Shock Theory Research Articles

Global simulation of the solar wind‐magnetosphere interaction: The importance of its numerical validity

A new three‐dimensional magnetohyrodynamic (MHD) simulation code based on the fourth‐order Runge‐Kutta‐Gill time advance and the direct finite space difference is applied to the detailed study of the solar wind interaction with the Earth's dipole field with special emphasis on its numerical soundness. The dynamic formation processes of the bow shock and the magnetopause are revealed, where the transient propagation characteristics of fast waves play the leading role. The plasma sheet formation process is also revealed. The high temperature, high density, and hence high pressure in the plasma sheet are caused by the fast waves which compress the dipole field. The study of the effects of the interplanetary magnetic field (IMF) on the plasma sheet finds that when the IMF is directed south, the plasma sheet is strongly compressed by the reconnected magnetic flux which is carried from the day side. The peak plasma sheet pressure that appears around 8 RE (RE∶ Earth's radius) on the nightside is almost exactly as large as the solar wind dynamic pressure in the absence of the IMF. When the IMF is north, the nightside lobe magnetic field is peeled off, so that the plasma sheet pressure becomes weakly depressed in comparison with the no‐IMF case. This indicates that the direction of the IMF largely influences the pressure of the plasma sheet. More interestingly and importantly, no Kelvin‐Helmholtz instability occurs along the magnetopause in an ideal MHD, contrary to the conventional understanding. Furthermore, no entry of mass, momentum, and energy through the magnetopause is observed at all in our simulation. This strongly ensures enough numerical accuracy and validity of the present work. Thus the simulation results of earlier works where a considerable amount of solar wind momentum is transported into the magnetosphere must be due to a numerical inaccuracy. As further evidence showing the numerical validity of the present code, the relationship between the standoff distance and the adiabatic constant is compared with the strong shock theory, and a fairly good agreement is obtained. On the other hand, the standoff distance is found to be weakly dependent upon the dynamic pressure of the solar wind in the realistic parameter range.

Structure of slow magnetosonic shocks in low beta plasmas

Slow magnetosonic shocks are an efficient way in which magnetic energy in a collisionless plasma is converted into particle flow and thermal energy. Previous analytic and simulation studies of slow shocks have suggested that their structure consists of a damped wavetrain beginning at the shock transition and extending into the downstream region. Spacecraft observations in the solar wind and the Earth's magnetotail have found structures that resemble slow shocks except that most of them do not possess a trailing wavetrain. To resolve the conflict between theory and observations of slow shocks, we have performed new simulations which correct some of the previous results and show that depending on the sonic Mach number and the ratio of electron to ion temperature, slow shocks may or may not possess a wavetrain.

Application of cosmic-ray shock theories to the Cygnus Loop - an alternative model

Steady state cosmic-ray shock models are investigated in light of observations of the Cygnus Loop supernova remnant. In this work the authors find that the model of Völk, Drury, and McKenzie, in which the plasma waves are generated by the streaming instability of the cosmic rays and are dissipated into the gas, can be made consistent with some observed characteristics of Cygnus Loop shocks. The waves heat the gas substantially in the cosmic-ray precursor, in addition to the usual heating in the (possibly weak) gas shock. The model is used to deduce upstream densities and shock velocities using known quantities for Cygnus Loop shocks. Compared to the usual pure gas shock interpretation, it is found that lower densities and approximately 3 times higher velocities are required. If the cosmic-ray models are valid, this could significantly alter our understanding of the Cygnus Loop's distance and age and of the energy released during the initial explosion.

Theory and simulation of collisionless parallel shocks

A one‐dimensional theory of shocks propagating parallel to the ambient magnetic field in a collisionless plasma is presented. We show that shock formation and plasma heating can result from parallel propagating electromagnetic ion beam‐driven instabilities for a wide range of Mach numbers and upstream plasma conditions. The plasma upstream from a parallel shock overtakes the slower, downstream plasma in the absence of any electrostatic or electromagnetic wave fields. An interface region is created that is unstable to electromagnetic ion beam‐driven growth. The waves grow until they can scatter and couple the upstream and downstream plasma populations and can provide the necessary entropy increase for the shock. The marginal firehose state is reached downstream from the shock if the Alfvén Mach number MA is high enough (MA ≡ Uu/CA, where Uu is the upstream shock velocity and CA is the upstream Alfvén speed). A one‐dimensional compression of the ions along the magnetic field line direction results for weaker shocks. We solve a set of jump conditions and show that the marginal firehose state is first reached at a small magnetosonic Mach number (less than 2). We derive various conditions for creating and maintaining the shock via the ion beam‐driven instability and show that these conditions are roughly equal. The results from many one‐dimensional hybrid simulation runs are compared with the predictions of the theory and are shown to be in good agreement. At low Mach numbers, resonant group‐standing waves are the most strongly amplified and scatter the ions over several wavelengths. The transition in the ion pressure tensor is smooth, going from an isotropic upstream state to an anisotropic firehose state downstream in several wavelengths. The ions are compressed in one dimension at small Mach numbers, and there is little change in the perpendicular ion temperature across the shock. At high Mach numbers a small fraction of the upstream ions are backscattered by large‐amplitude magnetic waves at the shock front. The backscattered ions resonantly generate waves in the foreshock region, which are then convected downstream and are strongly compressed and amplified at the shock front. The bulk of the ion population passes through the shock and is nonresonantly scattered and heated by the amplified downstream waves. The change in the pressure tensor across the shock is abrupt; most of the entropy increase occurs within one or two wavelengths beyond where the waves are compressed and amplified. We compare the theoretical predictions with recently published observations of quasi‐parallel interplanetary shocks and the Earth's quasi‐parallel bow shock and find good agreement. Some theoretical limits on the fraction of ions that can be scattered back upstream are derived, and the implications for cosmic ray injection, particle acceleration, and astrophysical shocks are discussed.

A self-consistent theory of photohydrodynamical shocks

A formalism is developed which simultaneously describes the evolution of both the photon distribution and the electron temperature in radiation-dominated shocks. The procedure permits the imposition of an arbitrary spectrum at any chosen optical depth and provides results which automatically satisfy the dynamical constraints derived by Blandford and Payne (1981). It is noted that radiation-dominated shocks may play an important role in a variety of astrophysical environments, from accreting neutron stars to quasars and the early universe.

Improved bow shock models for Herbig-Haro objects - Application to HH 2A-prime

An improved version of the bow shock theory previously applied to Herbig-Haro objects is presented. The modifications provide a more accurate calculation of the ionization state of material entering the bow shock. The revised preionization does not drastically affect the emission-line predictions for a 200 km/s bow shock model, though the effects will be more severe for slower shock velocities. The line profiles of the new models resemble the observed profiles somewhat more closely, and the relative emission-line intensities typically differ by 30 percent from those predicted by the older models. The models agree well with new IUE spectra and existing optical data for HH 2A-prime.

The MHD intermediate shock interaction with an intermediate wave: Are intermediate shocks physical?

Contrary to the usual belief that MHD intermediate shocks are extraneous, we have recently shown by numerical solutions of dissipative MHD equations that intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. In this paper, we clarify the differences between the conventional view and our results by studying the interaction of an MHD intermediate shock with an intermediate wave. The study reaffirms our results. In addition, the study shows that there exists a larger class of shocklike solutions in the time‐dependent dissipative MHD equations than are given by the MHD Rankine‐Hugoniot relations. It also suggests a mechanism for forming rotational discontinuities through the interaction of an intermediate shock with an intermediate wave. The results are of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models.

Travelling waves and shocks with pressure diffusion

This article explores possible implications of putative pressure diffusion for shocks in one-dimensional travelling waves in an ideal gas. From this new hypothesis all aspects of such shocks can be calculated except shock thickness. Unlike conventional shock theory, the concept of entropy is not needed or used. Our analysis shows that temperature rises near a shock, which is of course an experimental fact; however, it also predicts that very close to a shock, density increases faster than pressure. In other words, a shock itself is cold.

Stochastic model theory of broadband shock associated noise from supersonic jets

A method based on the work of Tam and Tanna (1982) for calculating the near field noise spectrum and the spatial distribution of broadband shock associated noise from supersonic jets is proposed. Multiple-scales expansion is used to decompose the quasi-periodic shock cells into time-independent waveguide modes of the jet flow, and the interaction of the instability waves with each of the waveguide modes is shown to generate unsteady disturbances which become part of the broadband shock associated noise when radiated to the far field. The observed broadband shock associated noise is composed of a superposition of the various distinct spectra of the different waveguide modes, and the multispectra can be easily identified in many of the existing far and near field noise measurements.

Propagation of medium strength shock waves through the atmosphere

The rise times and overpressures for shock waves from supersonic projectiles have been measured under a variety of atmospheric conditions. These measurements extend the overpressure for which weak shock theory adequately predicts measured values to 3 kPa. Predicted shock rise times agree reasonably well with theory for shock overpressures between 0.04 and 0.5 kPa with differences increasing at higher overpressures. At overpressures greater than 0.5 kPa, measured rise times might be limited by the experimental apparatus. No correlation between measured rise times and atmospheric turbulence was observed.

On MHD intermediate shocks

Contrary to the usual belief that MHD intermediate shocks are extraneous, we show in this paper by numerical solutions of resistive MHD equations that at least some of the intermediate shocks are admissible and can be formed through nonlinear steepening from a continuous wave. The result is of importance not only to the MHD shock theory but also to studies such as magnetic field reconnection models.

Molecular theory and cooperative mechanism of shock waves‐induced detonations in energetic molecular crystals

International Journal of Quantum ChemistryVolume 31, Issue 2 p. 331-331 ErratumFree Access Molecular theory and cooperative mechanism of shock waves-induced detonations in energetic molecular crystals S. Odiot, S. Odiot Laboratoire de Recherches Physiques, associé au CNRS No. 71, Université Pierre et Marie Curie, 4, place Jussieu, Tour 22, ler étage, 75230 Paris Cedex 05, FranceSearch for more papers by this authorM. Peyrard, M. Peyrard Laboratoire Optique du Réseau Cristallin, Faculté des Sciences, 6, Boulevard Gabriel, 211000 Dijon, FranceSearch for more papers by this authorJ. Schnur, J. Schnur Naval Research Laboratory, Washington, D.C. 20375Search for more papers by this authorE. Oran, E. Oran Naval Research Laboratory, Washington, D.C. 20375Search for more papers by this author S. Odiot, S. Odiot Laboratoire de Recherches Physiques, associé au CNRS No. 71, Université Pierre et Marie Curie, 4, place Jussieu, Tour 22, ler étage, 75230 Paris Cedex 05, FranceSearch for more papers by this authorM. Peyrard, M. Peyrard Laboratoire Optique du Réseau Cristallin, Faculté des Sciences, 6, Boulevard Gabriel, 211000 Dijon, FranceSearch for more papers by this authorJ. Schnur, J. Schnur Naval Research Laboratory, Washington, D.C. 20375Search for more papers by this authorE. Oran, E. Oran Naval Research Laboratory, Washington, D.C. 20375Search for more papers by this author First published: February 1987 https://doi.org/10.1002/qua.560310215AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume31, Issue2February 1987Pages 331-331 RelatedInformation

Observational tests of the bow shock theory of Herbig-Haro objects

We discuss four different tests of the bow-shock theory of Herbig-Haro objects, emphasizing especially tests based on position-velocity diagrams and on the appearance of “double layer” structures in the spatial maxima of the high- and low-velocity components of the emission lines. Though this latter effect is surprising, it is a fundamental consequence of the bow shock theory.

Nonlinear distortion of the bubble pulse in a layered inhomogeneous ocean

Many years ago, the author analyzed a representative deep‐fired long‐range underwater explosion waveform [J. Acoust. Soc. Am. 35, 800 (1963)]. The most striking feature was the so‐called “double shock” formation, e.g., a strong resemblance between the shock wave and bubble pulse in both amplitude and shape. The phenomenon is attributed to the combined effects of detonation depth and waveform propagation. In a previous paper the characteristics of an explosion waveform at the source, as function of shot depth was established [Proc. 11th ICA, Paris (1983), Vol. 1, pp. 345–348]. Weak shock theory was used to study nonlinear distortion of the bubble pulse as it propagates in an homogeneous, unbounded, dissipationless medium [Proc. 10th Int. Symp. Nonlinear Acoust., Kobe, Japan (1984), pp. 79–82]. It was found that the deepest fired shots suffer the greatest distortion but that, in general, extremely long range is required for shock wave formation. However, focusing due to inhomogeneous structure may substantially increase pulse strength thereby enhancing nonlinear effects. Here the effect of inhomogeneous layering on the range required for shock wave formation is investigated.

Molecular theory and cooperative mechanism of shock waves‐induced detonations in energetic molecular crystals

AbstractAt a microscopic level, two molecular models, respectively one‐ and two‐dimensional, for describing the shock‐induced detonationmechanism of an energetic crystal have been previously successively presented (after initiation).We put together, here, their characteristic features, and we discuss their respective contributions inorder to define the molecular and crystalline conditions that a crystal fulfills to sustain a shock induced wave detonation. The two‐dimensional model which allows longitunal but also transversal atomic motions, has enabled us to elicit the crystalline structure in relation with the existence of a wave detonation propagation in the crystal or not. By comparison to detonation experiments the coherence of the models is performed. It may thus be possible to form an idea as to why a molecular compound can detonate through a shock wave.

Production of Highly Relativistic Ions and Electrons by Quasi-Perpendicular Magnetosonic Shock Waves

It is shown that a non-relativistic theory for laminar shocks breaks down for a plasma having a rather high Alfvén speed, \(v_{\text{A}}{\gtrsim}c\)( m e / m i ) 1/2 . By using a 2-1/2 dimension, fully relativistic, fully electromagnetic particle code, time evolution of quasi-perpendicular shocks in such plasmas is studied. Some ions and electrons are accelerated simultaneously to highly relativistic speeds by the shock.

Depressed Elderly Women in Switzerland: An Example of Testing and of Generating Theories

Results of a Swiss study revealed that a high proportion of farm women were depressed. Their depression is accounted for through the development of a theory of culture shock which is based upon the conflict between traditional values and the realities of everyday life. The importance of using life histories to supplement survey data in theory development is illustrated.

Investigation of Mach reflection of a shock wave (Part 3, Strength of a reflected shock wave)

The reflection phenomena of a plane moving shock wave at a wedge surface have been investigated by many researchers, and four different types of reflection have been observed in previous shock tube experiments. The authors reported in the previous reports on the domains and boundaries of these four types of reflection and the shape of a reflected shock wave. In the present paper, the distribution of the strength of a reflected shock wave along its wave front has been calculated from its shape obtained by optical observations, and the relation between the strength and the shape of a reflected shock wave has been discussed detail. Furthermore, the Flow properties around the triple point in the case of Mach reflection have been calculated using experimental data, and the validity of the three shock theory has been examined.

A Theory of Cold-Plasma Shocks, Particle Bunching, and Virtual-Cathode Dynamics in Highly Symmetric Configurations

Virtual-cathode oscillations and particle bunching are proved to be shock-induced phenomena in one-dimensional configurations. The complete solution of one-dimensional problems is reduced to quadratures. Extension of the one-dimensional results to general configurations is included.

Structure of a Plasma-Focus Current Sheath from Magnetic and Optical Measurements

Simultaneous measurements of the magnetic-field distribution and the light intensity emitted by the current sheath (CS) generated in a Plasma Focus (PF) device are presented. For operating deuterium pressures in the range 0.55-2.5 mbar, we derive the plasma density and the mean hydrodynamic velocity in a frame of reference fixed to the sheath, where both quantities are in agreement with the ones predicted by the strong ionizing shock theory. The electric field in the quoted frame is also deduced, and the obtained values are consistent with those reported by other authors.