with frequencies in the range of 0.025 to 0.17 Hz, right-hand polarization and propagating along the magnetic field. These waves are detected principally in association with quasi-parallel shock. The Alfven waves are found to have plasma rest frame frequencies in the range of 1.1 to 6.3 mHz with wavelengths in the order of 4.8 x 10 to the 8th power to 2.7 x 10 to the 9th power cm. Similarly, the fast MHD modes have rest frame frequencies in the range 1.6 to 26 mHz with typical wavelengths about 2.19 x 10 to the 8th power cm. The magnetic field power spectrum in the vicinity of these interplanetary shocks is much steeper than f to the -s/3 at high frequencies. The observed spectra have a high frequency dependence of f to the -2/5 to f to the -4.

Journal ArticleDOI
TL;DR: In this article, a procedure for obtaining the structure of high Mach number, cosmic-ray-mediated shocks, including their overall compresion ratio, around a low Mach number viscous subshock is outlined.
Abstract: Cosmic-ray-mediated shocks may accelerate enough cosmic rays to high enough energies that they escape the shock, carrying an appreciable amount of energy before being convected to downstream infinity. Under such conditions, it is noted, the overall compression ratio cannot be determined from the conservation equations as in conventional hydrodynamic treatments, and the standard equations for shock acceleration admit arbitrarily high compression ratios. A procedure is outlined for obtaining the structure of high Mach number, cosmic-ray-mediated shocks, including their overall compresion ratio, around a low Mach number viscous subshock. Analytic solutions are obtained by quardrature for an energy-dependent diffusion coefficient in the limit of extreme sensitivity to energy, which, unlike previous solutions, include the finite thermal pressure of the preshock gas.

Journal ArticleDOI
TL;DR: In this paper, the authors derived shear viscosity and heat conduction coefficients of nuclear matter from the Uhlenbeck-Uehling equation and applied them to study a shock profile in nuclear matter, yielding results that are roughly consistent with cascade calculations.

Journal ArticleDOI
TL;DR: In this paper, the white-light coronal transient is regarded to be a fully developed magnetohydrodynamic flow that plows into a preexisting ambient atmosphere, where the ambient atmosphere has no magnetic field whereas the outflow carries a substantial axisymmetric magnetic field.
Abstract: In this theoretical study, the white-light coronal transient is regarded to be a fully developed magnetohydrodynamic flow that plows into a preexisting ambient atmosphere. To keep the mathematical problem simple, a model is considered where the ambient atmosphere has no magnetic field whereas the outflow carries a substantial axisymmetric magnetic field. A contact surface forms to drive a strong gasdynamic shock that travels ahead and compresses the ambient atmosphere. Such a global flow, with the effect of gravity included, is illustrated with a set of exact, analytic, self-similar solutions of magnetohydrodynamics. The governing nonlinear equations, derived in the first paper of this series, are solved with a general technique, constructing explicitly the gasdynamic shock and the trailing contact surface. Various types of magnetic field configurations 1 in the outflow behind the contact surface are shown to give rise to plasma structures which resemble those commonly observed in white-light transients, such as loops, voids, and blobs. It is advocated that the coronal transient is a result of a hydromagnetic system becoming gravitationally unstable in the low corona. This takes place when the magnetic tension force and solar gravity fail to counter the natural tendency of a magnetized plasma to expand. Amore » physical picture of this dynamic process is described, and some quantitative properties to relate to observation are pointed out. The original self-similar theory requires an adiabatic index ..gamma.. = 4/3. It is shown that this constraint can be relaxed to ..gamma..not = 4/3, raising interesting questions of heating and cooling in an expanding plasma.« less

Journal ArticleDOI
TL;DR: In this paper, the authors used ISEE-3 data to analyze variations in charged particle and magnetic field characteristics near plasma sheet boundaries in the distant magnetotail, and they demonstrated that several of the crossings had the properties of slow mode shocks.
Abstract: Recently Feldman et al. (1984) used ISEE-3 data to analyze variations in charged particle and magnetic field characteristics near plasma sheet boundaries in the distant magnetotail, and they demonstrated that several of the crossings had the properties of slow mode shocks. ISEE-3 plasma wave measurements at two of these crossings are presently discussed, and it is shown that all conventional characteristics of fast collisionless shock spectra are present. Upstream (lobe side) electron plasma oscillations are detected in association with electron heat flux enhancements, and pronounced spectral peaks at lower frequencies are found within the shock layer.