Shock Acceleration Research Articles

Electron Acceleration in Magnetic Islands in Quasi-parallel Shocks

We report new theories and simulations for electron acceleration in magnetic islands generated by magnetic reconnection in the shock turbulence in a quasi-parallel shock, using a 2 and 1/2 dimensional particle-in-cell simulation. When an island is moving, unmagnetized electrons are accelerated by the Hall electric field pointing toward the island center. In a stationary island, some electrons are energized by “island betatron acceleration” due to the induction electric field when the island core magnetic field changes with time. In the simulation, almost all of the high-energy electrons in the shock transition region that show a power-law distribution are accelerated in ion-skin-depth-scale magnetic flux ropes, and about half of them are accelerated by the Hall electric field and island betatron acceleration. These mechanisms can produce a power-law electron distribution, and also inject electrons into the diffusive shock acceleration. The mechanisms are applicable to quasi-parallel shocks with high Alfvén Mach numbers (M A > 10), including planetary bow shocks and shocks in astrophysical objects such as supernova remnants.

Design and shock isolation performances of two-layered ring-spring meta-isolation systems

Two-layered ring-spring-resonator (RSR) based meta-isolation system (RSR-M) has been developed to improve shock isolation effect. In the numerical calculations, shock acceleration ratio (SAR), shock displacement ratio (SDR) and relative displacement ratio (RDR) were introduced to evaluate the shock isolation performances of the conventional isolation system (CON) and the RSR-M, considering the effects of the excitation amplitude, the weight of the middle mass block and the stiffness of the lower isolators. The results demonstrate that the SAR of the RSR-M is always smaller than that of the CON, and the SDR of the RSR-M is first larger than that of CON in the shock amplification region and then smaller in the isolation region. The weight of middle mass blocks has little influence on the isolation performance of the RSR-M because of the softening behavior of the isolators. Finally, shock isolation experiments were also carried out to measure the damping ratios of the selected wire rope isolators and further analyze the isolation performance of the RSR-Ms. In general, meta-isolation system provides a new reference and idea for the design of the isolation system of engineering structures in some sense.

Investigation on the Effect of Energy Release Rate of Aluminized Explosive on the Damage of Underwater Targets

AbstractAs a type of high‐energy explosive, aluminized explosives are extensively used in underwater weapons and ammunition. This study aims to investigate the energy release rate on the damage of underwater targets caused by aluminized explosives (RDX/Al). The ship was selected as a target, and numerical simulations were conducted using AUTODYN software to study the energy release rate corresponding to different particle sizes of aluminum powder (25 nm −300 μm) in the underwater explosion process of RDX/Al, as well as its destructive effect on targets in the water. The research quantitatively evaluates the whole ship′s destruction results, including longitudinal bending deformations and crevasse. In addition, typical cabins were selected in this study to assess the local damage effects by analyzing stress, shock wave pressure, displacement, and acceleration shock response. Based on the damage results, it was revealed that RDX/Al with aluminum powder particle sizes ranging from 54 nm to 145 nm exhibited the most optimal damaging effects on ships after underwater explosions. These findings provide a basis for improving the destructive power of aluminized explosives against underwater targets, simultaneously, they can be utilized by ship designers to guide research and development of improved protective measures, aiming to reduce the vulnerability of ships to explosive attacks.

Probing Magnetic Fields in Young Supernova Remnants with IXPE

Synchrotron emission from the shocked regions in supernova remnants provides, through its polarization, crucial details about the magnetic field strength and orientation in these regions. This, in turn, provides information on particle acceleration in these shocks. Due to the rapid losses of the highest-energy relativistic electrons, X-ray polarization measurements allow for investigations of the magnetic field to be carried outvery close to the sites of particle acceleration. Measurements of both the geometry of the field and the levels of turbulence implied by the observed polarization degree thus provide unique insights into the conditions leading to efficient particle acceleration in fast shocks. The Imaging X-ray Polarimetry Explorer (IXPE) has carried out observations of multiple young SNRs, including Cas A, Tycho, SN 1006, and RX J1713.7−3946. In each, significant X-ray polarization detections provide measurements of magnetic field properties that show some common behavior but also considerable differences between these SNRs. Here, we provide a summary of results from IXPE studies of young SNRs, providing comparisons between the observed polarization and the physical properties of the remnants and their environments.

Electron scattering on small-scale electrostatic fields in the shock front

Electron heating and acceleration in collisionless shocks is a long-standing problem. Rapid isotropization of heated electrons cannot be explained solely by the cross-shock potential. In addition, the macroscopic cross-shock potential prevents efficient reflection and injection into the diffusive acceleration regime. Recent observations have shown that small-scale electric fields are present in the shock front, together with the large-scale cross-shock potential. These small-scale fields have been found also in the upstream and downstream regions. Electron heating in shocks is produced by the combined action of the large- and small-scale fields. The large-scale potential determines the energy transferred to the electrons. The small-scale electrostatic fields scatter electrons. Here we study the scattering of electrons on the typical waveforms, namely solitary bipolar spikes and wavepackets. The main effect is the generation of backstreaming electrons with large pitch angles. It is found that wavepackets are more efficient in electron reflection in the interaction of electrons both with a single spike and with multiple spikes.

Energetic seed particles in self-consistent particle acceleration modeling at interplanetary shock waves

Aims. The study investigates the relevance of the seed particle population in the results of particle acceleration in interplanetary shock waves, when wave–particle interactions are treated self-consistently. Methods. We employed the SOLar Particle Acceleration in Coronal Shocks (SOLPACS) model, which is a proton acceleration simulation in shocks with self-consistent nonlinear wave–particle interactions. We compared a suprathermal monoenergetic injection with a two-component injection, including the suprathermal monoenergetic component and a broad-spectrum energetic component corresponding to the observed background particle spectrum. Energetic particles in the beginning of the simulation could increase the local wave intensities sufficiently to increase the rate of acceleration for injected particles and even reshape the resulting particle energy spectra and spatial distributions. The resulting particle energy spectra, particle spatial distributions, and wave intensity spectra are compared to observations made by Solar Orbiter’s instrument suite of the 2021 October 30 energetic storm particle (ESP) event to evaluate the relevance of the seed particle population in the acceleration model. Results. The energetic component of the seed particle population shortens the needed acceleration time for particles and enhances the tail of the spectrum to a level that matches the observations. The highest compared energies (> 1 MeV) match only when an energetic component is included in the seed particle population. The wave intensities and spatial distributions, on the other hand, showed no significant differences with the monoenergetic and two-component injection. While the simulated and observed wave intensities match within five minutes before the shock passing, the simulated wave field is too intense farther out from the shock, probably due to a lack of wave damping and/or decay processes in the simulation, leading to particles being slightly overly trapped to regions closer to the shock.

Spectral Properties of Suprathermal Protons Associated with Interplanetary Shocks from WIND/STICS Data

Here are analyzed 3D velocity distribution functions (VDFs) of protons in the suprathermal energy-per-charge (E/Q) domain of 6.2 to 223.1 keV/e, as observed by the WIND Suprathermal Ion Composition Spectrometer (WIND/STICS) between 1995 and 2019, upon passage of interplanetary (IP) shocks. “Suprathermal” designates energies above the bulk, “thermal” solar wind, including inner-source pickup ions, cometary ions, solar energetic particles, and suprathermal tail particles. Within the WIND/STICS measurements, here treated as a standalone data set, only 3D VDFs within 9 hr prior to and following the shock passage are selected, as identified by the Center for Astrophysics (CfA) Harvard Interplanetary Shock Database. These are subsequently averaged, first over the STICS field of view, then over 3 hr intervals in the 9 hr about the shock. The averages, with errors assuming Poisson statistics, are then fitted using the Levenburg–Marquardt nonlinear least squares technique to two simple, observationally suggested functions arising from diffusive shock acceleration (DSA) formalism: a power law in E/Q with spectral index (model I), and a power-law with exponential rollover having a cutoff in E/Q (model II). The first result is a comparison of upstream spectral indices, e-folding energies, and normalization constants with corresponding downstream values. The second is a comparison of fitted spectral indices against those given by measured CfA shock compression ratios and a comparison of fitted e-folding energies with those given by measured ratios and shock normal angles, per DSA-derived predictions. There is additionally a comparison between fitted parameters given by the two functional forms. Little agreement is found with values given by DSA.

Quasi-monoenergetic ion acceleration and neutron generation from laser-driven transverse collisionless shocks

Experiments using the OMEGA EP laser system were performed to study collisionless shock acceleration of ions driven by the interaction of a relativistically intense laser pulse with underdense plasma. The energy spectrum of accelerated ions in the direction transverse to laser propagation is measured to have several narrow-band peaks which are quasi-monoenergetic with a typical energy bandwidth of 3%. In deuterium plasmas, these ions generate a significant number of fast fusion neutrons. Particle-in-cell simulations confirm that these ions were accelerated by the interaction of transverse shocks and that the appearance of quasi-monoenergetic spectral features depends on the growth of an ion-electron two-stream instability during the interaction.

Modeling Multiband SEDs and Light Curves of BL Lacertae Using a Time-dependent Shock-in-jet Model

The origin of fast flux variability in blazars is a long-standing problem, with many theoretical models proposed to explain it. In this study, we focus on BL Lacertae to model its spectral energy distribution (SED) and broadband light curves using a diffusive shock acceleration process involving multiple mildly relativistic shocks, coupled with a time-dependent radiation transfer code. BL Lacertae was the target of a comprehensive multiwavelength monitoring campaign in early 2021 July. We present a detailed investigation of the source’s broadband spectral and light-curve features using simultaneous observations at optical–UV frequencies with the Swift Ultraviolet/Optical Telescope, in X-rays with the Swift X-Ray Telescope and AstroSat-SXT/LAXPC, and in gamma rays with Fermi-LAT, covering the period from 2021 July to August (MJD 59400–59450). A fractional variability analysis shows that the source is most variable in gamma rays, followed by X-rays, UV, and optical. This allowed us to determine the fastest variability time in gamma rays to be on the order of a few hours. The AstroSat-SXT and LAXPC light curves indicate X-ray variability on the order of a few kiloseconds. Modeling simultaneously the SEDs of low- and high-flux states of the source and the multiband light curves provided insights into the particle acceleration mechanisms at play. This is the first instance of a physical model that accurately captures the multiband temporal variability of BL Lacertae, including the hour-scale fluctuations observed during the flare.

Origin of the break in the cosmic-ray electron plus positron spectrum at ∼1 TeV

Recent measurements of the cosmic-ray electron plus positron spectrum in several experiments have confirmed the presence of a break at ∼1 TeV. The origin of the break is still not clearly understood. In this work, we explored different possibilities for the origin, which include an electron source spectrum with a broken power law, a power law with an exponential or super-exponential cutoff, and the absence of potential nearby cosmic-ray sources. Based on the observed electron plus positron data from the DAMPE and the H.E.S.S experiments, and considering supernova remnants as the main sources of cosmic rays in the Galaxy, we find statistical evidence in favor of the scenario with a broken power-law source spectrum, with the best-fit source parameters obtained as Γ = 2.39 for the source spectral index, E0 ≈ 1.6 TeV for the break energy, and f = 1.59 × 1048 ergs for the amount of supernova kinetic energy injected into cosmic-ray electrons. This power-law break in the spectrum has been predicted for electrons confined inside supernova remnants after acceleration via diffusive shock acceleration process, and also indicated by the multi-wavelength study of supernova remnants. All of this evidence shows that the observed spectral break provides a strong indication of a direct link between cosmic-ray electrons and their sources. Our findings further show that electrons must undergo spectral changes while escaping the source region in order to reconcile the difference between the spectral index of electrons observed inside supernova remnants and that obtained from Galactic cosmic-ray propagation studies.

3D hybrid fluid-particle jet simulations and the importance of synchrotron radiative losses

Relativistic jets in active galactic nuclei are known for their exceptional energy output, and imaging the synthetic synchrotron emission of numerical jet simulations is essential for a comparison with observed jet polarization emission. Through the use of 3D hybrid fluid-particle jet simulations (with the PLUTO code), we overcome some of the commonly made assumptions in relativistic magnetohydrodynamic (RMHD) simulations by using non-thermal particle attributes to account for the resulting synchrotron radiation. Polarized radiative transfer and ray-tracing (via the RADMC-3D code) highlight the differences in total intensity maps when (i) the jet is simulated purely with the RMHD approach, (ii) a jet tracer is considered in the RMHD approach, and (iii) a hybrid fluid-particle approach is used. The resulting emission maps were compared to the example of the radio galaxy Centaurus A. We applied the Lagrangian particle module implemented in the latest version of the PLUTO code. This new module contains a state-of-the-art algorithm for modeling diffusive shock acceleration and for accounting for radiative losses in RMHD jet simulations. The module implements the physical postulates missing in RMHD jet simulations by accounting for a cooled ambient medium and strengthening the central jet emission. We find a distinction between the innermost structure of the jet and the back-flowing material by mimicking the radio emission of the Seyfert II radio galaxy Centaurus\,A when considering an edge-brightened jet with an underlying purely toroidal magnetic field. We demonstrate the necessity of synchrotron cooling as well as the improvements gained when directly accounting for non-thermal synchrotron radiation via non-thermal particles.

Spectral cleaving in solar type II radio bursts: Observations and interpretation

Context. Shock waves in the solar corona are associated with solar flares and coronal mass ejections (CMEs). Type II solar bursts are radio signatures of shock waves in the solar corona. They are driven by solar flares or CMEs. Despite extensive studies, the intricate spectral patterns observed in type II solar bursts occasionally pose new challenges for the theory of electron acceleration in shocks. Aims. We study a newly identified feature in type II solar bursts called spectral cleaving. This feature is characterized by the actual branching of a type II radio emission lane in radio spectral data. Methods. We analyzed the type II burst exhibiting spectral cleaving in high-fidelity dynamic spectra obtained using the URAN-2 radio telescope (8.25–33 MHz; Poltava region, Ukraine) on 2011 February 14. The high-resolution spectrograms were examined to ascertain its spectral morphology. Results. Our research represents the first recognition of spectral cleaving as a peculiarity of type II bursts that is yet to be classified. This effect occurs due to the shift (or migration) of radio source(s) along a shock front, which in turn is caused by changes in the magnetic field orientation ahead of the propagating shock front. Conclusions. The spectral cleaving observed in solar type II bursts reveals a distinct phenomenon that indicates complex interactions between shock waves and magnetic fields in the solar corona. This discovery enhances our understanding of the mechanisms behind solar radio emissions and emphasizes the need for further observational studies to verify these findings.

Flat Spectra of Energetic Particles in Interplanetary Shock Precursors

The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extending upstream of the shock for up to seven flux e-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy as ϵ −1, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from those traditionally employed in DSA models. We show that a standard (linear) DSA solution based on a widely accepted diffusive particle transport with an underlying resonant wave–particle interaction is inconsistent with the plateau in the particle flux. To resolve this contradiction, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivity κ on the particle flux F (nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. They lead to the particle diffusivity increasing with the particle energy as ∝ϵ 3/2 that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration.

Kinetic study of shock formation and particle acceleration in laser-driven quasi-parallel magnetized collisionless shocks

Kinetic study of shock formation and particle acceleration in laser-driven quasi-parallel magnetized collisionless shocks

Microphysics of Particle Reflection in Weibel-mediated Shocks

Particle-in-cell (PIC) simulations have shown that relativistic collisionless shocks mediated by the Weibel instability accelerate ∼1% of incoming particles, while the majority are transmitted through the shock and become thermalized. The microphysical processes that determine whether an incoming particle will be transmitted or reflected are poorly understood. We study the microphysics of particle reflection in Weibel-mediated shocks by tracking a shell of test particles in a PIC simulation of a shock in pair plasma. We find that electrons in positron-dominated filaments and positrons in electron-dominated filaments efficiently reflect off of strong magnetic structures at the shock. To participate in diffusive shock acceleration, however, these reflected particles headed toward the upstream must avoid getting advected downstream. This is enabled by incoming filaments, which trap reflected particles carrying the same sign of current as the filaments. The final injection efficiency on the order of ∼1% thus results from the effectiveness of the initial reflection at the shock and the reflected particles’ probability of survival in the upstream postreflection. We develop a model that predicts the fraction of high-energy particles as a function of the properties of Weibel filamentation.

Electron stochastic acceleration in laboratory-produced kinetic turbulent plasmas

The origin of energetic charged particles in universe remains an unresolved issue. Astronomical observations combined with simulations have provided insights into particle acceleration mechanisms, including magnetic reconnection acceleration, shock acceleration, and stochastic acceleration. Recent experiments have also confirmed that electrons can be accelerated through processes such as magnetic reconnection and collisionless shock formation. However, laboratory identifying stochastic acceleration as a feasible mechanism is still a challenge, particularly in the creation of collision-free turbulent plasmas. Here, we present experimental results demonstrating kinetic turbulence with a typical spectrum k−2.9 originating from Weibel instability. Energetic electrons exhibiting a power-law distribution are clearly observed. Simulations further reveal that thermal electrons undergo stochastic acceleration through collisions with multiple magnetic islands-like structures within the turbulent region. This study sheds light on a critical transition period during supernova explosion, where kinetic turbulences originating from Weibel instability emerge prior to collisionless shock formation. Our results suggest that electrons undergo stochastic acceleration during this transition phase.

Impact of the magnetic horizon on the interpretation of the Pierre Auger Observatory spectrum and composition data

The flux of ultra-high energy cosmic rays reaching Earth above the ankle energy (5 EeV) can be described as a mixture of nuclei injected by extragalactic sources with very hard spectra and a low rigidity cutoff.Extragalactic magnetic fields existing between the Earth and the closest sources can affect the observed CR spectrum by reducing the flux of low-rigidity particles reaching Earth. We perform a combined fit of the spectrum and distributions of depth of shower maximum measured with the Pierre Auger Observatory including the effect of this magnetic horizon in the propagation of UHECRs in the intergalactic space.We find that, within a specific range of the various experimental and phenomenological systematics, the magnetic horizon effect can be relevant for turbulent magnetic field strengths in the local neighbourhood in which the closest sources lieof order Brms ≃ (50–100) nG (20 Mpc/ds)( 100 kpc/Lcoh)1/2, with ds the typical intersource separation and Lcoh the magnetic field coherence length. When this is the case,the inferred slope of the source spectrum becomes softer and can be closer to the expectations of diffusive shock acceleration, i.e., ∝ E-2.An additional cosmic-ray population with higher source density and softer spectra, presumably also extragalactic and dominating the cosmic-ray flux at EeV energies, is also required to reproduce the overall spectrum and composition results for all energies down to 0.6 EeV.

Studying the role of supernova remnants as cosmic ray PeVatron with LHAASO observations

It is commonly believed that galactic cosmic rays are produced in supernova remnants (SNRs) and accelerated via a diffusive shock acceleration (DSA) mechanism in supernova blast waves driven by expanding SNRs. The latest theoretical advancement of the diffusive shock acceleration hypothesis in SNRs shows that cosmic rays may be accelerated up to the knee energy of the observed cosmic ray spectrum under the amplified magnetic field scenario. There is, however, no empirical evidence to support SNRs as sources of hadrons with energies larger than a few tens of TeV. Very recently, LHAASO observatory reported the very high-energy gamma ray emission between TeV to PeV energy range from two SNRs, Cassiopeia A and IC 443. Above 25 TeV energies, non-detection of gamma-ray flux by LHAASO yields a strong upper limit. In this work, we investigate the implications of the acceleration of cosmic ray protons in the SNR on energetic gamma rays produced in the hadronic interaction of cosmic rays with ambient matter. Our findings imply that when we consider the highest attainable energy of cosmic ray protons in the SNRs to be about 100 TeV, the observed gamma-ray spectra from the two SNRs can be described consistently. Therefore, we conclude that the Cassiopia A and IC 443 SNRs are unlikely to be cosmic ray PeVatrons.

High-impact dynamic loading method for calibration of triaxial acceleration sensors

Abstract In this study, a high-impact dynamic loading device was designed to generate a three-dimensional pulse excitation signal with high intensity shock acceleration and achieve triaxial synchronous calibration of a triaxial acceleration sensor. A light-gas gun interior ballistic model and a sensor mechanical response model were developed, and the relationships between the bullet impact velocity, barrel length, and initial chamber pressure were obtained. Additionally, the transformation relationship of the sensor’s triaxial acceleration in different coordinate systems was derived. Based on the stress wave theory and the finite element method, the influence of the bullet impact velocity on the variation pulse, and different slope and deflection angles on the triaxial acceleration were analyzed. By optimizing the parameter design, machining the prototype, and conducting high-impact dynamic loading tests, the results showed that the deviation between theoretical and measured values of the generated triaxial acceleration signal was small, and the maximum deviation was less than 4%. This indicated that the proposed high-impact dynamic loading device satisfied the calibration requirements for calibrating triaxial acceleration sensors, which can generate a three-dimensional acceleration with a peak value of not less than 700 000 m s−2.

Nonthermal Acceleration of Electrons, Positrons, and Protons at a Nonrelativistic Quasi-parallel Collisionless Shock

Energetic positrons have been observed in the interstellar medium, and high-energy positrons with relativistic energies up to approximately 1 TeV have been detected in Galactic cosmic rays. We conducted a study on the acceleration of particles, specifically positrons, in a nonrelativistic quasi-parallel collisionless shock induced by a plasma consisting of protons, electrons, and positrons. The positron-to-proton number density ratio in the plasma is 0.1. We focused on a representative shock with a sonic Mach number of 17.1 and an Alfvénic Mach number of 16.8 in the rest frame of the shock. To investigate the acceleration mechanisms of particles including positrons in the shock, we utilized 1D particle-in-cell simulations. It was found that all three species of particles in the shock can be accelerated and exhibit power-law spectra. At the shock front, a significant portion of incoming upstream particles are reflected and undergo significant energy increases, and these reflected particles can be efficiently injected into the process of diffusive shock acceleration (DSA). Moveover, the reflected positrons can be further accelerated by an electric field parallel to the magnetic field when they move along the magnetic field upstream of the shock. As a result, positrons can be preferentially accelerated to be injected in the DSA process compared to electrons.