Shock Acceleration Research Articles

An Analytical Treatment for Particle Acceleration at Shocks inside Coronal Mass Ejections near 1 au

Abstract We present an analytical treatment for time-dependent diffusive shock acceleration at shocks inside magnetic clouds (MCs) observed near 1 au. The model includes the effects of (i) spatial diffusion of test particles upstream and downstream of the shock, (ii) proton advection with the plasma inside MCs, (iii) a reflecting boundary at distance L upstream of the shock to mimic the boundary of the MCs, and (iv) particle leakage out of the system at a constant rate, possibly through open field lines introduced by magnetic reconnection between the closed field lines of the MC and open field lines in the corona or heliosphere. The analysis reveals that the mean time for accelerating particles from p 0 to p is naturally reduced if the MC characteristic length is much smaller than the spatial diffusion length of energetic protons upstream of the shock. However, because most shocks inside MCs observed at 1 au are located in the back half of the MC, the time that the shock has propagated into the MCs is not sufficient to cause significant SEP enhancement—even with a reflecting boundary—if particles are only injected from the low-beta plasma inside MCs. To cause large SEP enhancements inside the shock–MC structure, magnetic reconnection at the back MC is essential to allow particles energized by the shock prior to its interaction with the MC to enter the MC. These particles consequently become the seed energetic protons that are reaccelerated at the shock inside MC.

X-Ray through Very High Energy Intrabinary Shock Emission from Black Widows and Redbacks

Abstract Black widow and redback systems are compact binaries in which a millisecond pulsar heats and may even ablate its low-mass companion by its intense wind of relativistic particles and radiation. In such systems, an intrabinary shock can form as a site of particle acceleration and associated nonthermal emission. We model the X-ray and gamma-ray synchrotron and inverse Compton spectral components for select spider binaries, including diffusion, convection, and radiative energy losses in an axially symmetric, steady-state approach. Our new multizone code simultaneously yields energy-dependent light curves and orbital-phase-resolved spectra. Using parameter studies and matching the observed X-ray spectra and light curves, as well as Fermi Large Area Telescope spectra where available, with a synchrotron component, we can constrain certain model parameters. For PSR J1723–2837 these are notably the magnetic field and bulk flow speed of plasma moving along the shock tangent, the shock acceleration efficiency, and the multiplicity and spectrum of pairs accelerated by the pulsar. This affords a more robust prediction of the expected high-energy and very high energy gamma-ray flux. We find that nearby pulsars with hot or flaring companions may be promising targets for the future Cerenkov Telescope Array. Moreover, many spiders are likely to be of significant interest to future MeV-band missions such as AMEGO and e-ASTROGAM.

Diffusive acceleration in relativistic shocks: particle feedback

ABSTRACT The spectral index s of high-energy particles diffusively accelerated in a non-magnetized relativistic shock, such as in a γ-ray burst afterglow, depends on the unknown angular diffusion function $\mathcal {D}$, which itself depends on the particle distribution function f if acceleration is efficient. We develop a relaxation code to compute s and f for an arbitrary functional $\mathcal {D}$ that depends on f. A local $\mathcal {D}(f)$ dependence is motivated and shown, when rising (falling) upstream, to soften (harden) s with respect to the isotropic case, shift the angular distribution towards upstream (downstream) directions, and strengthen (weaken) the particle confinement to the shock; an opposite effect on s is found downstream. However, variations in s remain modest even when $\mathcal {D}$ is a strong function of f, so the standard, isotropic-diffusion results remain approximately applicable unless $\mathcal {D}$ is both highly anisotropic and not a local function of f. A mild, ∼0.1 softening of s, in both 2D and 3D, when $\mathcal {D}(f)$ rises sufficiently fast, may be realized in ab initio simulations.

High-energy Neutrinos and Gamma Rays from Nonrelativistic Shock-powered Transients

Abstract Shock interaction has been argued to play a role in powering a range of optical transients, including supernovae, classical novae, stellar mergers, tidal disruption events, and fast blue optical transients. These same shocks can accelerate relativistic ions, generating high-energy neutrino and gamma-ray emission via hadronic pion production. The recent discovery of time-correlated optical and gamma-ray emission in classical novae has revealed the important role of radiative shocks in powering these events, enabling an unprecedented view of the properties of ion acceleration, including its efficiency and energy spectrum, under similar physical conditions to shocks in extragalactic transients. Here we introduce a model for connecting the radiated optical fluence of nonrelativistic transients to their maximal neutrino and gamma-ray fluence. We apply this technique to a wide range of extragalactic transient classes in order to place limits on their contributions to the cosmological high-energy gamma-ray and neutrino backgrounds. Based on a simple model for diffusive shock acceleration at radiative shocks, calibrated to novae, we demonstrate that several of the most luminous transients can accelerate protons up to 1016 eV, sufficient to contribute to the IceCube astrophysical background. Furthermore, several of the considered sources—particularly hydrogen-poor supernovae—may serve as “gamma-ray-hidden” neutrino sources owing to the high gamma-ray opacity of their ejecta, evading constraints imposed by the nonblazar Fermi Large Area Telescope background. However, adopting an ion acceleration efficiency of ∼0.3%–1% motivated by nova observations, we find that currently known classes of nonrelativistic, potentially shock-powered transients contribute at most a few percent of the total IceCube background.

Performance Analysis of Absolute Acceleration Shock Response Spectrum

The Absolute Acceleration Shock Response Spectrum (AASRS), which is most commonly used in engineering is analyzed in detail, and the effects of shock duration, shock amplitude and shock waveform on AASRS are discussed respectively. Shock duration has the greatest influence on the shape and change trend of AASRS, followed by shock amplitude. However, shock amplitude only affects the amplitude of AASRS and does not change the overall change trend. Shock waveform has the smallest influence on AASRS and mainly affects the frequency point of peak acceleration.

Acceleration Signal Processing Method of Impact Response of Floating Shock Platform Based on Rigid Body Motion Model

Floating shock platform is generally used to test the antishock performance of large shipboard equipment. Shock acceleration signal will produce zero-shift phenomenon in the test measurement process, which will affect the subsequent shock response spectrum analysis. In this paper, a method of shock acceleration signal processing based on rigid body motion revision model is established. The rigid body motion revision model adopts the theory of ship’s seakeeping based on the hypothesis of KrylovFroude, in which the shock wave load of underwater explosion adopts the empirical formula. The bubble pulsation load adopts the GeersHunter spherical bubble model. The empirical mode decomposition method is used to eliminate the trend term of the low-frequency part of the acceleration signal, and the frequency filtering technology is used to eliminate the noise of the high frequency part. The response estimated by the rigid body motion model is used to modify the measured signal. The modified signal is analyzed by shock response spectrum to get the round design spectrum. The validity of the signal is determined by the Pauta criterion. Finally, the shock environment statistics of the whole platform is given. This method can eliminate the low-frequency trend term and high frequency noise and has good robustness. It can be applied to many kinds of signals. This method can provide technical support for antishock performance of shipboard equipment and also applied to other shock signal processing fields.

On the Size of the Flare Associated with the Solar Proton Event in 774 AD

Abstract The 774 AD solar proton event (SPE) detected in cosmogenic nuclides had an inferred >1 GV (>430 MeV) fluence estimated to have been ∼30–70 times larger than that of the 1956 February 23 ground level event (GLE). The 1956 GLE was itself ∼2.5 times larger at >430 MeV than the episode of strong GLE activity from 1989 August–October. We use an inferred soft X-ray (SXR) class of X20 ± 10 for the 1956 February 23 eruptive flare as a bridge to the source flare for the 774 SPE. A correlation of the >200 MeV proton fluences of hard-spectra post-1975 GLEs with the SXR peak fluxes of their associated flares yields an SXR flare class of X285 ± 140 (bolometric energy of ∼(1.9 ± 0.7) × 1033 erg) for the 774 flare. This estimate is within theoretical determinations of the largest flare the Sun could produce based on the largest spot group yet observed. Assuming a single eruptive flare source for the 774 SPE, the above estimate indicates that the Sun can produce a threshold-level 1033 erg superflare. If the 774 event originated in two closely timed, equal-fluence SPEs, the inferred flare size drops to X180 ± 90 (∼(1.4 ± 0.5) × 1033 erg). We speculate on favorable solar conditions that can lead to enhanced shock acceleration of high-energy protons in eruptive flares.

Electrostatic shock acceleration of ions in near-critical-density plasma driven by a femtosecond petawatt laser

With the recent advances in ultrahigh intensity lasers, exotic astrophysical phenomena can be investigated in laboratory environments. Collisionless shock in a plasma, prevalent in astrophysical events, is produced when a strong electric or electromagnetic force induces a shock structure in a time scale shorter than the collision time of charged particles. A near-critical-density (NCD) plasma, generated with an intense femtosecond laser, can be utilized to excite a collisionless shock due to its efficient and rapid energy absorption. We present electrostatic shock acceleration (ESA) in experiments performed with a high-density helium gas jet, containing a small fraction of hydrogen, irradiated with a 30 fs, petawatt laser. The onset of ESA exhibited a strong dependence on plasma density, consistent with the result of particle-in-cell simulations on relativistic plasma dynamics. The mass-dependent ESA in the NCD plasma, confirmed by the preferential reflection of only protons with two times the shock velocity, opens a new possibility of selective acceleration of ions by electrostatic shock.

An LSTM-based severity evaluation method for intermittent open faults of an electrical connector under a shock test

The intermittent open fault is the major fault mode in an electrical connector. Therefore, it is necessary to evaluate the severity of intermittent open faults accurately, which would effectively reduce maintenance cost and enhance the useful life. This paper proposes a severity evaluation method based on a Long Short Term Memory (LSTM) network to effectively evaluate the internal looseness degree and the shock acceleration separately. Firstly, a linear model based on the resistance Root Mean Square (RMS) and shock acceleration is constructed. Then the internal looseness feature independent of external shock is extracted. Secondly, the LSTM is used to strengthen the mining of the shape characteristics and evaluate the intermittent open fault severity accurately, whose input is the frequency-domain data of the contact resistance waveform. Results of the comparison verify that the proposed evaluation method not only reduces the number of calculations required, but also improves the severity evaluation accuracy.

Morphology of radio relics – I. What causes the substructure of synchrotron emission?

ABSTRACT High-resolution radio observations of cluster radio relics often show complex spatial and spectral features. However, it is not clear what these features reveal about the underlying magnetic field properties. We performed three-dimensional magnetohydrodynamical simulations of merger shock waves propagating through a magnetized, turbulent intracluster medium. Our model includes the diffusive shock acceleration (DSA) of cosmic ray electrons, their spatial advection and energy losses at run-time. With this set-up we can investigate the relation between radio substructure and pre-shock plasma conditions in the host cluster. We find that upstream turbulence plays a major role in shaping the properties of radio relics produced downstream. Within the assumption of DSA, we can reproduce the observed discrepancy between the X-ray derived Mach number of shocks, and the Mach number inferred from radio spectra. Our simulated spectral index maps and profiles across the radio relic also suggest that the standard deviation of the upstream magnetic field must be relatively small ($\sigma _B\le 1 \, \mu$G) in order to reproduce observations and therefore radio relics can potentially constrain the distribution of magnetic fields in galaxy clusters outskirts.

Evolution and observational signatures of the cosmic ray electron spectrum in SN 1006

ABSTRACT Supernova remnants (SNRs) are believed to be the source of Galactic cosmic rays (CRs). SNR shocks accelerate CR protons and electrons which reveal key insights into the non-thermal physics by means of their synchrotron and γ-ray emission. The remnant SN 1006 is an ideal particle acceleration laboratory because it is observed across all electromagnetic wavelengths from radio to γ-rays. We perform 3D magnetohydrodynamics (MHD) simulations where we include CR protons and follow the CR electron spectrum. By matching the observed morphology and non-thermal spectrum of SN 1006 in radio, X-rays, and γ-rays, we gain new insight into CR electron acceleration and magnetic field amplification. (1) We show that a mixed leptonic–hadronic model is responsible for the γ-ray radiation: while leptonic inverse-Compton emission and hadronic pion-decay emission contribute equally at GeV energies observed by Fermi, TeV energies observed by imaging air Cherenkov telescopes are hadronically dominated. (2) We show that quasi-parallel acceleration (i.e. when the shock propagates at a narrow angle to the upstream magnetic field) is preferred for CR electrons and that the electron acceleration efficiency of radio-emitting GeV electrons at quasi-perpendicular shocks is suppressed at least by a factor ten. This precludes extrapolation of current 1D plasma particle-in-cell simulations of shock acceleration to realistic SNR conditions. (3) To match the radial emission profiles and the γ-ray spectrum, we require a volume-filling, turbulently amplified magnetic field and that the Bell-amplified magnetic field is damped in the immediate post-shock region. Our work connects microscale plasma physics simulations to the scale of SNRs.

A perfect power-law spectrum even at the highest frequencies: The Toothbrush relic

Radio relics trace shock fronts generated in the intracluster medium (ICM) during cluster mergers. The particle acceleration mechanism at the shock fronts is not yet completely understood. We observed the Toothbrush relic with the Effelsberg and Sardinia Radio Telescope at 14.25 GHz and 18.6 GHz, respectively. Unlike previously claimed, the integrated spectrum of the relic closely follows a power law over almost three orders of magnitude in frequency, with a spectral index ofα58 MHz18.6 GHz= −1.16 ± 0.03. Our finding is consistent with a power-law injection spectrum, as predicted by diffusive shock acceleration theory. The result suggests that there is only little magnetic field strength evolution downstream of the shock. From the lack of spectral steepening, we find that either the Sunyaev–Zeldovich decrement produced by the pressure jump is less extended than ∼600 kpc along the line of sight or, conversely, that the relic is located far behind in the cluster. For the first time, we detect linearly polarized emission from the “brush” at 18.6 GHz. Compared to 8.3 GHz, the degree of polarization across the brush increases at 18.6 GHz, suggesting a strong Faraday depolarization toward lower frequencies. The observed depolarization is consistent with an intervening magnetized screen that arises from the dense ICM containing turbulent magnetic fields. The depolarization, corresponding to a standard deviation of the rotation measures as high asσRM = 212 ± 23 rad m−2, suggests that the brush is located in or behind the ICM. Our findings indicate that the Toothbrush relic can be consistently explained by the standard scenario for relic formation.

Electron energization in quasi-parallel shocks

Context. In situ observations of energetic particles at the Earth’s bow-shock that are attainable by the satellite missions have fostered the opinion for a long time that electrons are most efficiently accelerated in a quasi-perpendicular shock geometry. However, shocks that are deemed to be responsible for the production of cosmic ray electrons and their radiation from sources such as supernova remnants are much more powerful and larger than the Earth’s bow-shock. Their remote observations and also in situ measurements at Saturn’s bow shock, that is, the strongest shock in the Solar System, suggest that electrons are accelerated very efficiently in the quasi-parallel shocks as well. Aims. In this paper we investigate the possibility that protons that are accelerated to high energies create sufficient wave turbulence, which is necessary for the electron preheating and subsequent injection into the diffusive shock acceleration in a quasi-parallel shock geometry. Methods. An additional test-particle-electron population, which is meant to be a low-density addition to the electron core-distribution on which the hybrid simulation operates, is introduced. Our purpose is to investigate how these electrons are energized by the “hybrid” electromagnetic field. The reduced spatial dimensionality allowed us to dramatically increase the number of macro-ions per numerical cell and achieve the converged results for the velocity distributions of test electrons. Results. We discuss the electron preheating mechanisms, which can make a significant part of thermal electrons accessible to the ion-driven waves observed in hybrid simulations. We find that the precursor wave field supplied by ions has a considerable potential to preheat the electrons before they are shocked at the subshock. Our results indicate that a downstream thermal equilibration of the hot test electrons and protons does not occur. Instead, the resulting electron-to-proton temperature ratio is a decreasing function of the shock Mach number, MA, which has a tendency for a saturation at high MA.

Magnetospheric Multiscale Observations of Foreshock Transients at Their Very Early Stage

Abstract Foreshock transients are ion kinetic structures in the ion foreshock. Due to their dynamic pressure perturbations, they can disturb the bow shock and magnetosphere–ionosphere system. They can also accelerate particles contributing to shock acceleration. However, it is still unclear how exactly they form. Recent particle-in-cell simulations point out the important role of the electric field and Hall current in the formation process. To further examine this, we use data from the Magnetospheric Multiscale (MMS) mission to apply case studies on two small (1000–2000 km) foreshock transient events that just started to form. In event 1 where MMS was in a tetrahedral formation, we show that the current density configuration, which determined the magnetic field profile, was mainly driven by Hall currents generated by demagnetized foreshock ions. The resulting time variation of the magnetic field induced an electric field that drove cold plasma moving outward with magnetic field lines. In event 2 where MMS was in a string-of-pearls formation, we analyze the evolution of field and plasma parameters. We show that the magnetic flux and mass flux were transported outward from the core, resulting in the steepening of the boundary. The steepened boundary, which trapped more foreshock ions and caused stronger demagnetization of foreshock ions, nonlinearly further enhanced the Hall current. Based on our observations, we propose a physical formation process wherein the positive feedback of foreshock ions on the varying magnetic field caused by the foreshock ion Hall current enables an “instability” and the growth of the structure.

The application of the adiabatic compression scenario to the radio relic in the galaxy cluster Abell 3411−3412

ABSTRACT Although radio relics are understood to originate in intracluster shock waves resulting from merger shocks, the most widely used model for describing this (re-)acceleration process at shock fronts, the diffusive shock acceleration (DSA) model, has several challenges, including the fact that it is inefficient at low shock Mach numbers. In light of these challenges, it is worthwhile to consider alternative mechanisms. One possibility is the adiabatic compression by a shock wave of a residual fossil electron population which has been left over from a radio galaxy jet. This paper applies this model to the relic hosted in the merging galaxy cluster Abell 3411−3412, where a radio bridge between the relic and a radio galaxy has been observed, with the aim to reproduce the spatial structure of the spectral index of the relic. Four scenarios are presented, in which different effects are investigated, such as effects behind the shock front and different shock strengths. The results show that the adiabatic compression model can reproduce the observed spectral indices across the relic for a shock Mach number that is lower than the value required by the DSA-type modelling of this relic and is in accordance with the values derived from X-ray observations, if other mechanisms, such as an expansion phase or post-shock turbulence, are effective behind the shock front.

Transportation Monitoring of Geo-Location, Speed, Vibration, and Shock Acceleration for 110-kV Vehicular Mobile Transformers

As a kind of transformer installed on vehicles, the vehicular mobile transformer needs to realize frequent transportation quickly and safely. However, there are few studies on the on-line monitoring of vehicular mobile transformers. In this article, a transportation condition monitoring system for vehicular mobile transformers is introduced and developed. The transportation process of a 110-kV/40-MVA vehicular mobile transformer is monitored from Jiangsu Province to Guangdong Province, which is recognized as the first time that the transformer is monitored for more than 12 h and more than 1000-km transportation. The geo-location, driving speed, vibration, and shock acceleration in six different road sections are obtained in real-time. The results show that the vibration and shock acceleration has a strong positive correlation with the driving speed. The amplitude of the $y$ -axis acceleration is generally the lowest among three-axis accelerations, and the three-axis vibration and shock acceleration has the same trend of increase and decrease. During the whole transportation process, the driving speed of the 110-kV/40-MVA vehicular mobile transformer varies from 0 to 76 km/h, and the vibration and shock acceleration amplitudes obtained by the monitoring system do not exceed 1 g, which has great significance to the safe operation of power grid and can provide the strong evidence of online monitoring data to set transportation guidelines for vehicular mobile transformers.

Blast-induced ground motion effect on dynamic response of a cylindrical vertical water tank with piled raft foundation

This paper studies to estimate the dynamic behavior of a demineralized water tank with a piled raft foundation system considering soil-pile-structure-fluid interaction to shock-ground motion. A three-dimensional finite element model of a coupled system is constituted in ANSYS software. Interaction between pile and soil is represented with the frictional contact element. The frictionless contact elements are utilized to model between the water and tank shell to allow for displacement of the free surface adjacent to the tank wall. Shell elements are used for the tank body and its vault. The dynamic analyses of the tank including soil-pile-structure-fluid interaction are presented by using shock response spectra. Ground shock acceleration time histories, generated by using a developed computer program based on Fortran programming language, produce shock response spectra. The effects of the different charge weights and distances from the charge center are examined in the analyses. Also, the effect of the water fill level in the tank and the number of piles is also investigated. The results of the research are presented with the directional displacements and equivalent stresses. It seen from the analyses that the dynamic responses of the tank increase with the charge weight, while decreasing with the charge center distance. Moreover, the water fill level and the number of piles extremely affect the displacement and stress values of the coupled interaction system.

Solar Longitude Distribution of High-energy Proton Flares: Fluences and Spectra

Abstract The distribution of the longitudes of solar flares associated with the high-energy proton events called ground level events (GLEs) can be approximated by a Gaussian with a peak at ∼W60, with a full range from ∼E90 to ∼W150. The longitudes of flares associated with the top third (24 of 72) of GLEs in terms of their >430 MeV fluences (F 430) are primarily distributed over E20–W100 with a skew toward disk center. This 120° span in longitude is comparable to the latitudinal spans of powerful coronal mass ejections (CMEs) from limb flares. Only 5 of 24 strong GLEs are located within the W40–80 zone of good magnetic connection to Earth. GLEs with hard spectra, i.e., a spectral index SI30/200(= log(F 30/F 200)) < 1.5, also tend to avoid W40–80 source regions. Three-fourths of such events (16 of 21) arise in flares outside this range. The above tendencies favor a CME-driven shock source over a flare-resident acceleration process for high-energy solar protons. GLE spectra show a trend, with broad scatter, from hard spectra for events originating in eruptive flares beyond the west limb to soft spectra for GLEs with sources near central meridian. This behavior can be explained in terms of: (1) dominant near-Sun quasi-perpendicular shock acceleration of protons for far western (>W100) GLEs; (2) quasi-parallel shock acceleration for well-connected (W40–80) GLEs, and (3) proton acceleration/trapping at CME-driven bow shocks from central meridian (E20–W20) that strike the Earth.

Formation of Foreshock Transients and Associated Secondary Shocks

Abstract Upstream of shocks, the foreshock is filled with hot ions. When these ions are concentrated and thermalized around a discontinuity, a diamagnetic cavity bounded by compressional boundaries, referred to as a foreshock transient, forms. Sometimes, the upstream compressional boundary can further steepen into a secondary shock, which has been observed to accelerate particles and contribute to the primary shock acceleration. However, secondary shock formation conditions and processes are not fully understood. Using particle-in-cell simulations, we reveal how secondary shocks are formed. From 1D simulations, we show that electric fields play a critical role in shaping the shock’s magnetic field structure, as well as in coupling the energy of hot ions to that of the shock. We demonstrate that larger thermal speed and concentration ratio of hot ions favor the formation of a secondary shock. From a more realistic 2D simulation, we examine how a discontinuity interacts with foreshock ions leading to the formation of a foreshock transient and a secondary shock. Our results imply that secondary shocks are more likely to occur at primary shocks with higher Mach number. With the secondary shock’s previously proven ability to accelerate particles in cooperation with a planetary bow shock, it is even more appealing to consider them in particle acceleration of high Mach number astrophysical shocks.

Solar Cosmic Ray Acceleration at the Front of a Fast Shock in the Lower Solar Corona

Based on the theory of diffusive shock acceleration of charged particles, we have numerically studied the spectra of protons produced by a fast shock with a speed of 5000 km s–1 in the lower solar corona with known solar plasma parameters. We show that protons with energies $$ \gtrsim $$ 105 MeV can be produced at a distance up to 3 $${{R}_{ \odot }}$$ ( $${{R}_{ \odot }}$$ is the solar radius) within 274 s.