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NASA NTRS1992

Relativistic, perpendicular shocks in electron-positron plasmas

One-dimensional particle-in-cell plasma simulations are used to examine the mechanical structure and thermalization properties of collisionless relativistic shock waves in electron-positron plasmas. Shocks propagating perpendicularly to the magnetic field direction are considered. It is shown that these shock waves exist, and that they are completely parameterized by the ratio of the upstream Poynting flux to the upstream kinetic energy flux. The way in which the Rankine-Hugoniot shock jump conditions are modified by the presence of wave fluctuations is shown, and they are used to provide a macroscopic description of these collisionless shock flows. The results of a 2D simulation that demonstrates the generality of these results beyond the assumption of the 1D case are discussed. It is suggested that the thermalization mechanism is the formation of a synchrotron maser by the coherently reflected particles in the shock front. Because the downstream medium is thermalized, it is argued that perpendicular shocks in pure electron-positron plasmas are not candidates as nonthermal particle accelerators.

Gallant, Yves A.↗
NASA NTRS1992

H-alpha images of the Cygnus Loop - A new look at shock-wave dynamics in an old supernova remnant

Attention is given to deep H-alpha images of portions of the east, west, and southwest limbs of the Cygnus Loop which illustrate several aspects of shock dynamics in a multiphase interstellar medium. An H-alpha image of the isolated eastern shocked cloud reveals cloud deformation and gas stripping along the cloud's edges, shock front diffraction and reflection around the rear of the cloud, and interior remnant emission due to upstream shock reflection. A faint Balmer-dominated filament is identified 30 arcmin further west of the remnant's bright line of western radiative filaments. This detection indicates a far more westerly intercloud shock front position than previously realized, and resolves the nature of the weak X-ray, optical, and nonthermal radio emission observed west of NGC 6960. Strongly curved Balmer-dominated filaments along the remnant's west and southwest edge may indicate shock diffraction caused by shock wave passage in between clouds.

Fesen, Robert A.↗
NASA NTRS1992

Optical and TEM study of shock metamorphism from the Sedan test site

Thus far, detailed petrologic studies of shock metamorphism have been performed on samples recovered from laboratory experiments and on a few natural impactites. The loading history of these samples is quite different: In particular, laboratory experiments spend only a short time (less than 1 microsec) at peak pressure, whereas natural impactites may have stress pulses from 0.1 - 1 ms. On the other hand, laboratory experiments have known stress histories; natural impactites do not. Natural samples are also subjected to thousands or millions of years of postshock annealing and/or weathering. A useful intermediate case is that of nuclear detonation. Stress pulses for these events can reach 0.1 ms or higher, and samples are obtained in pristine condition. All three types of loading produce stresses of hundreds of kilobars. Samples studied were taken from the Sedan nulcear test site, and consist of a coarse-grained granodiorite containing quartz, K-feldspar, cordierite, and hornblende. Samples were studied optically in this section, then were thinned with an ion mill and studied by transmission electron microscopy (TEM). Optically, quartz and K-feldspar displayed numerous sets of planar deformation features (PDF's) identical to the nondecorated PDF's seen in laboratory samples and many natural impactites. TEM study showed that the PDF's in quartz and feldspar corresponded to densely packed wide transformation lamellae identical to those described in laboratory studies. The transformation lamellae in both minerals were amorphous, with no sign of high-pressure phases. In the case of K-feldspar only, narrow sublamellae extended outward from some wide lamellae. Quartz, which was more abundant and studied more extensively, contained no shock-induced dislocations. Some planar features were also seen in cordierite, but could not be identified due to rapid beam damage. No shock defects were seen in hornblende in TEM. The shock-induced defects present at the Sedan site are very similar to those seen in shock recovery experiments, and also to those present at certain natural events (e.g., Meteor Crater). This suggests that shock deformation in quartz is not strongly dependent on shock pulse duration, and that laboratory recovery experiments are useful simulations of natural impact events.

Gratz, A. J.↗
NASA NTRS1992

U-Pb isotopic results for single shocked and polycrystalline zircons record 550-65.5-Ma ages for a K-T target site and 2700-1850-Ma ages for the Sudbury impact event

The refractory mineral zircon develops distinct morphological features during shock metamorphism and retains these features under conditions that would anneal them in other minerals. In addition, weakly shocked zircon grains give primary ages for the impact site, while highly reconstituted (polycrystalline) single grains give ages that approach the age of the impact event. Data for a series of originally coeval grains will define a mixing line that gives both of these ages providing that no subsequent geological disturbances have overprinted the isotopic systematics. In this study, we have shown that the three zircon grain types described by Bohor, from both K-T distal ejecta (Fireball layer, Raton Basin, Colorado) and the Onaping Formation, represent a progressive increase in impact-related morphological change that coincides with a progressive increase in isotopic resetting in zircons from the ejecta and basement rocks. Unshocked grains are least affected by isotopic resetting while polycrystalline grains are most affected. U-Pb isotopic results for 12 of 14 single zircon grains from the Fireball layer plot on or close to a line recording a primary age of 550 +/- 10 Ma and a secondary age of 65.5 +/- 3 Ma. Data for the least and most shocked grains plot closest to the primary and secondary ages respectively. The two other grains each give ages between 300 and 350 Ma. This implies that the target ejecta was dominated by 550-Ma rocks and that the recrystallization features of the zircon were superimposed during the impact event at 65.5 Ma. A predominant age of 550 Ma for zircons from the Fireball layer provides an excellent opportunity to identify the impact site and to test the hypothesis that multiple impacts occurred at this time. A volcanic origin for the Fireball layer is ruled out by shock-related morphological changes in zircon and the fact that the least shocked grains are old. Basement Levack gneisses north of the Sudbury structure have a primary age of 2711 Ma. Data for three single zircons from this rock, which record a progressive increase in shock features, are displaced 24, 36, and 45 percent along a Pb-loss line toward the 1850 +/- 1 Ma minimum age for the impact as defined by the age of the norite. Southeast of the structure three shocked grains from the Murray granite record a primary age of 2468 Ma and are displaced 24, 41, and 56 percent toward the 1853 +/- 4 Ma even as defined by coexisting titanite.

Krogh, T. E.↗
NASA NTRS1993

Cosmic-ray acceleration during the impact of shocks on dense clouds

In order to elucidate the properties of diffusive shock acceleration in nonuniform environments, an extensive set of simulations of the dynamical interactions between plane nonradiative shocks and dense gas clouds was carried out initially in static equilibrium with their environments. These time-dependent calculations are based on the two-fluid model for diffusive cosmic ray transport, and include the dynamically active energetic proton component of the cosmic rays as well as passive electron and magnetic field components. Except when the incident shock is itself already dominated by cosmic ray pressure, it is found that the presence of the cloud adds little to the net acceleration efficiency of the original shock and can, in fact, reduce slightly the net amount of energy transferred to cosmic rays after a given time. It is found that, in 2D cloud simulations, the always-weak bow shock and the shock inside the cloud are less important to acceleration during the interaction than the tail shock.

Jones, T. W.↗
NASA NTRS1993

The gradient of galactic cosmic rays at the solar-wind termination shock

We report on a study of the expected spatial variation of the galactic cosmic-ray intensity in the outer heliosphere, in the vicinity of the solar-wind termination shock. Model simulations which contain all of the transport effects, including drifts, predict that the radial gradients change abruptly at the shock, and that the nature of the effect varies significantly with particle energy. At low energies, the radial gradient changes abruptly from a lower value inside the shock to a higher value outside, whereas at high energies, the higher value of the gradient is inside the shock. This effect, which is a consequence of the matching conditions at the shock and is closely related to diffusive shock acceleration, is qualitatively the same for both helisopheric magnetic polarity states and remains much the same in one-dimensional, two-dimensional, and three-dimensional models. Hence drifts do not change the nature of this phenomenon, although they change it quantitatively. The effect is, of course, not present in the absence of a terminal shock and may prove to be an important diagnostic tool for the study of the termination of the solar wind.

Jokipii, J. R.↗
NASA NTRS1992

Diffusive shock acceleration - Acceleration rate, magnetic-field direction and the diffusion limit

This paper reviews the concept of diffusive shock acceleration, showing that the acceleration of charged particles at a collisionless shock is a straightforward consequence of the standard cosmic-ray transport equation, provided that one treats the discontinuity at the shock correctly. This is true for arbitrary direction of the upstream magnetic field. Within this framework, it is shown that acceleration at perpendicular or quasi-perpendicular shocks is generally much faster than for parallel shocks. Paradoxically, it follows also that, for a simple scattering law, the acceleration is faster for less scattering or larger mean free path. Obviously, the mean free path can not become too large or the diffusion limit becomes inapplicable. Gradient and curvature drifts caused by the magnetic-field change at the shock play a major role in the acceleration process in most cases. Recent observations of the charge state of the anomalous component are shown to require the faster acceleration at the quasi-perpendicular solar-wind termination shock.

Jokipii, J. R.↗
NASA NTRS1993

Exploratory study of shock reflection near an expansion corner

Experiments were performed at Mach 8 in which a shock was reflected off a low Reynolds number, turbulent boundary layer past an expansion corner. The shock was generated by 2- and 4-deg sharp wedges, and the corner was either 2.5 or 4.25 deg. The inviscid shock reflection was one boundary layer thickness ahead or behind the corner or at the corner itself. All interactions were unseparated. The dynamic surface pressure distributions were examined together with the case of shock reflection on a flat plate. With shock reflection ahead of the corner, the mean surface pressure downstream was attenuated due to the proximity of the corner. With shock reflection downstream of the corner, the surface pressure distribution showed a reduced upstream influence. The highly swept expansion fan produced a surface pressure which rose gently downstream with no minima, unlike in supersonic flows with the same shock-corner separation distance. In many of the interactions, an anomalous pressure peak was found downstream. The surface pressure through the interaction exhibited unsteadiness.

Lu, Frank K.↗
NASA NTRS1993

Si-29 NMR spectroscopy of naturally-shocked quartz from Meteor Crater, Arizona: Correlation to Kieffer's classification scheme

We have applied solid state Si-29 nuclear magnetic resonance (NMR) spectroscopy to five naturally-shocked Coconino Sandstone samples from Meteor Crater, Arizona, with the goal of examining possible correlations between NMR spectral characteristics and shock level. This work follows our observation of a strong correlation between the width of a Si-29 resonance and peak shock pressure for experimentally shocked quartz powders. The peak width increase is due to the shock-induced formation of amorphous silica, which increases as a function of shock pressure over the range that we studied (7.5 to 22 GPa). The Coconino Sandstone spectra are in excellent agreement with the classification scheme of Kieffer in terms of presence and approximate abundances of quartz, coesite, stishovite, and glass. We also observe a new resonance in two moderately shocked samples that we have tentatively identified with silicon in tetrahedra with one hydroxyl group in a densified form of amorphous silica.

Boslough, M. B.↗
NASA NTRS1991

X ray emission from dynamical shock models in hot-star winds

The principal aim of this project was to determine whether x ray emission from instability-generated shocks in dynamical models of highly unstable hot-star winds could explain the x ray flux spectrum observed from such hot stars by Einstein and other x ray satellites. Our initial efforts focused on extending the earlier isothermal simulations of wind instabilities to include an explicit treatment of the energy balance between shock heating and simplified radiative cooling. It was found, however, that direct resolution of cooling regions behind shocks is often impractical, and thus additional, indirect methods for determining this shock x ray emission were also developed. The results indicate that the reverse shocks that dominate simple 1-D instability models typically have too little material undergoing a strong shock to produce the observed x ray emission. Other models with more strongly driven variability from the wind base sometimes show high-speed collisions between relatively dense clumps, and in these instances the computed x ray flux spectrum matches the observed spectrum quite well. This suggests that collisions between relatively large scale wind streams of different speeds may be more suited to producing the observed x rays than the reverse shocks arising from small-scale instabilities.

Owocki, Stanley P.↗
NASA NTRS1992

Evolution of the shock front and turbulence structures in the shock/turbulence interaction

The interaction of a weak shock front with isotropic turbulence has been investigated using Direct Numerical Simulation (DNS). Two problems were considered: the ability of the field equation (the equation for a propagating surface) to model the shock; and a quantitative study of the evolution of turbulence structure using the database generated by Lee et al. Field equation model predictions for front shape have been compared with DNS results; good agreement is found for shock wave interaction with 2D turbulence and for a single steady vorticity wave. In the interaction of 3D isotropic turbulence with a normal shock, strong alignment of vorticity with the intermediate eigenvector of the rate of strain tensor (S(sup *)(sub ij) = S(sub ij) - (1/3)(delta(sub ij))(S(sub kk))) is seen to develop upstream of the shock and to be further amplified on passage through the shock. Vorticity tends to align at 90 deg to the largest eigenvector, but there is no preferred alignment with the smallest eigenvector. Upstream of the shock, the alignments continue to develop even after the velocity derivative skewness saturates. There is a significant tendency, which increases with time throughout the computational domain, for velocity to align with vorticity. The alignment between velocity and vorticity is strongest in eddy regions and weakest in convergence regions.

Kevlahan, N.↗
NASA NTRS1993

Temporal variations in the termination shock distance

A kinematic analysis is made of solar wind driven temporal variations in the heliospheric termination shock distance. This has become possible because the large-scale dynamics of, and temporal variations in the distant solar wind are now well enough known from a combination of in situ and remote measurements. Conversely, nothing is known of the corresponding properties in the local interstellar medium, and hence these will be ignored. Given specific assumptions for how the termination shock responds to solar wind fluctuations, it is shown that the termination shock is very agile, moving in and out by up to a few AU in a month. This conclusion holds for a broad range of shock response assumptions. Because a spacecraft moves slowly in comparison to the termination shock, the shock will sweep back and forth over the spacecraft once the shock is first encountered.

Suess, S. T.↗
NASA NTRS1993

Solar wind conditions in the outer heliosphere and the distance to the termination shock

The Plasma Science experiment on the Voyager 2 spacecraft has measured the properties of solar wind protons from 1 to 40.4 AU. We use these observations to discuss the probable location and motion of the termination shock of the solar wind. Assuming that the interstellar pressure is due to a 5 micro-G magnetic field draped over the upstream face of the heliopause, the radial variation of ram pressure implies that the termination shock will be located at an average distance near 89 AU. This distance scales inversely as the assumed field strength. There are also large variations in ram pressure on time scales of tens of days, due primarily to large variations in solar wind density at a given radius. Such rapid changes in the solar wind ram pressure can cause large perturbations in the location of the termination shock. We study the nonequilibrium location of the termination shock as it responds to these ram pressure changes. The results of this study suggest that the position of the termination shock can vary by as much as 10 AU in a single year, depending on the nature of variations in the ram pressure, and that multiple crossings of the termination shock by a given outer heliosphere spacecraft are likely. After the first crossing, such models of shock motion will be useful for predicting the timing of subsequent crossings.

Belcher, John W.↗
NASA NTRS1971

Shock wave structure using nonlinear model Boltzmann equations

The structure of a strong plane shock wave in a monatomic rarefied perfect gas is one of the simplest problems able to be posed in kinetic theory, and one of the hardest to solve. Its simplicity lies in the absence of solid boundaries, geometrical complications, or internal molecular energy. Its difficulty arises from the great departure of the gas from equilibrium within the shock, which invalidates many of the techniques used successfully elsewhere in kinetic theory. In addition to this theoretical challenge, the modern development of ballistics and hypersonic flight has helped to stimulate extensive theoretical and experimental interest in the shock problem. The experimenters in turn have encountered great difficulties on account of the very small physical dimensions of shocks. In fact, until very recently indeed, any close comparisons of theoretical and experimental shock structure results have been rather unprofitable due to the inadequacies of both theory and experiment. During the last few years this situation has been appreciably improved by development of the Monte Carlo method. This allows idealized 'experiments' to be performed on large computers instead of in wind tunnels, using a known intermolecular force law. The most developed of these methods has been shown to be equivalent theoretically to the Boltzmann equation and to give results which agree extremely closely with measurements of high accuracy. Thus Monte Carlo results not only form the soundest basis for our present theoretical knowledge of shock wave structure, but, for purposes of developing other theories, can also be considered a very valuable experimental resource. However, such results remain very expensive to obtain. In this thesis we develop more economical kinetic theory methods for the approximate prediction of shock structure, and compare our results with those of the Monte Carlo method.

Segal, Ben Maurice↗
NASA NTRS1994

A variable cross-section model of the bow shock of Venus

Magnetohydrodynamics (MHD) parameters like the Alfvenic and the sonic Mach numbers and the direction of the interplanetary magnetic field profoundly affect the interaction of the solar wind with nonmagnetized conducting objects like Venus. The size of the bow shock depends on the two Mach numbers, whereas asymmetries in its shape are governed by the direction of the magnetic field. This paper introduces a new class of bow shock models in which both the shape and the size are controlled by the upstream plasma and field conditions. We use insights from the MHD theory of shocks for point objects and empirical information from actual bow shock crossings to obtain a semiempirical, semitheoretical model of the Cytherean bow shock. The model was developed from a limited data set obtained from the Galileo flyby of Venus but is also in substantial agreement with Pioneer Venus Orbiter observations. It is shown that the dozen bow shock crossing observed by Galileo under steady conditions of solar wind flow and density were caused by changes in the cross section of the bow shock induced by the changing direction of the interplanetary magnetic field.

Khurana, Krishan K.↗
NASA NTRS1994

The subcritical, quasi-parallel, switch-on shock

The conditions that lead to subcritical, quasi-parallel bow shocks are very rare. Even more rarely, a subcritical, quasi-parallel shock can also be termed a switch-on shock, where the tangential component of the magnetic field, which is very small upstream, is said to 'switch on' downstream. The Rankine-Hugoniot conservation relations predict that the jump in the tangential component of the magnetic field across the shock is very large for these upstream conditions. In this study, we find that the measured jumps in the plasma conditions are in accord with predictions made by the Rankine-Hugoniot conservation relations. The structure of the switch-on shock, not predicted by the Rankine-Hugoniot equations, is very similar to that of the subcritical, quasi-perpendicular shock, with the exception that the precursor wave in front of the shock ramp damps more slowly.

Farris, M. H.↗
NASA NTRS1994

Diffusive shock acceleration in the presence of current sheets

We study the nature of diffusive shock acceleration in the presence of current sheets which are oriented normal to the shock, so that the drift along the sheets carries particles either away from or toward the shock plane. We consider a system with periodic regions of alternating magnetic field direction. This can be taken to be a very crude representation of the termination of the solar wind, with the equator being one sheet and the pole, with its rapid opposite drift, being another. We find very important effects of the current sheets. For example, particle intensities at the shock will be enhanced near one sheet and depressed at the other. Furthermore, the intensity at high energies (averaged over the shock plane) may in fact be considerably larger than in the standard one-dimensional infinite shock case. Implications of these results for the possible acceleration of cosmic electrons up to high energies at the solar-wind termination shock will briefly be discussed.

Kota, J.↗
NASA NTRS1995

Two-dimensional structure of slow shocks

The two-dimensional (2-D) structure of switch-off slow magnetosonic shocks is investigated using an electromagnetic hybrid (fluid electrons, kinetic ions) code. It is shown that the basic physical processes occurring at 1-D slow shocks are also operative in 2-D. Specifically, the interaction between the upstream ions and those streaming away from the shock results in the excitation of Alfven/ions-cyclotron (AIC) waves. Depending on the plasma parameters, these waves may either stay in the upstream or convect back into the shock resulting in a non-steady shock behavior which prevents the formation of a trailing wave train. Despite this similarity, some slow shocks which are steady in 1-D are found to be non-steady in 2-D. Fourier analysis of the waves downstream of non-steady shocks identifies them as AIC, demonstrating that the waves remain on the same branch as they convect from upstream into the downstream region.

Omidi, N.↗