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DOE OSTI2015

Dynamics of cylindrical converging shock waves interacting with aerodynamic obstacle arrays

Cylindrical converging shock waves interacting with an array of aerodynamic obstacles are investigated numerically for diverse shock strengths and for different obstacle configurations in air in standard conditions. The considered number of obstacles N is 4, 6, 8, 16, and 24. Obstacles are lenticular airfoils with thickness-to-chord ratios t/c of 0.07, 0.14, and 0.21. The distances of the airfoil leading edge from the shock focus point (r{sub LE})/(r{sub LE}{sup ref}) are 1, 2, and 2.5, where r{sub LE}{sup ref}=7 is the dimensionless reference distance from the origin. Considered impinging shock Mach numbers M{sub s} are 2.2, 2.7, and 3.2 at the reference distance from the origin. The reference experimental configuration (N=8,t/c =0.14,r{sub LE}=7,M{sub s}=2.7) was proposed by Kjellander et al. [“Thermal radiation from a converging shock implosion,” Phys. Fluids 22, 046102 (2010)]. Numerical results compare fairly well to available one-dimensional models for shock propagation and to available experimental results in the reference configuration. Local reflection types are in good agreement with the classical criteria for planar shock waves. The main shock reshaping patterns are identified and their dependence on the shock strength and obstacle configuration is exposed. In particular, different shock patterns are observed after the leading edge reflection, which results in polygonal shock wave with N, 2N, 3N, and 4N sides. The largest temperature peak at the origin is obtained for the 8- and the 16-obstacle configurations and for the smallest thickness to length ratio, 0.07, located at distance from the origin of 2r{sub LE}{sup ref}. In terms of compression efficiency at the origin, the 16-obstacle configuration is found to perform slightly better than the reference 8-obstacle configuration—with an efficiency increase of about 2%-3%, which is well within the model accuracy—thus confirming the goodness of the obstacle arrangement proposed by Kjellander and collaborators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

SEP acceleration in CME driven shocks using a hybrid code

We perform hybrid simulations of a super-Alfvénic quasi-parallel shock, driven by a coronal mass ejection (CME), propagating in the outer coronal/solar wind at distances of between 3 to 6 solar radii. The hybrid treatment of the problem enables the study of the shock propagation on the ion timescale, preserving ion kinetics and allowing for a self-consistent treatment of the shock propagation and particle acceleration. The CME plasma drags the embedded magnetic field lines stretching from the sun, and propagates out into interplanetary space at a greater velocity than the in situ solar wind, driving the shock, and producing very energetic particles. Our results show that electromagnetic Alfvén waves are generated at the shock front. The waves propagate upstream of the shock and are produced by the counter-streaming ions of the solar wind plasma being reflected at the shock. A significant fraction of the particles are accelerated in two distinct phases: first, particles drift from the shock and are accelerated in the upstream region, and second, particles arriving at the shock get trapped and are accelerated at the shock front. A fraction of the particles diffused back to the shock, which is consistent with the Fermi acceleration mechanism.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

ION ACCELERATION AT THE QUASI-PARALLEL BOW SHOCK: DECODING THE SIGNATURE OF INJECTION

Collisionless shocks are efficient particle accelerators. At Earth, ions with energies exceeding 100 keV are seen upstream of the bow shock when the magnetic geometry is quasi-parallel, and large-scale supernova remnant shocks can accelerate ions into cosmic-ray energies. This energization is attributed to diffusive shock acceleration; however, for this process to become active, the ions must first be sufficiently energized. How and where this initial acceleration takes place has been one of the key unresolved issues in shock acceleration theory. Using Cluster spacecraft observations, we study the signatures of ion reflection events in the turbulent transition layer upstream of the terrestrial bow shock, and with the support of a hybrid simulation of the shock, we show that these reflection signatures are characteristic of the first step in the ion injection process. These reflection events develop in particular in the region where the trailing edge of large-amplitude upstream waves intercept the local shock ramp and the upstream magnetic field changes from quasi-perpendicular to quasi-parallel. The dispersed ion velocity signature observed can be attributed to a rapid succession of ion reflections at this wave boundary. After the ions’ initial interaction with the shock, they flow upstream along the quasi-parallel magnetic field. Each subsequent wavefront in the upstream region will sweep the ions back toward the shock, where they gain energy with each transition between the upstream and the shock wave frames. Within three to five gyroperiods, some ions have gained enough parallel velocity to escape upstream, thus completing the injection process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Importance of CME Radial Expansion on the Ability of Slow CMEs to Drive Shocks

Coronal mass ejections (CMEs) may disturb the solar wind by overtaking it or expanding into it, or both. CMEs whose front moves faster in the solar wind frame than the fast magnetosonic speed drive shocks. Such shocks are important contributors to space weather, by triggering substorms, compressing the magnetosphere, and accelerating particles. In general, near 1 au, CMEs with speed greater than about 500 km s{sup −1} drive shocks, whereas slower CMEs do not. However, CMEs as slow as 350 km s{sup −1} may sometimes, although rarely, drive shocks. Here we study these slow CMEs with shocks and investigate the importance of CME expansion in contributing to their ability to drive shocks and in enhancing shock strength. Our focus is on CMEs with average speeds under 375 km s{sup −1}. From Wind measurements from 1996 to 2016, we find 22 cases of such shock-driving slow CMEs, and for about half of them (11 out of the 22), the existence of the shock appears to be strongly related to CME expansion. We also investigate the proportion of all CMEs with speeds under 500 km s{sup −1} with and without shocks in solar cycles 23 and 24, depending on their speed. We find no systematic difference, as might have been expected on the basis of the lower solar wind and Alfvén speeds reported for solar cycle 24 versus 23. The slower expansion speed of CMEs in solar cycle 24 might be an explanation for this lack of increased frequency of shocks, but further studies are required.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2023

High-Energy (> 40 MeV) Proton Intensity Enhancements Associated with the Passage of Interplanetary Shocks at 1 au

We analyze periods with elevated >40 MeV proton intensities observed near Earth over a time span of 43 years (1973-2016) that coincide with the passage of interplanetary shocks. Typically, elevated proton intensities result from large solar energetic particle (SEP) events. The interplanetary shocks observed during these elevated-intensity periods may or may not be related to the origin of the SEP events. By choosing those cases when the shocks can be confidently associated with the solar eruption that generated the SEP event, we analyze the components of these SEP events that are localized in the vicinity of the shock (so-called “energetic storm particles (ESPs)"), focusing on those events where the ESP component exceeds 40 MeV. We examine the interdependence of these high-energy ESPs with (i) the properties of the solar eruptions that generated the shocks and the SEP events, and (ii) the parameters of the shocks at their arrival at 1 au. The solar eruptions at the origin of the shocks producing >40 MeV proton ESP intensity enhancements are within ±50° longitude of central meridian and are associated with fast coronal mass ejections (plane-of-sky speeds ≳1000 km s -1 ). The ESP events with the largest >40 MeV proton intensity increases tend to occur when there are structures such as intervening interplanetary coronal mass ejections and other unrelated shocks present in the solar wind through which the shock is propagating. Among the various local shock parameters considered, only the shock speed shows a certain degree of correlation with the observed ESP intensity increase.

Solar energetic particles↗

NASA NTRS2023

Relativistic Electron Beams Accelerated By an Interplanetary Shock

Context: Collisionless shock waves have long been considered to be among the most prolific particle accelerators in the universe. Shocks alter the plasma they propagate through, and often exhibit complex evolution across multiple scales. Interplanetary (IP) traveling shocks have been recorded in situ for over half a century and act as a natural laboratory for experimentally verifying various aspects of large-scale collisionless shocks. A fundamentally interesting problem in both heliophysics and astrophysics is the acceleration of electrons to relativistic energies (> 300 keV) by traveling shocks. Aims: The reason for an incomplete understanding of electron acceleration at IP shocks is due to scale-related challenges and a lack of instrumental capabilities. This Letter presents the first observations of field-aligned beams of relativistic electrons upstream of an IP shock, observed thanks to the instrumental capabilities of Solar Orbiter. This study presents the characteristics of the electron beams close to the source and contributes to the understanding of their acceleration mechanism. Methods: On 25 July 2022, Solar Orbiter encountered an IP shock at 0.98 AU. The shock was associated with an energetic storm particle event, which also featured upstream field-aligned relativistic electron beams observed 14 min prior to the actual shock crossing. The distance of the beam’s origin was investigated using a velocity dispersion analysis (VDA). Peak-intensity energy spectra were analyzed and compared with those obtained from a semi-analytical fast-Fermi acceleration model. Results: By leveraging Solar Orbiter’s high temporal resolution Energetic Particle Detector (EPD), we successfully showcase an IP shock’s ability to accelerate relativistic electron beams. Our proposed acceleration mechanism offers an explanation for the observed electron beam and its characteristics, while we also explore the potential contributions of more complex mechanisms.

acceleration of particles↗

DOE OSTI2024

Shock Response of Polymethyl Methacrylate (PMMA) Under Explosive Loading

Abstract The dynamic response of polymethyl methacrylate (PMMA) is well understood for one-dimensional planar impact shocks, but limited research has been performed on the response of PMMA under spherical shock loading. In this work, the shock decay of an explosively-driven shock wave into PMMA was experimentally measured. PMMA cubes of various geometries were explosively loaded with an RP-80 detonator to produce the explosive shock wave. High-speed schlieren imaging was implemented to measure the explosively-driven shock wave velocity throughout the PMMA cubes. Photon Doppler velocimetry (PDV) was used to measure the particle velocity imparted by the shock wave at the surface of the cubes. The material shock response was studied at distances from 21.91 to 133.3 mm from the explosive source. The particle velocity history measured by PDV was compared to the wave profile visualized in the high-speed images. The shock wave pulse amplitude decreased with increased distance from the source. The conducted experiments extend the PMMA shock Hugoniot relating to the lower shock and particle velocity regime.

Torres, S. M. (ORCID:0009000287177206)↗

DOE OSTI2026

Efficacy of Gadolinium Gallium Garnet (GGG) as a High-Impedance Optical Window for Shock Wave Experiments

We conducted a series of plate impact experiments to examine the efficacy of < 111>-oriented gadolinium gallium garnet (GGG) single crystals as high-impedance optical window for Photonic Doppler velocimetry (PDV) under shock and double-shock loading. At ~ 123 GPa, shocked GGG remains fully transparent to 1550 nm light for at least 250 ns without any signal degradation. Above 135 GPa, PDV data measured through GGG exhibit a gradual loss of fringe contrast following shock entrance, which eventually leads to transparency loss. The duration for which shocked GGG remains transparent decreases with increasing pressure, and at ~ 148 GPa, it becomes opaque within ~ 20–30 ns. This limits the use of GGG as an interferometry window between ~ 110–140 GPa under single shock loading. Within this pressure range, the refractive index of GGG increases linearly with density: n = 1.552 + 0.054ρ. In contrast to single shock loading, where GGG becomes opaque rapidly above ~ 140 GPa, double-shocked GGG remains optically transparent for over 100 ns when it is first shocked to ~ 123 GPa and then reshocked to significantly higher pressures (215–233 GPa). Our findings raise the exciting possibility of GGG being used as a high-impedance optical window in multi-shock and shock-ramp loading experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

The influence of the shock-to-reshock time on the Richtmyer–Meshkov instability in reshock

Experiments on the Richtmyer–Meshkov instability (RMI) in a dual driver vertical shock tube (DDVST) are described. An initially planar, stably stratified membraneless interface is formed by flowing air from above and sulfur hexafluoride from below the interface location using the method of Jones & Jacobs ( Phys. Fluids , vol. 9, issue 1997, 1997, pp. 3078–3085). A random three-dimensional, multi-modal initial perturbation is imposed by vertically oscillating the gas column to produce Faraday waves. The DDVST design generates two shock waves, one originating above and one below the interface, with these shocks having independently controllable strengths and interface arrival times. The shock waves have nominal strengths of $M_L=1.17$ and $M_H=1.18$ for the shock wave originating in the light and heavy gas, respectively, with these strengths chosen to result in arrested bulk interface motion following reshock. The influence of the length of the shock-to-reshock time, as well as the order of shock arrival, on the post-reshock RMI is examined. The mixing layer width grows according to $h\propto t^\theta$ , where $\theta _H=0.36\pm 0.018$ (95 %) and $\theta _L=0.38\pm 0.02$ (95 %) for heavy and light shock first experiments, respectively, indicating no strong dependence on the order of shock wave arrival. Volume integrated specific turbulent kinetic energy (TKE) in the mixing layer versus time is found to decay according to $E_{tot}/\bar {\rho }\propto t^p$ with $p_H=-0.823\pm 0.06$ (95 %) and $p_L=-1.061\pm 0.032$ (95 %) for heavy and light shock first experiments, respectively. Notably, the 95 % confidence intervals do not overlap. Analysis on the influence of the shock-to-reshock time on turbulent length scales, transition criteria, spectra and mixing layer anisotropy are also presented.

Ferguson, Kevin (ORCID:0000000166537482)↗

DOE OSTI2018

Diffusive shock re-acceleration

Here, we have performed two-dimensional hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles (‘seeds’); such a study applies, for instance, to the re-acceleration of galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call diffusive shock re-acceleration. We determine that re-accelerated seeds can drive the streaming instability in the shock upstream and produce effective magnetic field amplification. This can later trigger the injection of thermal protons even at oblique shocks that ordinarily cannot inject thermal particles. We characterize the current in reflected seeds, finding that it tends to a universal value $J\simeq en_{\text{CR}}v_{\text{sh}}$ , where $en_{\text{CR}}$ is the seed charge density and $v_{\text{sh}}$ is the shock velocity. When applying our results to SNRs, we find that the re-acceleration of galactic CRs can excite the Bell instability to nonlinear levels in less than ${\sim}10~\text{yr}$ , thereby providing a minimum level of magnetic field amplification for any SNR shock. Finally, we discuss the relevance of diffusive shock re-acceleration also for other environments, such as heliospheric shocks, galactic superbubbles and clusters of galaxies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids A and B creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well-known damped oscillations. We present the conditions required for producing such a standing shock wave, which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio R critical , in terms of the adiabatic indices of the two fluids, and a critical Mach number M critical s of the incident shock wave, which produces a standing reflected wave. If the initial density ratio R of the two fluids is less than R critical then a standing shock wave is possible at M s =M critical s . Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity, which affects the damping rate of the oscillations. Furthermore, we point out that nonlinear bubble and spike amplitudes depend relatively weakly on the viscosity of the fluids and that the interface area is a better diagnostic.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1974

Effects of interplanetary shock waves on energetic charged particles

Experimental data on the influence of interplanetary perpendicular and oblique shock waves on the ambient energetic protons are presented along with a theoretical analysis of the acceleration of particles in almost perpendicular shock waves. It was found that low-energy protons can be accelerated in perpendicular shock waves by repeated crossings of the shock front up to a maximum energy given by the product of their initial energy times the ratio of the magnetic fields. High-energy protons need to stay at the shock front for longer times than low-energy protons in order to reach the same relative energy gain. In the theoretical study of proton acceleration at almost perpendicular shock waves, it was found that protons reflected at shock waves with the angle between the upstream magnetic field and the shock normal greater than about 80 deg achieve large energy gains at the shock front. The larger this angle, the higher the energy gain. However, the reflection and energization of protons at these shock waves is not 'instantaneous', neither is it a one-step process: it is performed through repeated crossings of the shock front.

Sarris, E. T.↗

NASA NTRS1979

Second sound shock waves and critical velocities in liquid helium 2

Large amplitude second-sound shock waves were generated and the experimental results compared to the theory of nonlinear second-sound. The structure and thickness of second-sound shock fronts are calculated and compared to experimental data. Theoretically it is shown that at T = 1.88 K, where the nonlinear wave steepening vanishes, the thickness of a very weak shock must diverge. In a region near this temperature, a finite-amplitude shock pulse evolves into an unusual double-shock configuration consisting of a front steepened, temperature raising shock followed by a temperature lowering shock. Double-shocks are experimentally verified. It is experimentally shown that very large second-sound shock waves initiate a breakdown in the superfluidity of helium 2, which is dramatically displayed as a limit to the maximum attainable shock strength. The value of the maximum shock-induced relative velocity represents a significant lower bound to the intrinsic critical velocity of helium 2.

Turner, T. N.↗

NASA NTRS1986

Subcritical and supercritical interplanetary shocks - Magnetic field and energetic particle observations

A study of 34 forward interplanetary shocks observed by ISEE 3 during 1978 and 1979 has been conducted. Magnetic field and high-energy particle data have been used, and for each shock the first critical Mach number has been determined. The first surprising result is that the majority of the observed shocks appear to be supercritical, and consistent with their supercritical character, many shocks have a foot and/or an overshoot in the magnetic field structure. Large-amplitude low-frequency waves (period of about 20 s in the spacecraft frame) are commonly observed upstream of all supercritical shocks (except for a few quasi-perpendicular shocks) and also upstream of the few subcritical shocks. Intense particle events are frequently observed at many shocks: spikes at quasi-perpendicular shocks and energetic storm particle events associated with quasi-parallel shocks can be comparably intense. The correlation of the high-energy particle peak flux with various shock parameters is in agreement with the acceleration mechanisms proposed by previous studies.

Bavassano-Cattaneo, M. B.↗

NASA NTRS1988

Modified non-linear Burgers' equations and cosmic ray shocks

A reductive perturbation scheme is used to derive a generalized non-linear Burgers' equation, which includes the effects of dispersion, in the long wavelength regime for the two-fluid hydrodynamical model used to describe cosmic ray acceleration by the first-order Fermi process in astrophysical shocks. The generalized Burger's equation is derived for both relativistic and non-relativistic cosmic ray shocks, and describes the time evolution of weak shocks in the theory of diffusive shock acceleration. The inclusion of dispersive effects modifies the phase velocity of the shock obtained from the lower order non-linear Burger's equation through the introduction of higher order terms from the long wavelength dispersion equation. The travelling wave solution of the generalized Burgers' equation for a single shock shows that larger cosmic ray pressures result in broader shock transitions. The results for relativistic shocks show a steepening of the shock as the shock speed approaches the relativistic cosmic ray sound speed. The dependence of the shock speed on the cosmic ray pressure is also discussed.

Zank, G. P.↗

NASA NTRS1990

MHD intermediate shocks in coronal mass ejections

A simplified model of coronal mass ejections is considered in which at least a portion of the interaction with the background corona involves a shock wave, and the allowable shock solutions and their compressive signatures are examined. The MHD shock-jump equations have a maximum of three possible types of solutions with an entropy rise for fixed values of the physical variables (slow, intermediate, and fast shocks). However, one of the three solution classes (the intermediate shock) is widely believed to not occur in nature and is regarded as nonevolutionary or extraneous. Without the intermediate shock, there is no multiplicity of solutions in that only one shock (or none) can occur for given physical values. All three potential shock types are considered, and it is shown solely on the basis of the shock-jump equations, that intermediate shocks must exist along some segment of the shock front for certain parametric regimes and for conditions that probably occur in some coronal mass ejections.

Steinolfson, R. S.↗

NASA NTRS1990

Giotto magnetic field observations at the outbound quasi-parallel bow shock of Comet Halley

The investigation of the outbound bow shock of Comet Halley using Giotto magnetometer data leads to the following results: the shock is characterized by strong magnetic turbulence associated with an increasing background magnetic field and a change in direction by 60 deg as one goes inward. In HSE-coordinates, the observed normal turned out to be (0.544, - 0.801, 0.249). The thickness of the quasi-parallel shock was 120,000 km. The shock is shown to be a new type of shock transition called a 'draping shock'. In a draping shock with high beta in the transonic transition region, the transonic region is characterized by strong directional variations of the magnetic field. The magnetic turbulence ahead of the shock is characterized by k-vectors parallel or antiparallel to the average field (and, therefore, also to the normal of the quasi-parallel shock) and almost isotropic magnetic turbulence in the shock transition region. A model of the draping shock is proposed which also includes a hypothetical subshock in which the supersonic-subsonic transition is accomplished.

Neubauer, F. M.↗

NASA NTRS1992

Coronal shock waves

The formation of magnetohydrodynamic (MHD) shocks near the leading edge of Coronal Mass Ejections (CME's) is considered using results from both shock theory and numerical simulations. By using just the shock theory results and a simplified model corona, the following is shown: a slow shock front should be concave upward (away from the solar surface); a configuration containing intermediate shocks should also be concave upward near the center of the CME and concave downward at some distance from the CME centerline; and a fast shock configuration should be concave downward. These results are verified with numerical simulations of the MHD equations for the propagation of shocks through a quiescent coronal streamer. By examining the characteristic wave speeds in the ambient streamer, it is estimated that the various shock configurations should form for CME speeds within the following speed increments: slow shocks, 200 to 300 km/sec; intermediate shocks, 300 to 900 km/sec; and fast shocks, greater than 900 km/sec.

Steinolfson, Richard S.↗