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NASA NTRS1987

Fast shocks at the edges of hot diamagnetic cavities upstream from the earth's bow shock

Recently, several events described as hot expanding diamagnetic cavities have been observed upstream from the earth's bow shock using the ISEE 1 and 2 spacecraft. It has been suggested that fast shocks may form at the edges of some of these events because of the rapid expansion of the cavities. Here, plasma density, temperature, velocity, and total field changes across the edges of several events were examined, and these changes were found to be consistent with the presence of shocks there. The presence of flat-topped electron distributions and occasional electron beams at and down-stream from the edges provides additional evidence for shocks. Plasma wave observations also show shocklike electrostatic noise at the edges of several events. It is concluded that the edges of diamagnetic cavity events are often shocks, with a range of shock strengths similar to that observed in the interplanetary medium. The range of shock strengths may be the result of different convection and/or expansion speeds of the cavities.

Fuselier, S. A.↗

NASA NTRS1987

Heliospheric shocks (excluding planetary bow shocks)

A summary of advances made during 1983-1985 in the theory of collisionless heliospheric shocks is presented (with reference to the latest observations of slow shocks in the geomagnetic tail) together with a summary of recently developed simulations of shock structure and shock propagation. Consideration is also given to the theoretical basis for the production of energetic particles by shocks in the solar wind and the corona. Finally, satellite-based observations related to interplanetary and coronal shocks and to heliospheric boundary shock are discussed.

Mihalov, J. D.↗

NASA NTRS1988

Observational test of shock drift and Fermi acceleration on a seed particle population upstream of earth's bow shock

The efficiency of proposed shock acceleration mechanisms as they operate at the bow shock in the presence of a seed energetic particle population was examined using data from simultaneous observations of energetic solar-origin protons, carried out by the IMP 7 and 8 spacecraft in the vicinity of the quasi-parallel (dawn) and quasi-perpendicular (dusk) regions of the earth's bow shock, respectively. The results of observations (which include acceleration effects in the intensities of the energetic protons with energies as high as 4 MeV observed at the vicinity of the dusk bow shock, but no evidence for any particle acceleration at the energy equal to or above 50 keV at the dawn side of the bow shock) indicate that the acceleration of a seed particle population occurs only at the quasi-perpendicular bow shock through shock drift acceleration and that the major source of observed upstream ion populations is the leakage of magnetospheric ions of energies not less than 50 keV, rather than in situ acceleration.

Anagnostopoulos, G. C.↗

NASA NTRS1991

Shock loading predictions from application of indicial theory to shock-turbulence interactions

A sequence of steps that permits prediction of some of the characteristics of the pressure field beneath a fluctuating shock wave from knowledge of the oncoming turbulent boundary layer is presented. The theory first predicts the power spectrum and pdf of the position and velocity of the shock wave, which are then used to obtain the shock frequency distribution, and the pdf of the pressure field, as a function of position within the interaction region. To test the validity of the crucial assumption of linearity, the indicial response of a normal shock is calculated from numerical simulation. This indicial response, after being fit by a simple relaxation model, is used to predict the shock position and velocity spectra, along with the shock passage frequency distribution. The low frequency portion of the shock spectra, where most of the energy is concentrated, is satisfactorily predicted by this method.

Keefe, Laurence R.↗

NASA NTRS1992

Shock drift acceleration of energetic protons at a planetary bow shock

Results are presented of numerical orbit integrations of the interaction of suprathermal charged particles (protons) with a planetary bow shock, performed in order to investigate the effect of the changing geometry of the shock, due to its curvature, on the kinematics of the particle/shock interaction. Results obtained for both the 2D and 3D bow-shock geometries show that the introduction of shock curvature to the shock in the simulations leads to an increase of the reflection probability of incident suprathermal protons. It was also found that the curvature of the planetary bow shock allows protons to enter at a given value of theta(Bn) (where theta(Bn) is the angle between the local shock normal and the incident magnetic field) and to exit at a different theta(Bn) value. The result has consequences in the characteristics of the energetic charged particle environment in the planetary foreshock.

Giacalone, Joe↗

NASA NTRS1994

On the hydrodynamic interaction of shock waves with interstellar clouds. 1: Nonradiative shocks in small clouds

The interstellar medium (ISM) is inhomogeneous, with clouds of various temperatures and densities embedded in a tenuous intercloud medium. Shocks propagating through the ISM can ablate or destroy the clouds, at the same time significantly altering the properties of the intercloud medium. This paper presents a comprehensive numerical study of the simplest case of the interaction between a shock wave and a spherical cloud, in which the shock far from the cloud is steady and planar, and in which radiative losses, thermal conduction, magnetic fields, and gravitational forces are all neglected. As a result, the problem is completely specified by two numbers: the Mach number of the shock, M, and the ratio of the density of the cloud to that of the intercloud medium, Chi. For strong shocks we show that the dependence on M scales out, so the primary independent parameter is Chi. Variations from this simple case are also considered: the potential effect of radiative losses is assessed by calculations in which the ratio of specific heats in the cloud is 1.1 instead of 5/3; the effect of the initial shape of the cloud is studied by using a cylindrical cloud instead of a spherical one; and the role of the initial shock is determined by considering the case of a cloud embedded in a wind. Local adaptive mesh refinement techniques with a second-order, two-fluid, two-dimensional Godunov hydrodynamic scheme are used to address these problems, allowing heretofore unobtainable numerical resolution. Convergence studies to be described in a subsequent paper demonstrate that about 100 zones per cloud radius are needed for accurate results; previous calculations have generally used about a third of this number. The results of the calculations are analyzed in terms of global quantities which provide an overall description of te shocked cloud: the size and shape of the cloud, the mean density, the mean pressure, the mean velocity, the velocity dispersion, and the total circulation.

Klein, Richard I.↗

NASA NTRS1994

Shock normal determination for multiple-ion shocks

We have adapted the single-ion Vinas and Scudder (1986) solution to the Rankine-Hugoniot (R-H) problem to a multiple-on solution. Using this technique, we can calculate a shock normal direction, shock speed, best estimate of the upstream and downstream magnetic field and plasma asymptotic states, and theta(sub Bn), the angle between the shock normal and the upstream magnetic field. We test the multi-ion solution with a theoretical case but are restricted to a perpendicular shock in order to close the multi-ion Rankine-Hugoniot equations. For this test case both single-ion and multi-ion solutions are equally valid. We examine parameter regimes to look for differences between single-ion and multi-ion solutions of the R-H equations, and we find that the largest differences occur for quasi-parallel shocks, small values of solar wind speed, large values of heavy ion density, and very strong and very weak shocks. For both the inbound and outbound crossing of comet Halley we have a slow solar wind speed, small values of water group ions and fairly weak shocks. We examine both the quasi-perpendicular inbound crossing and the quasi-parallel outbound crossing at comet Halley.

Kessel, R. L.↗

NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗

NASA NTRS1998

Performance of Low Dissipative High Order Shock-Capturing Schemes for Shock-Turbulence Interactions

Abstract Accurate and efficient direct numerical simulation of turbulence in the presence of shock waves represents a significant challenge for numerical methods. The objective of this paper is to evaluate the performance of high order compact and non-compact central spatial differencing employing total variation diminishing (TVD) shock-capturing dissipations as characteristic based filters for two model problems combining shock wave and shear layer phenomena. A vortex pairing model evaluates the ability of the schemes to cope with shear layer instability and eddy shock waves, while a shock wave impingement on a spatially-evolving mixing layer model studies the accuracy of computation of vortices passing through a sequence of shock and expansion waves. A drastic increase in accuracy is observed if a suitable artificial compression formulation is applied to the TVD dissipations. With this modification to the filter step the fourth-order non-compact scheme shows improved results in comparison to second-order methods, while retaining the good shock resolution of the basic TVD scheme. For this characteristic based filter approach, however, the benefits of compact schemes or schemes with higher than fourth order are not sufficient to justify the higher complexity near the boundary and/or the additional computational cost.

Sandham, N. D.↗

NASA NTRS2021

Evaluating the De Hoffmann-Teller Cross-Shock 2 Potential at Real Collisionless Shocks

Shock waves are common in the heliosphere and beyond. The collisionless nature of most astrophysical plasmas allows for the energy processed by shocks to be partitioned amongst particle sub-populations and electromagnetic fields via physical mechanisms that are not well understood. The electrostatic potential across such shocks is frame dependent. In a frame where the incident bulk velocity is parallel to the magnetic field, the deHoffmann-Teller frame, the potential is linked directly to the ambipolar electric field established by the electron pressure gradient. Thus measuring and understanding this potential solves the electron partition problem, and gives insight into other competing shock processes. Integrating measured electric fields in space is problematic since the measurements can have offsets that change with plasma conditions. The offsets, once integrated, can be as large or larger than the shock potential. Here we exploit the high-quality field and plasma measurements from NASA’s Magnetospheric Multiscale mission to attempt this calculation. We investigate recent adaptations of the deHoffmann-Teller frame transformation to include time variability, and conclude that in practice these face difficulties inherent in the 3D time-dependent nature of real shocks by comparison to 1D simulations. Potential estimates based on electron fluid and kinetic analyses provide the most robust measures of the deHoffmann-Teller potential, but with some care direct integration of the electric fields can be made to agree. These results suggest that it will be difficult to independently assess the role of other processes, such as scattering by shock turbulence, in accounting for the electron heating.

Steven J Schwartz↗

DOE OSTI2022

Structure of Shock Waves and Inelasticity in Shock-Compressed Cemented Tungsten Carbides

In this study, shock wave experiments are conducted on General Carbide cemented tungsten carbide with 3.7wt.% cobalt binder to determine its shock-induced compression behavior up to 100 GPa. The measured wave profiles indicate the cemented tungsten carbide to undergo elastic-plastic deformation during shock compression. A three-stage particle velocity profile is observed in the experiments -- an initial elastic-rise to the Hugoniot Elastic Limit (HEL), an elastic-plastic ramp indicating substantial post-yield hardening, and finally a rise to the peak shocked Hugoniot state. The results of the experiments are used to determine the HEL, the shock velocity (U s ) vs. particle velocity (u p ) Hugoniot relation, and the longitudinal stress (σ x ) vs. specific volume (V) curve for the samples. The HEL of the material was determined to lie between 4.41 GPa and 4.58 GPa. The U s - u p relation was determined to be U s = 4.97 + 1. 457u p for particle velocities greater than 0.75 km/s. The measured plastic shock velocities for particle velocities less than 0.7 km/s were found to be larger than those predicted using the linear U s - u p Hugoniot relationship, indicating the cemented WC samples to preserve substantial shear strength in the post-yield deformation region. No phase transformation was observed up to 100 GPa.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Numerical investigation of shock interaction with one-dimensional transverse array of particles in air

In this paper, we present numerical simulations of shock propagation in air over a one-dimensional transverse array of particles. Simulations are carried out by varying the particle spacing and shock Mach number. We compute the unsteady inviscid drag coefficient as a function of time and make relevant comparisons to that for a single particle. We find that deviations in the drag coefficient in time from that of a single particle can be correlated to the acoustic-particle interaction time. Finally, we investigate and classify the interaction of the bow shocks in front of the transverse array of particles.

42 ENGINEERING↗

DOE OSTI2015

Pre-strain effect on frequency-based impact energy dissipation through a silicone foam pad for shock mitigation [Pre-strain effect on the frequency response of shock mitigation through a silicone foam pad]

Silicone foams have been used in a variety of applications from gaskets to cushioning pads over a wide range of environments. Particularly, silicone foams are used as a shock mitigation material for shock and vibration applications. Understanding the shock mitigation response, particularly in the frequency domain, is critical for optimal designs to protect internal devices and components more effectively and efficiently. The silicone foams may be subjected to pre-strains during the assembly process which may consequently influence the frequency response with respect to shock mitigation performance. A Kolsky compression bar was modified with pre-compression capabilities to characterize the shock mitigation response of silicone foam in the frequency domain to determine the effect of pre-strain. Lastly, a silicone sample was also intentionally subjected to repeated pre-strain and dynamic loadings to explore the effect of repeated loading on the frequency response of shock mitigation.

36 MATERIALS SCIENCE↗

DOE OSTI2013

X-ray Thomson scattering measurements of temperature and density from multi-shocked CH capsules

Proof-of-principle measurements of the electron densities, temperatures, and ionization states of spherically compressed multi-shocked CH (polystyrene) capsules have been achieved using spectrally resolved x-ray Thomson scattering. A total energy of 13.5 kJ incident on target is used to compress a 70 μm thick CH shell above solid-mass density using three coalescing shocks. Separately, a laser-produced zinc He-α x-ray source at 9 keV delayed 200 ps-800 ps after maximum compression is used to probe the plasma in the non-collective scattering regime. The data show that x-ray Thomson scattering enables a complete description of the time-dependent hydrodynamic evolution of shock-compressed CH capsules, with a maximum measured density of ρ > 6 g cm –3 . Additionally, the results demonstrate that accurate measurements of x-ray scattering from bound-free transitions in the CH plasma demonstrate strong evidence that continuum lowering is the primary ionization mechanism of carbon L-shell electrons.

42 ENGINEERING↗

DOE OSTI2013

Release path temperatures of shock-compressed tin from dynamic reflectance and radiance measurements

Dynamic reflectance and radiance measurements were conducted for tin samples shock compressed to 35 GPa and released to 15 GPa using high explosives. We determined the reflectance of the tin samples glued to lithium fluoride windows using an integrating sphere with an internal xenon flashlamp as an illumination source. The dynamic reflectance (R) was determined at near normal incidence in four spectral bands with coverage in visible and near-infrared spectra. Uncertainties in R/R{sub 0} are <2%, and uncertainties in absolute reflectance are <5%. In complementary experiments, thermal radiance from the tin/glue/lithium fluoride interface was recorded with similar shock stress and spectral coverage as the reflectance measurements. The two sets of experiments were combined to obtain the temperature history of the tin surface with an uncertainty of <2%. The stress at the interface was determined from photonic Doppler velocimetry and combined with the temperatures to obtain temperature-stress release paths for tin. We discuss the relationship between the experimental release paths and release isentropes that begin on the principal shock Hugoniot.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Magnetohydrodynamic structure of a plasmoid in fast reconnection in low-beta plasmas: Shock-shock interactions

The shock structure of a plasmoid in magnetic reconnection in low-beta plasmas is investigated by two-dimensional magnetohydrodynamic simulations. Using a high-accuracy code with unprecedented resolution, shocks, discontinuities, and their intersections are resolved and clarified. Contact discontinuities emanate from triple-shock intersection points, separating fluids of different origins. Shock-diamonds inside the plasmoid appear to decelerate a supersonic flow. New shock-diamonds and a slow expansion fan are found inside the Petschek outflow. A sufficient condition for the new shock-diamonds and the relevance to astrophysical jets are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Investigation of radiative bow-shocks in magnetically accelerated plasma flows

We present a study of the formation of bow shocks in radiatively cooled plasma flows. This work uses an inverse wire array to provide a quasi-uniform, large scale hydrodynamic flow accelerated by Lorentz forces to supersonic velocities. This flow impacts a stationary object placed in its path, forming a well-defined Mach cone. Interferogram data are used to determine a Mach number of ∼6, which may increase with radial position suggesting a strongly cooling flow. Self-emission imaging shows the formation of a thin (<60 μm) strongly emitting shock region, where T{sub e} ∼ 40–50 eV, and rapid cooling behind the shock. Emission is observed upstream of the shock position which appears consistent with a radiation driven phenomenon. Data are compared to 2-dimensional simulations using the Gorgon MHD code, which show good agreement with the experiments. The simulations are also used to investigate the effect of magnetic field in the target, demonstrating that the bow-shocks have a high plasma β, and the influence of B-field at the shock is small. This consistent with experimental measurement with micro bdot probes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

An investigation of shock formation vs shock mitigation of colliding plasma jets

Here, this work studies the interaction between colliding plasma jets to understand regimes in which jet merging results in shock formation vs regimes in which the shock formation is mitigated due to the collisionless interpenetration of the jets. A kinetic model is required for this study because fluid models will always produce a shock upon the collision of plasma jets. The continuum-kinetic, Vlasov–Maxwell–Dougherty model with one velocity dimension is used to accurately capture shock heating, along with a novel coupling with a moment equation to evolve perpendicular temperature for computational efficiency. As a result, this relatively inexpensive simulation can be used for detailed scans of the parameter space toward predictions of shocked vs shock-mitigated regimes, which is of interest for several fusion concepts such as plasma-jet-driven magneto-inertial fusion, high-energy-density plasmas, astrophysical phenomena, and other laboratory plasmas. The initial results obtained using this approach are in agreement with the preliminary outcomes of the plasma liner experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗