Shock Acceleration Research Articles

Dynamic parameters of multi-cabin protective structure subjected to low-impact load – Numerical and experimental investigations

The dynamic response of a multi-cabin protective structure subjected to impact load directly affects the protective performance of materials; thus, studying the dynamic response and communication law of wave effect of the load plays an important role in the prediction of protective performance. In this study, the protection experiments of box-structure under air- and/or water-medium are conducted, the dynamic response of the structure subjected to low-impact load is analyzed, and the corresponding numerical simulations are analyzed using the theory of finite element method (FEM). Combined with experimental and FEM simulations, the shock strain distribution, acceleration attenuation, and signal energy in defensive materials are determined. Based on the results, the metal structure exhibits good absorption characteristics for shock vibration. Using the experimental data, we also show that the attenuation of shock wave in water medium should be significantly better than that in air medium, and the protective structure should be designed for a combination of water and air mediums. Meanwhile, the numerical simulation can provide a quantitative analysis process for dynamic analysis of defensive materials.

Converging shock waves in a Van der Waals gas of variable density

SummaryThe converging problem of cylindrically or spherically symmetric strong shock wave collapsing at the axis/centre of symmetry, is studied in a non-ideal inhomogeneous gaseous medium. Here, we assume that the undisturbed medium is spatially variable and the density of a gas is decreasing towards the axis/centre according to a power law. In the present work, we have used the perturbation technique to the implosion problem and obtained a global solution that also admits Guderley’s asymptotic solution in a very good agreement which holds only in the vicinity of the axis/centre of implosion. The similarity exponents together with their corresponding amplitudes are determined by expanding the flow parameters in powers of time. We also refined the leading similarity exponents near the axis/centre of convergence. We compared our calculated results with the already existing results and found them in good agreements up to two decimal places. Shock position and flow parameters are analysed graphically with respect to the variation of values of different parameters. It is observed that an increase in the density variation index, adiabatic exponent and Van der Waals excluded volume, causes the time of shock collapse to decrease due to which the shock acceleration gets increased and shock reaches the axis/centre much faster.

Interplanetary Protons versus Interacting Protons in the 2017 September 10 Solar Eruptive Event

Abstract We analyze the relativistic proton emission from the Sun during the eruptive event on 2017 September 10, which caused a ground-level enhancement (GLE 72) registered by the worldwide network of neutron monitors. Using the neutron monitor data and interplanetary transport modeling both along and across interplanetary magnetic field (IMF) lines, we deduce parameters of the proton injection into the interplanetary medium. The inferred injection profile of the interplanetary protons is compared with the profile of the >100 MeV γ-ray emission observed by the Fermi Large Area Telescope, attributed to pion production from the interaction of >300 MeV protons at the Sun. GLE 72 started with a prompt component that arrived along the IMF lines. This was followed by a more prolonged enhancement caused by protons arriving at the Earth across the IMF lines from the southwest. The interplanetary proton event is modeled using two sources—one source at the root of the Earth-connected IMF line and another source situated near the solar western limb. The maximum phase of the second injection of interplanetary protons coincides with the maximum phase of the prolonged >100 MeV γ-ray emission that originated from a small area at the solar western limb, below the current sheet trailing the associated coronal mass ejection (CME). A possible common source of interacting protons and interplanetary protons is discussed in terms of proton acceleration at the CME bow shock versus coronal (re-)acceleration in the wake of the CME.

Shock acceleration efficiency in radio relics

Context. Radio relics in galaxy clusters are giant diffuse synchrotron sources powered in cluster outskirts by merger shocks. Although the relic–shock connection has been consolidated in recent years by a number of observations, the details of the mechanisms leading to the formation of relativistic particles in this environment are still not well understood. Aims. The diffusive shock acceleration (DSA) theory is a commonly adopted scenario to explain the origin of cosmic rays at astrophysical shocks, including those in radio relics in galaxy clusters. However, in a few specific cases it has been shown that the energy dissipated by cluster shocks is not enough to reproduce the luminosity of the relics via DSA of thermal particles. Studies based on samples of radio relics are required to further address this limitation of the mechanism. Methods. In this paper, we focus on ten well-studied radio relics with underlying shocks observed in the X-rays and calculate the electron acceleration efficiency of these shocks that is necessary to reproduce the observed radio luminosity of the relics. Results. We find that in general the standard DSA cannot explain the origin of the relics if electrons are accelerated from the thermal pool with an efficiency significantly smaller than 10%. Our results show that other mechanisms, such as shock re-acceleration of supra-thermal seed electrons or a modification of standard DSA, are required to explain the formation of radio relics.

Diffusive shock acceleration of cosmic rays in low-Mach galaxy cluster shocks.

Astrophysical shocks are known to accelerate particles to high relativistic velocities. This process requires the particles to repeatedly cross the shock, a process that can only occur if the particle is reflected by the local magnetic field. Such particles are observed on Earth as cosmic rays. This phenomenon has been studied in considerable detail for high-Mach shocks, such as the shocks that occur in colliding stellar winds and supernova explosions, but remains relatively unexplored for low-Mach shocks, such as the shocks of colliding clusters of galaxies. Recent simulations using the particle-in-cell (PIC) method have shown that, depending on the exact Mach number, even low-Mach shocks can accelerate charged particles to the point where they start to deviate from the thermal velocity distribution. However, the computationally intensive nature of the PIC calculations makes it difficult to continue the simulations to determine whether the particles can reach relativistic speeds. We now present new simulations, using a combined PIC and magnetohydrodynamics (MHD) technique. This model, which takes advantage of the computational efficiency of MHD, allows us to simulate a much larger physical volume and study the behaviour of the particles over a longer period of time in order to determine to what extent the acceleration process continues and whether these shocks are capable of contributing to the cosmic ray spectrum.

Multiwavelength Emission from Galactic Jets: The Case of the Microquasar SS433

Abstract SS433 is a Galactic microquasar with powerful jets, where very-high-energy particles are produced. We study particle acceleration in the jets of SS433 through the use of recent multiwavelength data from radio to TeV gamma-ray. We first present a general framework for the particle acceleration, cooling, and transport in relativistic jets. We then apply this to two X-ray knots in the jets of SS433, focusing on leptonic emission. Our detailed treatment of particle transport and evolution produces substantially different predictions from previous papers. For both regions, our model can account for the multiwavelength data except for the GeV data. This suggests that GeV emission is mostly from different regions and/or mechanisms. We find that the acceleration process should be efficient, which could be realized by diffusive shock acceleration close to the Bohm limit. Provided that protons are accelerated at the same efficiency as electrons, our results imply that SS433 is a PeVatron, i.e., can accelerate protons beyond a PeV. Future hard X-ray and MeV gamma-ray observations can critically test our models by detecting the spectral turnover or cutoff.

Cosmic-ray acceleration and escape from post-adiabatic supernova remnants

Context. Supernova remnants are known to accelerate cosmic rays on account of their nonthermal emission of radio waves, X-rays, and gamma rays. Although there are many models for the acceleration of cosmic rays in supernova remnants, the escape of cosmic rays from these sources has not yet been adequately studied. Aims. We aim to use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. Methods. We performed spherically symmetric 1D simulations in which we simultaneously solved the transport equations for cosmic rays, magnetic turbulence, and the hydrodynamical flow of the thermal plasma in a volume large enough to keep all cosmic rays in the simulation. The transport equations for cosmic rays and magnetic turbulence were coupled via the cosmic-ray gradient and the spatial diffusion coefficient of the cosmic rays, while the cosmic-ray feedback onto the shock structure can be ignored. Our simulations span 100 000 years, thus covering the free-expansion, the Sedov–Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution. Results. At later stages of the evolution, cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration, and feature breaks in the 10 − 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. We further find the gamma-ray luminosity to peak around an age of 4000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media generally emit more inverse-Compton radiation, matching the fact that the brightest known supernova remnants – RCW86, Vela Jr., HESS J1731−347 and RX J1713.7−3946 – are all expanding in low density environments.

The Determination of Shock Accelerations on a Small Nuclear Power Plant Structural Elements When Falling to the Surface

The article conducts research one of the expansion phase of emergency with an Intercontinental Ballistic Missile, accompanied by an carrier explosion, an ejection of the reentry vehicle from a silo and its subsequent fall. The simulation of the collision of the reentry vehicle with a weakly deformable barrier in the event of fall is performed, the result calculation valuation and experiment are carried out.

Turbulence Particle Acceleration and UHECR

The standard model to produce non-thermal particles is the particle acceleration at shocks. However, the photon spectra in high-energy objects, such as blazars, frequently show very hard feature, which seems inconsistent with the standard shock acceleration theory. The alternative model is the particle acceleration by turbulence. If we adopt a hard-sphere-like acceleration, in which the acceleration timescale is independent of the particle energy, the electron energy distribution becomes consistent with blazar photon spectra. Adopting this model to the deceleration phase of gamma-ray burst jets, ultra high-energy cosmic-rays can be produced. The resultant spectrum is harder than other models, so that the secondary neutrino production in their propagation is relatively suppressed. As a candidate of the hard-sphere acceleration mechanism, we propose the acceleration by large scale compressible MHD waves, where the transit time damping (TTD) is a key mechanism. We find that the acceleration efficiency is higher than previously considered.

On the injection of relativistic electrons in the jet of 3C 279

ABSTRACTThe acceleration of electrons in 3C 279 is investigated through analysing the injected electron energy distribution (EED) in a time-dependent synchrotron self-Compton+external Compton emission model. In this model, it is assumed that relativistic electrons are continuously injected into the emission region, and the injected EED [$Q_{\rm e}^\prime (\gamma ^\prime)$] follows a single power-law form with low- and high-energy cut-offs $\rm \gamma _{min}^{\prime }$ and $\rm \gamma _{max}^{\prime }$, respectively, and the spectral index n, i.e. $Q_{\rm e}^\prime (\gamma ^\prime)\propto \gamma ^{\prime -n}$. This model is applied to 14 quasi-simultaneous spectral energy distributions of 3C 279. The Markov Chain Monte Carlo (MCMC)-fitting technique is performed to obtain the best-fitting parameters and the uncertainties on the parameters. The results show that the injected EED is well constrained in each state. The value of n is in the range of 2.5–3.8, which is larger than that expected by the classic non-relativistic shock acceleration. However, the large value of n can be explained by the relativistic oblique shock acceleration. The flaring activity seems to be related to an increased acceleration efficiency, reflected in an increased $\gamma ^{\prime }_{\rm min}$ and electron injection power.

Hydrodynamic computational modelling and simulations of collisional shock waves in gas jet targets

We study the optimization of collisionless shock acceleration of ions based on hydrodynamic modelling and simulations of collisional shock waves in gaseous targets. The models correspond to the specifications required for experiments with the $\text{CO}_{2}$ laser at the Accelerator Test Facility at Brookhaven National Laboratory and the Vulcan Petawatt system at Rutherford Appleton Laboratory. In both cases, a laser prepulse is simulated to interact with hydrogen gas jet targets. It is demonstrated that by controlling the pulse energy, the deposition position and the backing pressure, a blast wave suitable for generating nearly monoenergetic ion beams can be formed. Depending on the energy absorbed and the deposition position, an optimal temporal window can be determined for the acceleration considering both the necessary overdense state of plasma and the required short scale lengths for monoenergetic ion beam production.

Simulation of Accelerated Particle Diffusion in Collisionless Shocks with an Admixture of Heavier-than-Hydrogen Ions

We report on the results of hybrid simulation of diffusive shock acceleration of ions with different charge-to-mass ratios in quasi-parallel collisionless shocks. We consider a hydrogen medium with dynamically insignificant admixtures of helium and carbon ions in various charge states. Spatial regions of applicability of the Bohm approximation as well as the quasi-linear diffusion theory are determined. The possibility of nondiffusive propagation in regions far ahead of the shock is considered.

Features of an explosive lower extremities injury protected by sapper shoes

The purpose of the work is to conduct experimental studies that reveal the characteristic features of explosive injuries of the lower extremities using various samples of sapper protective shoes of domestic and foreign production. The subjects of experiment were the amputated by medical reasons lower extremities of a person. The severity of explosive damage during contact blasting and the parameters of shock accelerations acting on the lower extremities, as well as approximate periods of disability and the forecast of possible disability, are determined. The results of the study can serve as initial data when testing safety shoes. In addition, using the proposed modeling technique, it is possible to compare the protective properties of various samples of anti-mine shoes, assess the presence (or absence) of signs of aggravation of damage during an anti-personnel mine detonation, and carry out a forensic medical assessment of an explosive injury.

Hysteresis and stop-and-go waves in traffic flows

Stop-and-go waves, also called phantom jams, are often observed in real traffic flows but can be produced neither by the classical Lighthill–Whitham–Richards (LWR) model nor by its known variants. To capture stop-and-go waves, we add hysteresis to the LWR model. For the model we propose, all possible viscous waves are found, and necessary and sufficient conditions for their existence are provided. In particular, deceleration and acceleration shocks appear; the latter were never rigorously defined before, in spite of the fact that they were observed in real traffic flows. Stop-and-go waves can be constructed by a pair of deceleration and acceleration shocks that completes a hysteresis cycle, illustrating how hysteresis loops lead to stop-and-go waves. In contrast, in the phase region where anticipation (i.e. negative hysteresis) loops exist, stop-and-go waves are not present, and speed variations decay. Riemann solutions are then found for all possible Riemann data. We explicitly show that, in the phase region where hysteresis loops exist, a sufficient deviation in speed of a few vehicles in an otherwise uniform car platoon can generate stop-and-go waves, confirming observations of real traffic experiments.

DHybridR: A Hybrid Particle-in-cell Code Including Relativistic Ion Dynamics

Abstract We present the first plasma simulations obtained with the code dHybridR, a hybrid particle-in-cell code with fluid electrons and both thermal and energetic ions that retain relativistic dynamics. dHybridR is constructed to study astrophysical and space-physics problems where a few energetic nonthermal particles (i.e., cosmic rays, CRs) affect the overall dynamics of a nonrelativistic plasma, such as CR-driven instabilities, collisionless shocks, magnetic reconnection, turbulence, etc. In this method paper we provide some applications to linear (resonant/nonresonant CR streaming instability) and strongly nonlinear (parallel shocks) problems that show the capabilities of the code. In particular, we provide the first self-consistent hybrid runs that show the acceleration of relativistic ions at nonrelativistic shocks; CRs develop a power law in momentum, which translates into a broken power law in energy that exhibits a steepening around the ion rest mass, as predicted by the theory of diffusive shock acceleration. We present examples of 2D dHybridR runs relevant for fast shocks in radio supernovae, whose evolution can be followed in real time, and 3D runs of low-Mach-number heliospheric shocks, which can be compared with in situ spacecraft observations.

Multi-wavelength Variability Signatures of Relativistic Shocks in Blazar Jets

Abstract Mildly relativistic shocks that are embedded in colliding magnetohydrodynamic flows are prime sites for relativistic particle acceleration and the production of strongly variable, polarized multi-wavelength emission from relativistic jet sources such as blazars and gamma-ray bursts. The principal energization mechanisms at these shocks are diffusive shock acceleration and shock drift acceleration. In recent work, we had self-consistently coupled shock acceleration and radiation transfer simulations in blazar jets in a basic one-zone scenario. These one-zone models revealed that the observed spectral energy distributions (SEDs) of blazars strongly constrain the nature of the hydromagnetic turbulence in the shock layer. In this paper, we expand our previous work by including full time dependence and treating two zones, one being the site of acceleration and the other a larger emission zone. This construction is applied to multi-wavelength flares of the flat-spectrum radio quasar (FSRQ) 3C 279, fitting snapshot SEDs and generating light curves that are consistent with observed variability timescales. We also present a generic study for the typical flaring behavior of the BL Lac object Mrk 501. The model predicts correlated variability across all wavebands, but cross-band time lags depending on the type of blazar (FSRQ versus BL Lac), as well as distinctive spectral hysteresis patterns in all wavelength bands, from millimeter radio waves to gamma-rays. These evolutionary signatures serve to provide diagnostics on the competition between acceleration and radiative cooling.

The Origin of Cosmic Rays: How Their Composition Defines Their Sources and Sites and the Processes of Their Mixing, Injection, and Acceleration

Galactic cosmic-ray source compositions, (Z/H)GCRS from H to Pb and ~10^8 - 10^14 eV, differ from solar-local interstellar, (Z/H)SS or (Z/H)ISM by ~20-200x. Both are mostly just mixes of core collapse (CCSN) and thermonuclear (SN Ia) supernova ejecta. The (Z/H)ISM come from steady unbiased accumulation over Gyrs. But the cosmic ray mass mixing ratio, universal ISM/CCSN ~4:1 of swept-up ISM and ~10x metallicity ejecta show that (Z/H)GCRS come from basic Sedov-Taylor bulk mixing of homologous, expanding CCSN in their OB cluster self-generated superbubbles, further enriched by highly biased grain-sputtering injection during diffusive shock acceleration (DSA). Moreover, this mixing ratio now reveals that the cosmic rays are primarily accelerated as their evolving reverse shock radius and energy passes through their maxima. Refractories and volatiles, first deposited in fast ejecta and ISM grains in freely expanding ejecta, are simultaneously Coulomb-sputtered FCS by turbulent H and He as suprathermal ions into DSA that carries them to cosmic-ray energies. This bulk mixing selectively increases source mix abundancies (Z/H)SM / (Z/H)SS by ~2-10; and injection by grain condensation and implantation fractions FGC, by another ~6, while Z^0.67 Coulomb grain sputtering enrichments FCS give an added ~4-20. Applying these basic processes of mixing and injection to solar system (Z/H)SS produces grain-injected, source-mix (Z/H)SMGI that match major cosmic ray abundances (Z/H)GCRS to within 35 % with no free parameters. Independently confirming grain injection, (Z/H)GCRS shows no detectable contribution of Fe from SN Ia, although producing ~1/2 Fe in ISM, but there is also no dust in SN Ia remnants, unlike CCSN.

A pressure- or velocity-dependent acceleration rate law for the shock-to-detonation transition process in PBX 9502 high explosive

Shock-to-detonation transition profiles of PBX 9502 explosive are analyzed to develop a rate law for shock acceleration. The shock motion profiles are seen to follow a common trend in the shock acceleration–velocity frame, aside from an early time transient that is dependent on the initiating shock strength. The duration of the early time transient is seen to correlate with the initial shock strength. The common shock acceleration profile is seen to be Arrhenius-like with respect to the local particle velocity or pressure. A dual-rate pressure-dependent Arrhenius-type rate law is developed with the duration of the early rate set by the initial shock strength. The rate law is able to predict the shock motion for all tests well in both particle velocity and pressure space. In addition to directly measuring commonalities in the acceleration profiles of the experimental shock motion, this work provides insight into the functional form of the reaction rate laws for this TATB-based high explosive. The rate law also supports the concept that shock-driven reaction in heterogenous high explosives is driven by localized ignition and growth of hotspots.

Early acceleration of electrons and protons at the nonrelativistic quasiparallel shocks with different obliquity angles

The early acceleration of protons and electrons in the nonrelativistic collisionless shocks with three obliquities are investigated through 1D particle-in-cell simulations. In the simulations, the charged particles possessing a velocity of 0.2 c flow towards a reflecting boundary, and the shocks with a sonic Mach number of 13.4 and an Alfven Mach number of 16.5 in the downstream shock frame are generated. In these quasi-parallel shocks with the obliquity angles θ = 15°, 30° and 45°, some of the protons and the electrons can be injected into the acceleration processes, and their downstream spectra in the momentum space show a power law tail at a time of , where ωpe is the electron plasma frequency. Moreover, the charged particles reflected at the shock excite magnetic waves upstream of the shock. The shock drift acceleration is more prominent with a larger obliquity angle for the shocks, but the accelerated particles diffuse parallel to the shock propagation direction more easily to participate in the diffusive shock acceleration. In the early acceleration stage, more energetic protons and electrons appear in the downstream of the shock for θ = 15° compared with the other two obliquities. Moreover, in the upstream region, the spectrum of the accelerated electrons is the hardest for θnB = 45° among the three obliquities, whereas the proton spectra for θnB = 15° and 45° are similar as a result of the competition of the effectiveness of the shock drift acceleration and the diffusive shock acceleration.

Improvement of proton acceleration via collisionless shock acceleration by laser-foil interaction with an external magnetic field

Effects of the external intense axial magnetic field on collisionless shock acceleration (CSA) are investigated by using two-dimensional particle-in-cell simulations. Proton beams accelerated by CSA show different properties when left-hand circularly polarized (LHCP) or right-hand circularly polarized (RHCP) lasers are individually applied to a foil target with or without the magnetic field. It can be attributed to the difference of the dispersion relationship for the laser propagating in a plasma. Protons achieve more efficient acceleration when magnetized plasma is irradiated by the RHCP laser compared with the LHCP laser. Furthermore, the effect of different amplitudes of the magnetic field is studied numerically. It shows that the induced electrostatic charge-separation field arises deep in the target with huge strength of the magnetic field. Protons in the upstream are accelerated before the shock arrives, leading to less efficient acceleration. As a result, an appropriate magnetic field should be applied to enhance the CSA regime.