Rankine-Hugoniot Shock Research Articles

Partially ionized two-fluid shocks with collisional and radiative ionization and recombination – multilevel hydrogen model

ABSTRACT Explosive phenomena are known to trigger a wealth of shocks in warm plasma environments, including the solar chromosphere and molecular clouds where the medium consists of both ionized and neutral species. Partial ionization is critical in determining the behaviour of shocks, since the ions and neutrals locally decouple, allowing for substructure to exist within the shock. Accurately modelling partially ionized shocks requires careful treatment of the ionized and neutral species, and their interactions. Here we study a partially ionized switch-off slow-mode shock using a multilevel hydrogen model with both collisional and radiative ionization and recombination rates that are implemented into the two-fluid (PIP) code, and study physical parameters that are typical of the solar chromosphere. The multilevel hydrogen model differs significantly from magnetohydrodynamic (MHD) solutions due to the macroscopic thermal energy loss during collisional ionization. In particular, the plasma temperature both post-shock and within the finite-width is significantly cooler that the post-shock MHD temperature. Furthermore, in the mid to lower chromosphere, shocks feature far greater compression than their single-fluid MHD analogues. The decreased temperature and increased compression reveal the importance of non-equilibrium ionized in the thermal evolution of shocks in partially ionized media. Since partially ionized shocks are not accurately described by the Rankine-Hugoniot shock jump conditions, it may be incorrect to use these to infer properties of lower atmospheric shocks.

Advective Accretion onto a Nonspherical Accretor in White Dwarf and Neutron Star Binaries: A New Scenario of Shock Formation

Abstract Numerous studies on hydrodynamics of the Keplerian as well as the sub-Keplerian accretion disk around a compact object (e.g., white dwarf (WD), neutron star (NS), or a black hole) have attempted to explain the observed UV, soft, and hard X-ray spectra. Although, when the compact object (e.g., a WD or an NS) has a finite surface, its rapid rotation, the stellar magnetic field could cause deformation of the spherical symmetry. Earlier studies on the Keplerian disk showed that a deviation from the spherical symmetry of the compact object could affect the observed light curve and spectra at high frequencies. Here, we have explored the effect of the nonspherical nature of a compact object on the hydrodynamics of an optically thin, geometrically thick sub-Keplerian advective flow. We find that due to the nonspherical shape of the central accretor, there is a possibility to trigger Rankine–Hugoniot shock in the sub-Keplerian advective flow close to the accretor without considering any general relativistic effect or presence of the hard surface of the star. Our results are more relevant for accretion onto a WD as hardly any general relativistic effect will come into the picture. We propose that some observational features, e.g., high significance of fitting the spectra with multi-temperature plasma models rather than single-temperature models, and variable efficiency of X-ray emission (X-ray luminosity in comparison with the optical and UV luminosity of the disk) in nonmagnetic cataclysmic variables can be explained by the presence of a shock in the sub-Keplerian advective flow.

Rankine–Hugoniot Shock Conditions for Space and Astrophysical Plasmas Described by Kappa Distributions

Abstract This paper provides the set of Rankine–Hugoniot (R–H) jump conditions for shocks in space and astrophysical plasmas described by kappa, distributions. The characteristic result is the development of a new R–H condition that transforms the values of kappa upstream and downstream the shock. The kappa index parameterizes and labels kappa distributions, and it is necessary for characterizing the thermodynamics of space plasmas. This first approach is restricted to non-magnetized plasmas, and the whole achievement is derived by following first principles of statistical mechanics and thermodynamics. The results show that, depending on the shock strength, the kappa indices across the shock may decrease or increase, indicating cases of shock acceleration or deceleration, respectively.

Shock-Induced Hot Spot Formation and Spalling in 1,3,5-trinitroperhydro-1,3,5-triazine Containing a Cube Void.

The initial reaction mechanism of energetic materials under impact loading and the role of crystal properties in impact initiation and sensitivity are still unclear. In this paper, we report reactive molecular dynamics simulations of shock initiation of 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) crystals containing a cube void. Shock-induced void collapse, hot spots formation and growth, as well as spalling are revealed to be dependent on the shock velocity. The void collapse times are 1.5 and 0.7 ps, for the shock velocity of 2 and 4 km·s–1, respectively. Results indicate that the initial hot spot formation consists of two steps: one is the temperature rise caused by local plastic deformation and the other is the temperature increase resulting from the collision of upstream and downstream particles during the void collapse. Whether hot spots will continue to grow or quench depends on sensitive balance between energy release caused by local physical and chemical reactions and various heat dissipation mechanisms. In our simulations, hot spot would grow for Up = 4 km·s–1; hot spot is weak to some extent for Up = 2 km·s–1. The tensile wave reflected by the shock wave after reaching the free surface causes the spalling, which depends on the initial shock velocity. Typical spalling occurs for the shock velocity 2 km·s–1, while the tensile wave induces the microsplit region in RDX crystals in the case of Up = 4 km·s–1. Chemical reactions are studied for Rankine–Hugoniot shock pressures Ps = 14.4, 57.8 GPa. For the weak shock, there is almost no decomposition reaction of the RDX molecules near the spalling region. On the contrary, there are large number of small molecule products, such as H2O, CO2, NO2, and so forth, around the microsplit regions for the strong shock. The ruptures of N–NO2 bond are the main initial reaction mechanisms for the shocked RDX crystal and are not affected by shock strength, while the microsplit slows down the decomposition rate of RDX. The work in this paper can shed light on a thorough understanding of thermal ignition, hot spot growth, and other physical and chemical phenomena of energetic materials containing voids under impact loading.

Global constraints on diffusive particle acceleration by strong non-relativistic shocks

Estimating the cosmic-ray acceleration efficiency $ \epsilon $ in supernova remnants (SNRs) through observations is a challenging task in general. Based on the Rankine-Hugoniot shock conditions, we find an anticorrelation between $ \epsilon $ and the power-law spectral index $ \alpha $ of relativistic particle distribution produced via diffusive particle acceleration by nonrelativistic shocks, implying more efficient acceleration in older SNRs with harder radio spectra. Then $ \epsilon $ may be estimated from some hard radio spectral index measurements. Assuming the particle distribution in downstream of strong shocks to be a nonrelativistic Maxwellian plus a relativistic power law with a high-energy cutoff, we also find that the injection rate for relativistic particles $ \eta $ needs to $ \gtrsim 10^{-6} $ for a prominent decrease of the adiabatic index in SNRs, which implies higher compression ratio and lower values of $ \alpha $. This threshold of $ \eta $ increases with the shock speed $ u_1 $, which may explain the relatively harder radio spectra of older SNRs with lower $ u_1 $. We show that $ \eta $ and/or the relativistic cutoff momentum $ p_\text{m} $ need to be low for old SNRs, and expect a gradual increase of $ \epsilon $ as SNR evolves with gradually decreasing $ \eta $ and $ p_\text{m} $.

Spherical accretion in giant elliptical galaxies: multitransonicity, shocks, and implications on AGN feedback

Isolated massive elliptical galaxies, or that are present at the center of cool-core clusters, are believed to be powered by hot gas accretion directly from their surrounding hot X-ray emitting gaseous medium. This leads to a giant Bondi-type spherical/quasi-spherical accretion flow onto their host SMBHs, with the accretion flow region extending well beyond the Bondi radius. In this work, we present a detailed study of Bondi-type spherical flow in the context of these massive ellipticals by incorporating the effect of entire gravitational potential of the host galaxy in the presence of cosmological constant $\Lambda$, considering a five-component galactic system (SMBH + stellar + dark matter + hot gas + $\Lambda$). The current work is an extension of Ghosh \& Banik (2015), who studied only the cosmological aspect of the problem. The galactic contribution to the potential renders the (adiabatic) spherical flow to become {\it multi-transonic} in nature, with the flow topology and flow structure significantly deviating from that of classical Bondi solution. More notably, corresponding to moderate to higher values of galactic mass-to-light ratios, we obtain Rankine-Hugoniot shocks in spherical wind flows. Galactic potential enhances the Bondi accretion rate. Our study reveals that there is a strict lower limit of ambient temperature below which no Bondi accretion can be triggered; which is as high as $\sim 9 \times 10^6 \, K$ for flows from hot ISM-phase, indicating that the hot phase tightly regulates the fueling of host nucleus. Our findings may have wider implications, particularly in the context of outflow/jet dynamics, and radio-AGN feedback, associated with these massive galaxies in the contemporary Universe.

HUBBLE SPACE TELESCOPE CONSTRAINTS ON THE WINDS AND ASTROSPHERES OF RED GIANT STARS*

ABSTRACT We report on an ultraviolet spectroscopic survey of red giants observed by the Hubble Space Telescope, focusing on spectra of the Mg ii h and k lines near 2800 Å in order to study stellar chromospheric emission, winds, and astrospheric absorption. We focus on spectral types between K2 III and M5 III, a spectral type range with stars that are noncoronal, but possessing strong, chromospheric winds. We find a very tight relation between Mg ii surface flux and photospheric temperature, supporting the notion that all K2-M5 III stars are emitting at a basal flux level. Wind velocities (V w ) are generally found to decrease with spectral type, with V w decreasing from ∼40 km s−1 at K2 III to ∼20 km s−1 at M5 III. We find two new detections of astrospheric absorption, for σ Pup (K5 III) and γ Eri (M1 III). This absorption signature had previously only been detected for α Tau (K5 III). For the three astrospheric detections, the temperature of the wind after the termination shock (TS) correlates with V w , but is lower than predicted by the Rankine–Hugoniot shock jump conditions, consistent with the idea that red giant TSs are radiative shocks rather than simple hydrodynamic shocks. A full hydrodynamic simulation of the γ Eri astrosphere is provided to explore this further.

Solution of the Noh problem using the universal symmetry of the gas dynamics equations

Noh’s constant-velocity shock problem is considered as a two-region solution of the one-dimensional (1D) Euler compressible flow equations, where the equation of state (EOS) closure model is included in the energy equation via an adiabatic bulk modulus. Regardless of the EOS model employed, the resulting system of equations is invariant under a universal group of scaling transformations. When combined with the required velocity field, the resulting equivalent system of ordinary differential equations coupled with the Rankine–Hugoniot shock jump conditions produces at least semi-analytic algebraic Noh solutions in 1D planar symmetry for any EOS. It is also shown for 1D curvilinear symmetries that the existence of a Noh solution is guaranteed only under more restrictive EOS conditions. In the context of this work, example Noh solutions—in some cases featuring arbitrary strength shocks—are derived for various closure models, including ideal gas, a two-parameter Clausius-like EOS, stiff gas, and a Mie–Gruneisen form. A code verification study is provided in the latter case, as an example of the application of the broader theoretical concepts.

Molecular Dynamics Simulations of the Collapse of a Cylindrical Pore in the Energetic Material α-RDX

Molecular dynamics simulations were used to study the shock-induced collapse of cylindrical pores in oriented single crystals of the energetic material α-1,3,5-trinitroperhydro-1,3,5-triazine (α-RDX). The shock propagation direction was parallel to the [100] crystal direction and the cylinder axis of the initially 35.0 nm diameter pore was parallel to [010]. Features of the collapse were studied for Rankine–Hugoniot shock pressures P s = 9.71, 24.00, and 42.48 GPa. Pore collapse for the weak shock is dominated by visco-plastic deformation in which the pore pinches shut without jet formation and with little penetration of the upstream material into the downstream pore wall. For the strong shock the collapse is hydrodynamic-like and results in the formation of a jet that penetrates significantly into the downstream pore wall. Material flow during collapse was characterized by examining the spread and mixing of sets of initially contiguous molecules and evolution of local velocity fields. Local disorder during collapse was assessed using time autocorrelation functions for molecular rotation. Energy deposition and localization was studied using spatial maps of temperature and pressure calculated as functions of time.

General Three-Dimensional Relation for Oblique Shocks on Swept Ramps

A mathematical relation is formulated to calculate the properties of oblique shocks generated from swept ramps. Ramp sweep extends the oblique shock relations from two to three dimensions in a manner analogous to the way unswept ramp deflection extends the Rankine–Hugoniot shock relations from one to two dimensions. A new theta–beta–Mach-sweep (–Mach-sweep) relation is formulated, which reduces to the standard theta–beta–Mach (–Mach) relation for the special case of two-dimensional shocks from unswept ramps. The swept formulation may be expressed as a cubic equation with coefficients that are simple modifications of the cubic coefficients for the standard unswept formulation. The solution of this swept cubic equation allows the shock angle and downstream properties to be determined directly from the upstream Mach number, geometric ramp angle, and sweep. Several notable properties of sweep on the “strong” and “weak” solutions are depicted and discussed. The new formulation simplifies the process of placing, aligning, and focusing shocks for a sequence of swept ramps.

Molecular dynamics simulations of shock waves in cis-1,4-polybutadiene melts

Molecular dynamics simulations of supported shock waves in monodisperse melts of cis-1,4-polybutadiene initially at atmospheric pressure and T = 413 K were performed to study the shock-induced structural changes and post-shock relaxation. Simulations were performed for Rankine-Hugoniot shock pressures between 7.22 GPa and 8.26 GPa using the united-atom force field due to Smith and Paul [G. D. Smith and W. Paul, J. Phys. Chem. A 102, 1200 (1998)] for systems composed of chains containing 32, 64, or 128 united atoms. The sensitivity of the results to the non-bonded interaction potential was studied by comparing results obtained using the Lennard-Jones 12–6 potential from the original Smith and Paul force field to ones obtained when the 12–6 potential was replaced by the Buckingham exponential–6 potential. Several structural and mechanical properties were studied as functions of distance (time) behind the shock front. Bulk relaxation was characterized by calculating profiles of temperature, density, and principal and shear stress. Microscopic shock-induced structural rearrangement and relaxation were studied by calculating the ratio of Cartesian components of the mean-squared radius of gyration to corresponding values for the equilibrated material; dihedral angle distributions; and the distribution of, and second Legendre polynomial order parameter for, the angle formed by covalent bond vectors and the shock propagation direction.

Fast sweeping methods for hyperbolic systems of conservation laws at steady state

Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton–Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of conservation laws. By exploiting the flow of information along characteristics, these fast sweeping methods can compute solutions very efficiently. Furthermore, the methods capture shocks sharply by directly imposing the Rankine–Hugoniot shock conditions. We present convergence analysis and numerics for several one- and two-dimensional examples to illustrate the use and advantages of this approach.

Application of picosecond terawatt laser pulses for fast ignition of fusion

AbstractIn this research, we presented the application of picosecond terawatt laser pulses for ultrahigh acceleration of plasma blocks for fast ignition of fusion. Ultrahigh acceleration of plasma blocks after irradiation of picosecond laser pulses of around terawatt power in the range of 1020 cm/s2was discovered by Sauerbrey (1996) as measured by Doppler effect where the laser intensity was up to about 1018W/cm2. This is several orders of magnitude higher than acceleration by irradiation based on thermal interaction of lasers has produced. This ultrahigh acceleration resulted from hydrodynamic computations at plane target interaction in 1978 at comparable conditions where the interaction was dominated by the nonlinear (generalized ponderomotive) forces where the laser energy was instantly converted into plasma motion in contrast to slow and delayed thermal collision processes. After clarifying this basic result, the application of the plasma blocks for side-on ignition of solid density or modestly compressed fusion fuel following the theory of Chu (1971) is updated in view of later discovered plasma properties and the ignition of deuterium tritium and of proton-11B appeared possible for a dozen of PW-PS laser pulses if an extremely high contrast ratio avoided relativistic self-focusing. A re-evaluation of more recent experiment confirms the acceleration by the nonlinear force, and the generation of the fusion flame with properties of Rankine-Hugoniot shocks is reported.

Simulation of the vapor explosion of tin and aluminum oxide fragments in water

The vapor explosion process involves an explosive phase change from a thin liquid film into a vapor with a dramatic change in material properties across a high-pressure shock wave. The energy released during the explosion process can reach a level of chemical explosions associated with detonating high explosives. Because no fuel-air chemical reaction is needed for initiating a vapor explosion, the process can be considered as a green reaction that generates zero pollutants. However, the phase change that accompanies a thousand-fold increase in the vapor volume during the rapid film evaporation is a natural consequence of a sudden change in density across the phase front; this feature closely resembles the process of blast wave generation. The high-pressure vapor produced without a chemical reaction expands as a spherical wave at a uniform velocity predicted through the Rankine-Hugoniot shock conditions. In this paper, a new methodology based on a simple shock wave and a phase field theory is proposed to formulate the vapor explosion process.

Shock-Induced Inelastic Deformation in Oriented Crystalline Pentaerythritol Tetranitrate

Molecular dynamics simulations were used to study the mechanisms of shock-induced inelastic deformation in oriented single crystals of the energetic material pentaerythritol tetranitrate (PETN). Supported planar shock waves with Rankine–Hugoniot shock pressures PR–H ∼ 9 GPa were propagated along two different crystal directions: one that is sensitive to initiation ([001]) and another that is relatively insensitive to initiation ([100]). Qualitatively, it was observed that for the sensitive orientation only elastic compression occurred, leading to the propagation of a single wave through the material, whereas for the insensitive direction elastic compression at and immediately behind the shock front was followed by inelastic deformation, leading to a two-wave structure in which the sharp elastic front moves through the crystal at a higher speed than the broader plastic wave. The detailed responses were characterized by calculating several structural and thermal properties including: relative center-of-mass...

Review about acceleration of plasma by nonlinear forces from picoseond laser pulses and block generated fusion flame in uncompressed fuel

AbstractIn addition to the matured “laser inertial fusion energy” with spherical compression and thermal ignition of deuterium-tritium (DT), a very new alternative for the fast ignition scheme may have now been opened by using side-on block ignition aiming beyond the DT-fusion with igniting the neutron-free reaction of proton-boron-11 (p-11B). Measurements with laser pulses of terawatt power and ps duration led to the discovery of an anomaly of interaction, if the prepulses are cut off by a factor 108(contrast ratio) to avoid relativistic self focusing in agreement with preceding computations. Applying this to petawatt (PW) pulses for Bobin-Chu conditions of side-on ignition of solid fusion fuel results after several improvements in energy gains of 10,000. This is in contrast to the impossible laser-ignition of p-11B by the usual spherical compression and thermal ignition. The side-on ignition is less than ten times only more difficult than for DT ignition. This is essentially based on the instant and direct conversion the optical laser energy by the nonlinear force into extremely high plasma acceleration. Genuine two-fluid hydrodynamic computations for DT are presented showing details how ps laser pulses generate a fusion flame in solid state density with an increase of the density in the thin flame region. Densities four times higher are produced automatically confirming a Rankine-Hugoniot shock wave process with an increasing thickness of the shock up to the nanosecond range and a shock velocity of 1500 km/s which is characteristic for these reactions.

MARKARIAN 6: SHOCKING THE ENVIRONMENT OF AN INTERMEDIATE SEYFERT

Markarian 6 is a nearby (D~78 Mpc) Seyfert 1.5, early-type galaxy, with a double set of radio bubbles. The outer set spans ~7.5 kpc and is expanding into the halo regions of the host galaxy. We present an analysis of our new Chandra observation, together with archival XMM-Newton data, to look for evidence of emission from shocked gas around the external radio bubbles, both from spatially resolved regions in Chandra and from spectral analysis of the XMM data. We also look for evidence of a variable absorbing column along our line of sight to Mrk 6, to explain the evident differences seen in the AGN spectra from the various, non-contemporaneous, observations. We find that the variable absorption hypothesis explains the differences between the Chandra and XMM spectra, with the Chandra spectrum being heavily absorbed. The intrinsic N_H varies from ~8x10^{21} atoms*cm^{-2} to ~3x10^{23} atoms*cm^{-2} on short timescales (2-6 years). The past evolution of the source suggests this is probably caused by a clump of gas close to the central AGN, passing in front of us at the moment of the observation. Shells of thermal X-ray emission are detected around the radio bubbles, with a temperature of ~0.9 keV. We estimate a temperature of ~0.2 keV for the external medium using luminosity constraints from our Chandra image. We analyse these results using the Rankine-Hugoniot shock jump conditions, and obtain a Mach number of ~3.9, compatible with a scenario in which the gas in the shells is inducing a strong shock in the surrounding ISM. This could be the third clear detection of strong shocks produced by a radio-powerful Seyfert galaxy. These results are compatible with previous findings on Centaurus A and NGC 3801, supporting a picture in which these AGN-driven outflows play an important role in the environment and evolution of the host galaxy.

Homogeneous dislocation nucleation in cyclotrimethylene trinitramine under shock loading

The propagation of shock waves normal to (111) in the energetic molecular crystal cyclotrimethylene trinitramine (RDX) has been studied using large-scale molecular dynamics simulations. Partial dislocation loops with Burgers vector 0.16[010] are nucleated homogeneously on (001) at Rankine–Hugoniot shock pressures greater than 1.3 GPa. Calculations of the [010] cross-section of the (001) generalized stacking fault energy surface as a function of applied pressure along [001] reveals that the stacking fault enclosed by the partial dislocation loops is rendered metastable by a stress-induced change in molecular conformation. Furthermore, large-scale molecular dynamics simulations performed on quasi-two-dimensional (111)-oriented single crystals show a two-wave elastic-plastic response with a “galloping” plastic wave. We propose that the onset of homogeneous dislocation nucleation accounts for the abrupt change in the elastic-plastic response of macroscopic (111)-oriented RDX single crystals observed in recent experiments by giving rise to an anomalous plastic hardening.

Dissipative accretion flows around a rotating black hole

We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy ⁠, the specific angular momentum (λ) and the accretion rate of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate ⁠, the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.

Shock-induced shear bands in an energetic molecular crystal: Application of shock-front absorbing boundary conditions to molecular dynamics simulations

The response of the energetic molecular crystal cyclotrimethylene trinitramine (RDX) to the propagation of planar shock waves normal to (100) has been studied using large-scale molecular dynamics simulations that employ an accurate and transferable nonreactive potential. The propagation of the shock waves was simulated using nonequilibrium molecular dynamics. Shear bands were nucleated during shocks with a particle velocity of $1.0\text{ }\text{km}\text{ }{\text{s}}^{\ensuremath{-}1}$ and corresponding Rankine-Hugoniot shock pressure of 9.7 GPa. These defects propagate into the compressed material at $45\ifmmode^\circ\else\textdegree\fi{}$ to [100] in the [010] zone. The shear bands evolve slowly compared to the time scales routinely accessible to nonequilibrium molecular dynamics toward a liquidlike state as a result of viscous heating. A recently developed shock-front absorbing boundary condition [A. V. Bolesta et al., Phys. Rev. B 76, 224108 (2007)] was applied to the simulation cells at the moment of maximum compression to sustain the shock-compressed state. Molecular dynamics simulations were then employed to study the temporal and structural evolution of the shock-induced shear bands toward a steady-fluctuating state. Owing to the intense, viscous flow-driven heating within the shear bands, these defects can be considered to be homogeneously nucleated hot spots.