Shock Acceleration Research Articles

Theory of Electron Injection at Oblique Shock of Finite Thickness

Abstract A theory of electron injection into diffusive shock acceleration (DSA) for the generation of cosmic-ray electrons at collisionless shocks is presented. We consider a recently proposed particle acceleration mechanism called stochastic shock drift acceleration (SSDA). We find that SSDA may be understood as a diffusive particle acceleration mechanism at an oblique shock of finite thickness. More specifically, it is described by a solution to the diffusion–convection equation for particles with the characteristic diffusion length comparable to the shock thickness. On the other hand, the same equation yields the standard DSA if the diffusion length is much longer than the thickness. Although SSDA predicts, in general, a spectral index steeper than DSA, it is much more efficient for low-energy electron acceleration and is favorable for injection. The injection threshold energy corresponds to the transition energy between the two different regimes. It is of the order of 0.1–1 MeV in typical interstellar and interplanetary conditions if the dissipation scale of turbulence around the shock is determined by the ion inertial length. The electron injection is more efficient at high M A / cos θ Bn , where M A and θ Bn are the Alfvén Mach number and the shock obliquity, respectively. The theory suggests that efficient acceleration of electrons to ultrarelativistic energies will be more easily realized at high Mach number, young supernova remnant shocks, but not at weak or moderate shocks in the heliosphere unless the upstream magnetic field is nearly perpendicular to the shock normal.

A Multi-Event Study of Early-Stage SEP Acceleration by CME-Driven Shocks—Sun to 1 AU

The solar corona between below 10 solar radii is an important region for early acceleration and transport of solar energetic particles (SEPs) by coronal mass ejection-driven shock waves. There, these waves propagate into a highly variable dynamic medium with steep gradients and rapidly expanding coronal magnetic fields, which modulates the particle acceleration near the shock/wave surfaces, and the way SEPs spread into the heliosphere. We present a study modeling the acceleration of SEPs in global coronal shock events in the corona, as well as their transport to 1 au, based on telescopic observations coupled with dynamic physical models. As part of the project Solar Particle Radiation Environment Analysis and Forecasting—Acceleration and Scattering Transport (SPREAdFAST), we model the interaction of observed off-limb coronal bright fronts (CBF) with the coronal plasma from synoptic magnetohydrodynamic (MHD) simulations. We then simulate the SEP acceleration in analytical diffusive shock acceleration (DSA) model. The simulated fluxes are used as time-dependent inner boundary conditions for modeling the particle transport to 1 au. Resulting flux time series are compared with 1 au observations for validation. We summarize our findings and present implications for nowcasting SEP acceleration and heliospheric connectivity.

Possible hadronic origin of TeV photon emission from SNR G106.3+2.7

Context. Recently, HAWC, ASγ, and LHAASO experiments have reported the gamma-ray spectrum of supernova remnant (SNR) G106.3+2.7 above 40 TeV, indicating that SNR G106.3+2.7 is a promising PeVatron candidate. However, the origin of the gamma-ray spectrum is still debated. Thus, a dedicated theoretical model with self-consistent descriptions is required to decipher the properties of the gamma-ray spectrum for this specific source. Aims. We construct a theoretical model to explain the multiband photon emission from the PeVatron SNR G106.3+2.7. Methods. In our model, the acceleration and propagation of particles from the Bohm-like diffusion region inside the SNR to the Galactic diffusion region outside the SNR are described through nonlinear diffusive shock acceleration (NLDSA). The main content of our NLDSA model is solving the hydrodynamic equations numerically for gas density, gas velocity, and gas pressure and the equation for the quasi-isotropic particle momentum distribution. The consequent multiband nonthermal emission stems from two different regions, namely the acceleration region and the escaping region. Results. Our model is capable of explaining the multiband photon emission via the dominant synchrotron radiation of the electrons accelerated inside the SNR. The photons with energy of ≳GeV are naturally produced by the protons inside and outside the SNR. Moreover, photons in the energy range of ~1−~ 100 TeV are due to the interaction of escaped protons with dense molecular clouds. Conclusions. For photons with energy Eγ ≳ 1 GeV from SNR G106.3+2.7, our results here favor a hadronic origin, where the photons in the energy range of ~1G eV to ~1 TeV are produced inside the SNR through proton-proton interaction, while photons with Eγ ≳ 1 TeV originate from the interaction of escaped protons with a dense molecular cloud.

Turbulence-dominated Shock Waves: 2D Hybrid Kinetic Simulations

Abstract We investigate the interaction of turbulence with shock waves by performing 2D hybrid kinetic simulations. We inject force-free magnetic fields upstream that are unstable to the tearing-mode instability. The magnetic fields evolve into turbulence and interact with a shock wave whose sonic Mach number is 2.4. Turbulence properties, the total and normalized residual energy and the normalized cross helicity, change across the shock wave. While the energy of velocity and magnetic fluctuations is mostly distributed equally upstream, the velocity fluctuations are amplified dominantly downstream of the shock wave. The amplitude of turbulence spectra for magnetic, velocity, and density fluctuations are also increased at the shock wave while their spectral index remains unchanged. We compare our results with the Zank et al. model of turbulence transmission across a shock, and find that it provides a reasonable explanation for the spectral change across the shock wave. We find that particles are efficiently accelerated at the shock front, and a power-law spectrum forms downstream. This can be explained by diffusive shock acceleration, in which particles gain energy by being scattered upstream and downstream of a shock wave. The trajectory of an accelerated particle suggests that upstream turbulence plays a role scattering of particles.

Acceleration of Solar Energetic Particles through CME-driven Shock and Streamer Interaction

Abstract On 2013 June 21, a solar prominence eruption was observed, accompanied by an M2.9 class flare, a fast coronal mass ejection, and a type II radio burst. The concomitant emission of solar energetic particles (SEPs) produced a significant proton flux increase, in the energy range 4–100 MeV, measured by the Low and High Energy Telescopes on board the Solar TErrestrial RElations Observatory (STEREO)-B spacecraft. Only small enhancements, at lower energies, were observed at the STEREO-A and Geostationary Operational Environmental Satellite (GOES) spacecraft. This work investigates the relationship between the expanding front, coronal streamers, and the SEP fluxes observed at different locations. Extreme-ultraviolet data, acquired by the Atmospheric Imaging Assembly (AIA) instrument on board the Solar Dynamics Observatory (SDO), were used to study the expanding front and its interaction with streamer structures in the low corona. The 3D shape of the expanding front was reconstructed and extrapolated at different times by using SDO/AIA, STEREO/Sun Earth Connection Coronal and Heliospheric Investigation, and Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph observations with a spheroidal model. By adopting a potential field source surface approximation and estimating the magnetic connection of the Parker spiral, below and above 2.5 R ⊙, we found that during the early expansion of the eruption, the front had a strong magnetic connection with STEREO-B (between the nose and flank of the eruption front) while having a weak connection with STEREO-A and GOES. The obtained results provide evidence, for the first time, that the interaction between an expanding front and streamer structures can be responsible for the acceleration of high-energy SEPs up to at least 100 MeV, as it favors particle trapping and hence increases the shock acceleration efficiency.

Exploring the GRB population: robust afterglow modelling

ABSTRACT Gamma-ray bursts (GRBs) are ultra-relativistic collimated outflows, which emit synchrotron radiation throughout the entire electromagnetic spectrum when they interact with their environment. This afterglow emission enables us to probe the dynamics of relativistic blast waves, the microphysics of shock acceleration, and environments of GRBs. We perform Bayesian inference on a sample of GRB afterglow data sets consisting of 22 long GRBs and 4 short GRBs, using the afterglow model scalefit, which is based on 2D relativistic hydrodynamic simulations. We make use of Gaussian processes to account for systematic deviations in the data sets, which allows us to obtain robust estimates for the model parameters. We present the inferred parameters for the sample of GRBs and make comparisons between short and long GRBs in constant-density and stellar-wind-like environments. We find that in almost all respects such as energy and opening angle, short, and long GRBs are statistically the same. Short GRBs however have a markedly lower prompt gamma-ray emission efficiency than long GRBs. We also find that for long GRBs in ISM (interstellar medium)-like ambient media there is a significant anticorrelation between the fraction of thermal energy in the magnetic fields, ϵB, and the beaming corrected kinetic energy. Furthermore, we find no evidence that the mass-loss rates of the progenitor stars are lower than those of typical Wolf–Rayet stars.

Pyroshock Response Prediction of Spacecraft Structure in Wide Frequency Domain Based on Acceleration FRF

The initiating explosive shock environment of an aerospace mission has the characteristics of instantaneity, high amplitude and a wide frequency domain. An improved method based on the acceleration frequency response function (FRF) and virtual mode synthesis method (VMSS) is proposed to predict the pyroshock response of a spacecraft structure in a wide frequency domain. Firstly, the statistical energy analysis (SEA) model of the spacecraft structure was established, and the FRF and modal density of the model were obtained. Then, the paper explains how, due to the small number of modes in the low-frequency band, the calculation results of the SEA method in the low-frequency band were not accurate enough. The FRF of the SEA model in the low-frequency band was modified by an FRF test of the structure. Finally, the shock response spectrum (SRS) was obtained based on the VMSS and the modified FRF. A shock experiment on the spacecraft structure was conducted by using the shock experiment system, which is based on a light-gas gun. The accurate shock force function and acceleration response results were obtained. The numerical results based on the improved method are in line with those in the experiment. This verifies that the novel method can better grasp the response characteristics of the structure in the broadband domain. The novel method effectively improves the response prediction accuracy of the SEA model in the relatively low-frequency band. While ensuring the computational efficiency, more accurate shock response results in a wide frequency domain were obtained. The novel method presented in this paper provides support of numerical analysis for pyroshock response prediction of spacecraft structure in a wide frequency domain.

Probing the environments surrounding ultrahigh energy cosmic ray accelerators and their implications for astrophysical neutrinos

We explore inferences on ultrahigh energy cosmic ray (UHECR) source environments---constrained by the spectrum and composition of UHECRs and nonobservation of extremely high energy neutrinos---and their implications for the observed high energy astrophysical neutrino spectrum. We find acceleration mechanisms producing power-law cosmic ray (CR) spectra $\ensuremath{\propto}{E}^{\ensuremath{-}2}$ are compatible with UHECR data, if CRs at high rigidities are in the quasiballistic diffusion regime as they escape their source environment. Both gas-dominated and photon-dominated source environments are able to account for UHECR observations, however photon-dominated sources give a better fit. Additionally, gas-dominated sources are in tension with current neutrino constraints. Accurate measurement of the neutrino flux at $\ensuremath{\sim}10\text{ }\text{ }\mathrm{PeV}$ will provide crucial information on the viability of gas-dominated sources, as well as whether diffusive shock acceleration is consistent with UHECR observations. We also show that UHECR sources are able to give a good fit to the high energy portion of the astrophysical neutrino spectrum, above $\ensuremath{\sim}\mathrm{PeV}$. This common origin of UHECRs and high energy astrophysical neutrinos is natural if air shower data is interpreted with the sibyll2.3c hadronic interaction model, which gives the best-fit to UHECRs and astrophysical neutrinos in the same part of parameter space, but not for epos-lhc.

Cosmic rays from massive star clusters: a close look at Westerlund 1

ABSTRACT We study the effect of cosmic ray (CR) acceleration in the massive compact star cluster Westerlund 1 in light of its recent detection in γ-rays. Recent observations reveal a 1/r radial distribution of the CR energy density. Here, we theoretically investigate whether or not this profile can help to distinguish between (1) continuous CR acceleration in the star cluster stellar wind-driven shocks and (2) discrete CR acceleration in multiple supernovae (SNe) shocks – which are often debated in the literature. Using idealized two-fluid simulations and exploring different acceleration sites and diffusion coefficients, we obtain the CR energy density profile and luminosity to find the best match for the γ-ray observations. We find that the inferred CR energy density profiles from observations of γ-ray luminosity and mass can be much different from the true radial profile. CR acceleration at either the cluster core region or the wind termination shock can explain the observations, if the diffusion coefficient is κcr ∼ 1027 cm2 s−1 and a fraction of ${\approx}10-20{{\ \rm per\ cent}}$ of the shock power/post-shock pressure is deposited into the CR component. We also study the possibility of discrete SNe explosions being responsible for CR acceleration and find that with an injection rate of 1 SN in every ∼0.03 Myr, one can explain the observed γ-ray profile. This multiple SN scenario is consistent with X-ray observations only if the thermal conductivity is close to the Spitzer value.

High-yield and high-angular-fluence neutron generation from deuterons accelerated by laser-driven collisionless shock

A bright collimated neutron source is an essential tool for global security missions and fundamental scientific research. In this paper, we study a compact high-yield and high-angular-fluence neutron source particularly suitable for high-energy neutron applications utilizing the breakup reaction of laser-driven deuterons in a 9Be converter. The neutron generation scaling from such a reaction is used to guide the choice and optimization of the acceleration process for bulk ions in a low density CD2 foam. In particular, the collisionless shock acceleration mechanism is exploited with proper choice in the laser and target parameter space to accelerate these ions toward energies above the temperature of the distribution. Particle-in-cell and Monte Carlo simulations are coupled here to investigate this concept and possible adverse effects as well as the contribution from the surface ions accelerated and the optimal converter design. The simulation results indicated that our design can be a practical approach to increase both the neutron yield and angular fluence of laser-driven neutron sources, reaching >1011 neutron/pulse (or >108 neutron/J) and >1011 neutron/sr (or >108 neutron/sr/J) with present-day kJ-class high-power lasers. Such developments will advance fundamental neutron science, high precision radiography, and other global security applications with laser-driven sources.

In situ ultrasound imaging of shear shock waves in the porcine brain

Direct measurement of brain motion at high spatio-temporal resolutions during impacts has been a persistent challenge in brain biomechanics. Using high frame-rate ultrasound and high sensitivity motion tracking, we recently showed shear waves sent to the ex vivo porcine brain developing into shear shock waves with destructive local accelerations inside the brain, which may be a key mechanism behind deep traumatic brain injuries. Here we present the ultrasound observation of shear shock waves in the acoustically challenging environment of the in situ porcine brain during a single-shot impact with sinusoidal and haversine time profiles. The brain was impacted to generate surface amplitudes of 25–33g, and to propagate a 40–50 Hz shear waves into the brain. Simultaneously, images of the moving brain were acquired at 2193 images/s, using a custom sequence with 8 interleaved ultrasound propagation events. For a long field-of-view, wide-beam emissions were designed using time-reversal ultrasound simulations and no compounding was used to avoid motion blurring. For a 40 Hz, 25g sinusoidal impact, a shock-front acceleration of 102g was measured 7.1 mm deep inside the brain. Using a haversine pulse that models a realistic impact more closely, a shock acceleration of 113g was observed 3.0 mm inside the brain, from a 50 Hz, 33g excitation. The experimental velocity, acceleration, and strain-rate waveforms in brain for the monochromatic impact are shown to be in excellent agreement with theoretical predictions from a custom higher-order finite volume method hence demonstrating the capabilities to measure rapid brain motion despite strong acoustical reverberations from the porcine skull.

Shock Acceleration with Oblique and Turbulent Magnetic Fields

Abstract We investigate shock acceleration in a realistic astrophysical environment with density inhomogeneities. The turbulence induced by the interaction of the shock precursor with upstream density fluctuations amplifies both upstream and downstream magnetic fields via the turbulent dynamo. The dynamo-amplified turbulent magnetic fields (a) introduce variations of shock obliquities along the shock face, (b) enable energy gain through a combination of shock drift and diffusive processes, (c) give rise to various spectral indices of accelerated particles, (d) regulate the diffusion of particles both parallel and perpendicular to the magnetic field, and (e) increase the shock acceleration efficiency. Our results demonstrate that upstream density inhomogeneities and dynamo amplification of magnetic fields play an important role in shock acceleration, and thus shock acceleration depends on the condition of the ambient interstellar environment. The implications on understanding radio spectra of supernova remnants are also discussed.

Magnetic Field Amplification by a Plasma Cavitation Instability in Relativistic Shock Precursors

Abstract Plasma streaming instabilities play an important role in magnetic field amplification and particle acceleration in relativistic shocks and their environments. However, in the far shock precursor region where accelerated particles constitute a highly relativistic and dilute beam, streaming instabilities typically become inefficient and operate at very small scales when compared to the gyroradii of the beam particles. We report on a plasma cavitation instability that is driven by dilute relativistic beams and can increase both the magnetic field strength and coherence scale by orders of magnitude to reach near-equipartition values with the beam energy density. This instability grows after the development of the Weibel instability and is associated with the asymmetric response of background leptons and ions to the beam current. The resulting net inductive electric field drives a strong energy asymmetry between positively and negatively charged beam species. Large-scale particle-in-cell simulations are used to verify analytical predictions for the growth and saturation level of the instability and indicate that it is robust over a wide range of conditions, including those associated with pair-loaded plasmas. These results can have important implications for the magnetization and structure of shocks in gamma-ray bursts, and more generally for magnetic field amplification and asymmetric scattering of relativistic charged particles in plasma astrophysical environments.

Electron Preacceleration at Weak Quasi-perpendicular Intracluster Shocks: Effects of Preexisting Nonthermal Electrons

Abstract Radio relics in the outskirts of galaxy clusters imply the diffusive shock acceleration (DSA) of electrons at merger-driven shocks with Mach number M s ≲ 3–4 in the intracluster medium (ICM). Recent studies have suggested that electron preacceleration and injection, prerequisite steps for DSA, could occur at supercritical shocks with M s ≳ 2.3 in the ICM, thanks to the generation of multiscale waves by microinstabilities such as the Alfvén ion cyclotron (AIC) instability, the electron firehose instability (EFI), and the whistler instability (WI). On the other hand, some relics are observed to have subcritical shocks with M s ≲ 2.3, leaving DSA at such weak shocks as an outstanding problem. Reacceleration of preexisting nonthermal electrons has been contemplated as one of possible solutions for that puzzle. To explore this idea, we perform particle-in-cell simulations for weak quasi-perpendicular shocks in high-β (β = P gas/P B ) plasmas with power-law suprathermal electrons in addition to Maxwellian thermal electrons. We find that suprathermal electrons enhance the excitation of electron-scale waves via the EFI and WI. However, they do not affect the ion reflection and the ensuing generation of ion-scale waves via the AIC instability. The presence of ion-scale waves is the key for the preacceleration of electrons up to the injection momentum; thus, the shock criticality condition for electron injection to DSA is preserved. Based on the results, we conclude that preexisting nonthermal electrons in the preshock region alone would not resolve the issue of electron preacceleration at subcritical ICM shocks.

The Solar Eruption of 2017 September 10: Wavy with a Chance of Protons

Abstract High-resolution SUVI images reveal an interesting new picture of particle acceleration in powerful solar eruptions. Typically, powerful solar eruptions include a coronal wave component, as well the traditional CME and flare components. At low solar altitudes, coronal waves refract downward, toward the solar surface, because of the slower Alfvén speeds at the base of the corona. The refracted wave plus the shock wave ahead of an intense CME allow for a two-step shock acceleration process that can result in relativistic or GLE particles. This mechanism may be particularly applicable to the first-to-arrive, prompt relativistic particles measured by the Fort Smith neutron monitor during GLE # 72 on 2017 September 10.

Role of the radiative stage for cosmic ray acceleration in SNRs

ABSTRACT We consider diffusive shock acceleration in supernova remnants throughout their evolution including a radiative stage. It is found that a more efficient acceleration and fast exit of particles at the radiative stage results in the hardening of the source cosmic ray proton and electron spectra at energies ∼100–500 GeV. The effect is stronger for cosmic ray electrons.

Non-linear particle reacceleration by multiple shocks

ABSTRACT When the pressure of particles accelerated at shock waves is no longer negligible compared to the kinetic pressure of the gas, the linear theory of diffusive shock acceleration breaks down. This is expected in particular when the shock sweeps up pre-existing cosmic rays, or when multiple shocks reaccelerate successively the same particles. To describe these systems, one has to account for the non-linear backreaction of the particles on the magnetohydrodynamic flow. Using an up-to-date semi-analytical model of particle reacceleration at non-linear shocks, we show that the presence of pre-existing energetic particles strongly affects the shock profile, in such a way that the reacceleration of non-thermal particles or the acceleration of particles from the thermal bath becomes less efficient. We further describe the evolution of the distribution of particles after several shocks and study the properties of the asymptotic solution. We detail the case of identical shocks as well as more realistic scenarios, including the heating of the medium or superbubble environments. When the particles are efficiently confined in the acceleration region, it is generally found that the spectrum converges toward a concave solution after a few tens of shocks, with a spectral index around 3.5 at the highest energy. The post-shock cosmic ray pressure reaches an asymptotic value of about 4–5 per cent of the ram pressure of one shock. Most of the shock pressure is transferred to escaping particles.

Comment on “Non-interacting coronal mass ejections and solar energetic particles near the quadrature configuration of solar terrestrial relations observatory”: CME shocks are fast magnetosonic shocks and not intermediate Alfvén shocks

Aims.The expression for the shock Mach number used by Ravishankar and Michalek (2020, A&A, 638, A42) is incorrect. We wish to provide a correct expression so they can redo their analyses.Methods.Coronal mass ejection (CME) shocks are fast magnetosonic shocks and not intermediate Alfvén shocks. We give the steps for calculating the shock normal, shock velocity, and, thus, the shock Mach number. We also mention that the shock properties, such as being quasi-perpendicular or quasi-parallel, are another important parameter for the shock acceleration of energetic particles.Results.We have corrected the errors existing in the Astronomy and Astrophysics literature concerning the mathematical expression for the Mach number for a CME shock. Hopefully, future authors will use the now-correct expression for the Mach number.Conclusions.The correct shock Mach number expression has been given to Ravishankar and Michalek. It is hoped that they will redo their calculations (including using other shock properties) to see if their 2020 conclusions still hold true or not.

Multi-spacecraft observations of the structure of the sheath of an interplanetary coronal mass ejection and related energetic ion enhancement

Context. Sheath regions ahead of coronal mass ejections (CMEs) are large-scale heliospheric structures that form gradually with CME expansion and propagation from the Sun. Turbulent and compressed sheaths could contribute to the acceleration of charged particles in the corona and in interplanetary space, but the relation of their internal structure to the particle energization process is still a relatively little studied subject. In particular, the role of sheaths in accelerating particles when the shock Mach number is low is a significant open research problem. Aims. This work seeks to provide new insights on the internal structure of CME-driven sheaths with regard to energetic particle enhancements. A good opportunity to achieve this aim was provided by multi-point, in-situ observations of a sheath region made by radially aligned spacecraft at 0.8 and ∼1 AU (Solar Orbiter, the L1 spacecraft Wind and ACE, and BepiColombo) on April 19−21, 2020. The sheath was preceded by a weak and slowly propagating fast-mode shock. Methods. We apply a range of analysis techniques to in situ magnetic field, plasma and particle observations. The study focuses on smaller scale sheath structures and magnetic field fluctuations that coincide with energetic ion enhancements. Results. Energetic ion enhancements were identified in the sheath, but at different locations within the sheath structure at Solar Orbiter and L1. Magnetic fluctuation amplitudes at inertial-range scales increased in the sheath relative to the solar wind upstream of the shock, as is typically observed. However, when normalised to the local mean field, fluctuation amplitudes did not increase significantly; magnetic compressibility of fluctuation also did not increase within the sheath. Various substructures were found to be embedded within the sheath at the different spacecraft, including multiple heliospheric current sheet (HCS) crossings and a small-scale flux rope. At L1, the ion flux enhancement was associated with the HCS crossings, while at Solar Orbiter, the ion enhancement occurred within a compressed, small-scale flux rope. Conclusions. Several internal smaller-scale substructures and clear difference in their occurrence and properties between the used spacecraft was identified within the analyzed CME-driven sheath. These substructures are favourable locations for the energization of charged particles in interplanetary space. In particular, substructures that are swept from the upstream solar wind and compressed into the sheath can act as effective acceleration sites. A possible acceleration mechanism is betatron acceleration associated with a small-scale flux rope and warped HCS compressed in the sheath, while the contribution of shock acceleration to the latter cannot be excluded.

Acceleration of Solar Energetic Particles by the Shock of Interplanetary Coronal Mass Ejection

Abstract Interplanetary coronal mass ejection (ICME) shocks are known to accelerate particles and contribute significantly to solar energetic particle events. We have performed magnetohydrodynamic-particle in cell simulations of ICME shocks to understand the acceleration mechanism. These shocks vary in Alfvénic Mach numbers as well as in magnetic field orientations (parallel and quasi-perpendicular). We find that diffusive shock acceleration plays a significant role in accelerating particles in a parallel ICME shock. In contrast, shock drift acceleration (SDA) plays a pivotal role in a quasi-perpendicular shock. High-Mach shocks are seen to accelerate particles more efficiently. Our simulations suggest that background turbulence and local particle velocity distribution around the shock can indirectly hint at the acceleration mechanism. Our results also point toward a few possible in situ observations that could validate our understanding of the topic.