Shock Acceleration Research Articles

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.

Particle Acceleration and Magnetic Field Amplification by Relativistic Shocks in Inhomogeneous Media

Particle acceleration and magnetic field amplification in relativistic shocks propagating in inhomogeneous media are investigated by three-dimensional magnetohydrodynamical (MHD) simulations and test-particle simulations. The MHD simulations show that the interaction between the relativistic shock and dense clumps amplifies the downstream magnetic field to the value expected from observations of the gamma-ray burst. The test-particle simulations in the electromagnetic field given by the MHD simulation show that particles are accelerated by the downstream turbulence and the relativistic shock. We provide the injection energy to the shock acceleration in this system. If the amplitude of upstream density fluctuations is sufficiently large, low-energy particles are initially accelerated to the injection energy by the downstream turbulence and then rapidly accelerated to higher energies by the relativistic shock. Therefore, the density fluctuation significantly affects particle acceleration in the relativistic shock.

Dynamic acceleration of energetic protons by an interplanetary collisionless shock

Context. Interplanetary collisionless shocks are known to be capable of accelerating charged particles up to hundreds of MeV. However, the underlying acceleration mechanisms are still under debate. Aims. We present the dynamic behaviors of energetic protons that are accelerated by an interplanetary shock that was observed with unprecedented high-resolution measurements by the Electron-Proton Telescope sensor of the Energetic Particle Detector suite on board the Solar Orbiter spacecraft on 2021 November 3. We constrain the potential acceleration mechanisms and processes. Methods. We first reconstructed the proton pitch-angle distributions (PADs) in the solar wind frame. Then, we examined the temporal flux profile, PAD, and the velocity distribution function of energetic protons close to the shock, and we qualitatively compared the observations with theoretical predictions. Moreover, we applied a velocity dispersion analysis (VDA) to an observed velocity dispersion event and derived the proton path length and release time at the shock. Then, we tested this derivation by comparing it with the shock motion and the magnetic field configuration. Results. We find that ∼1000–4000 keV protons exhibit a rapid-rise, rapid-decay temporal flux profile with a clear velocity dispersion ∼2 min before the shock, similar to impulsive solar energetic particle events. The proton path length based on the VDA of this event is consistent with the length derived from the shock motion and magnetic field configuration. The peak spectrum in this event appears to be steeper than the spectrum at the shock. Furthermore, we find that ∼50–200 keV proton fluxes peak between ∼10 and ∼20 s before the shock, with an inverse velocity dispersion. The velocity dispersion event and the inverse velocity dispersion event are both accompanied by magnetic kinks or switchbacks. In addition, two distinct proton populations appear near the shock. The first population at energies below ∼300 keV is characterized by a power-law spectrum with an index of ∼6–7 and a flux profile that increases before and decreases after the shock. The other population at energies above ∼300 keV shows a long-lasting, anti-sunward-beamed PAD across the shock and a flux profile that remains relatively constant before and increases slightly after the shock. Conclusions. These results suggest that the shock acceleration of energetic protons is highly dynamic due to temporal and/or spatial variations at the shock front. The observation of the velocity dispersion event further suggests that shock acceleration can be impulsive and efficient, which may be due to the interaction between the shock and magnetic kinks or switchbacks. Moreover, these results may support shock-drift acceleration and diffusive shock acceleration as candidate acceleration mechanisms at interplanetary shocks.

Feedback of Efficient Shock Acceleration on Magnetic-field Structure Inside Young Type Ia Supernova Remnants

Using an effective adiabatic index γ eff to mimic the feedback of efficient shock acceleration, we simulate the temporal evolution of a young type Ia supernova remnant (SNR) with two different background magnetic field (BMF) topologies: a uniform and a turbulent BMF. The density distribution and magnetic-field characteristics of our benchmark SNR are studied with two-dimensional cylindrical magnetohydrodynamic simulations. When γ eff is considered, we find that: (1) the two-shock structure shrinks and the downstream magnetic-field orientation is dominated by the Rayleigh–Taylor instability structures; (2) there exists more quasi-radial magnetic fields inside the shocked region; and (3) inside the intershock region, both the quasi-radial magnetic energy density and the total magnetic energy density are enhanced: in the radial direction, with γ eff = 1.1, they are amplified about 10–26 times more than those with γ eff = 5/3. While in the angular direction, the total magnetic energy densities could be amplified about 350 times more than those with γ eff = 5/3, and there are more grid cells within the intershock region where the magnetic energy density is amplified by a factor greater than 100.

Deciphering Radio Emissions from Accretion Disk Winds in Radio-quiet Active Galactic Nuclei

Unraveling the origins of radio emissions from radio-quiet active galactic nuclei (RQ AGNs) remains a pivotal challenge in astrophysics. One potential source of this radiation is the shock interaction between AGN disk winds and the interstellar medium (ISM). To understand this phenomenon, we construct a spherical, one-zone, and self-similar expansion model of shock structure between ultrafast outflows (UFOs) and the ISM. We then calculate the energy density distribution of nonthermal electrons by solving the transport equation, considering diffusive shock acceleration as the acceleration mechanism and synchrotron and inverse Compton cooling as the cooling mechanisms. Based on the derived energy distribution of nonthermal electrons, we model the radio synchrotron spectrum of the shocked ISM. For the 15 nearby RQ AGNs hosting UFOs, we investigate the shocked ISM parameters required to model their observed radio spectra based on X-ray observations and measured UFO velocities. Radio spectra of 11 out of 15 nearby RQ AGNs would be explained by the AGN disk wind model. This is a compelling indication that shock interactions between AGN disk winds and the ISM could indeed be the source of their radio emissions. The typical predicted source size and magnetic field strength are several 100 pc and 0.1 mG, respectively. We also discuss whether our prediction can be tested by future radio observations.

Return Currents in Collisionless Shocks

Collisionless shocks tend to send charged particles into the upstream, driving electric currents through the plasma. Using kinetic particle-in-cell simulations, we investigate how the background thermal plasma neutralizes such currents in the upstream of quasi-parallel non-relativistic electron–proton shocks. We observe distinct processes in different regions: the far upstream, the shock precursor, and the shock foot. In the far upstream, the current is carried by nonthermal protons, which drive electrostatic modes and produce suprathermal electrons that move toward upstream infinity. Closer to the shock (in the precursor), both the current density and the momentum flux of the beam increase, which leads to electromagnetic streaming instabilities that contribute to the thermalization of suprathermal electrons. At the shock foot, these electrons are exposed to shock-reflected protons, resulting in a two-stream type instability. We analyze these processes and the resulting heating through particle tracking and controlled simulations. In particular, we show that the instability at the shock foot can make the effective thermal speed of electrons comparable to the drift speed of the reflected protons. These findings are important for understanding both the magnetic field amplification and the processes that may lead to the injection of suprathermal electrons into diffusive shock acceleration.

Stochastic acceleration in extreme TeV BL Lacs through MCMC

Extreme TeV BL Lacs are a class of blazars with unique spectral and temporal features that are not easily reproducible using standard one-zone models based on single shock acceleration. To account for their peculiar properties, we elaborated a two-step acceleration model in which a recollimation shock and the subsequent downstream turbulence energize non-thermal electrons. We applied the model to a sample of extreme TeV BL Lacs with well-characterized spectral energy distributions. Since we used several sources, we automatized the exploration of the parameter space. This allowed us to derive the parameter distributions and study the correlations among them. We numerically solved a system of two coupled nonlinear differential equations to obtain the non-thermal particles and turbulence spectra. We calculated the spectral energy distribution via the synchrotron self-Compton emission model. The automatization of the parameter space exploration is possible through a Markov chain Monte Carlo (MCMC) ensemble sampler, in our case emcee We derived well-defined posterior distributions for the parameters, showing that the model is well constrained by available data and demonstrating the suitability of our method. The cross-correlations among some of the physical parameters are not trivial.\ Therefore, we conclude that MCMC sampling is a key instrument for characterizing the complexity of our multiparameter phenomenological model.

Individual particle approach to diffusive shock acceleration. Effect of the non-uniform flow velocity downstream of the shock

The momentum distribution of particles accelerated at strong non-relativistic shocks may be influenced by the spatial distribution of the flow speed around the shock. This phenomenon becomes evident in the cosmic-ray-modified shock, where the particle spectrum itself determines the profile of the flow velocity upstream. However, the effects of a non-uniform flow speed downstream are unclear. Hydrodynamics indicates that the spatial variation of flow speed over the length scales involved in the acceleration of particles in supernova remnants (SNRs) could be noticeable. In the present paper, we address this question. We initially followed Bell's approach to particle acceleration and then also solved the kinetic equation. We obtained an analytical solution for the momentum distribution of particles accelerated at the cosmic-ray-modified shock with spatially variable flow speed downstream. We parameterised the downstream speed profile to illustrate its effect on two model cases: the test particle and non-linear acceleration. The resulting particle spectrum is generally softer in Sedov SNRs because the distribution of the flow speed reduces the overall shock compression accessible to particles with higher momenta. On the other hand, the flow structure in young SNRs could lead to harder spectra. The diffusive properties of particles play a crucial role as they determine the distance the particles can return from to the shock, and, as a consequence, the flow speed that they encounter downstream. We discuss a possibility that the plasma velocity gradient could be (at least partially) responsible for the evolution of the radio index and for the high-energy break visible in gamma rays from some SNRs. We expect the effects of the gradient of the flow velocity downstream to be prominent in regions of SNRs with higher diffusion coefficients and lower magnetic field, that is, where acceleration of particles is not very efficient.

Soft-landing dynamics of a type of four-legged space lander

Analyzing the landing dynamics response is essential for enhancing the success rate of surface explorations on celestial bodies like Mars, the moon, and asteroids. This paper develops a comprehensive dynamics model for a space lander equipped with four sets of buffer legs. Each set comprises a primary strut, two secondary struts, and a footpad. The compression force of the buffer struts is determined through interpolation of real experimental data, while the contact force between the footpad and the ground is calculated using Archimedes law for granular media. The Lagrange equation of the second kind is employed to construct the dynamical model for the lander with minimal degrees of freedom. The proposed dynamics model is validated through experiments involving touchdowns of a single legged lander and a four legged lander. Moreover, key physical quantities such as the buffer force, energy absorption and body acceleration are computed for both 1-2-1 and 2-2 landing configurations. The results indicate that the buffer strut is capable of absorbing approximately half of the impact energy, leading to a 50-fold reduction in the shock acceleration of the main body in both landing configurations. However, it is observed that the maximum compression of the buffer strut is greater in the 1-2-1 landing configuration than in the 2-2 landing configuration. Furthermore, these simulations can be completed within seconds, enabling extensive simulations for the design and optimization of soft landing processes.

Analysis of the mechanical response of solid rocket engine propellant under acceleration shock

The increased-range solid rocket engine of new ammunition often needs to withstand extremely high acceleration overload, leading to damage to the propellant’s structural integrity. To address this issue, this paper constructs a nonlinear viscoelastic constitutive model for the CMDB propellant by using low- and high-strain rate mechanical property tests. Combined with the secondary development of explicit dynamics and numerical simulation technology, the mechanical response of a certain type of solid rocket propellant under different acceleration impacts is analyzed. The results show that under acceleration impact loads, the propellant will compress, rebound, and recover over time, continuously cycling. Its axial displacement, maximum equivalent stress, and maximum equivalent strain exhibit irregular sinusoidal wave-like periodic cycles. Looking at the time when the peaks appear, the time when the maximum equivalent stress appears always lags behind the time when the maximum axial displacement peak appears. Due to the viscous effect of the viscoelastic material of the propellant, the time when the equivalent strain peak appears will lag behind the equivalent stress. Because of the material’s damping effect, both the peak values of the maximum equivalent stress and equivalent strain decrease over time. Under continuous high acceleration impact loads, this viscous damping phenomenon continuously diminishes, and the peak value of the propellant’s axial displacement gradually increases.

Supernova Remnants in Gamma Rays

In the 1960s, the remnants of supernova explosions (SNRs) were indicated as a possible source of galactic cosmic rays through the Diffusive Shock Acceleration (DSA) mechanism. Since then, the observation of gamma-ray emission from relativistic ions in these objects has been one of the main goals of high-energy astrophysics. A few dozen SNRs have been detected at GeV and TeV photon energies in the last two decades. However, these observations have shown a complex phenomenology that is not easy to reduce to the standard paradigm based on DSA acceleration. Although the understanding of these objects has greatly increased, and their nature as efficient electron and proton accelerators has been observed, it remains to be clarified whether these objects are the main contributors to galactic cosmic rays. Here, we review the observations of γ-ray emission from SNRs and the perspectives for the future.

Evolution of Electron Acceleration by Corotating Interaction Region Shocks at 1 au

We present the first observations of in situ electron acceleration at corotating interaction region (CIR) shocks near 1 au, utilizing measurements from Wind and Magnetospheric Multiscale (MMS) mission in the interplanetary medium. As the forward (reverse) shock of the 2018 January CIR (the 2020 February CIR) moves from Wind at [206, 92, −7]R E ([257, 25, 3]R E ) to MMS1 at [24, 2, 7]R E ([25, 3, 0.5]R E ), the shock’s thickness becomes 8 (3) times thinner, but the convective electric field E drift gets weaker (stronger) along the shock; both the upstream and shocked suprathermal electrons exhibit a flatter flux energy spectrum, while the electron shock acceleration becomes less (more) significant. For the shocked suprathermal electrons with significant flux enhancement, the flux ratio across the shock appears to peak in the direction perpendicular to the magnetic field. Therefore, the CIR shock acceleration of solar wind suprathermal electrons at 1 au exhibits an efficiency increasing with the E drift strength. These results also suggest that such acceleration through the interplanetary medium can contribute to the formation of solar wind suprathermal electrons.

Investigating the Properties of the Relativistic Jet and Hot Corona in AGN with X-ray Polarimetry

X-ray polarimetry has been suggested as a prominent tool for investigating the geometrical and physical properties of the emissions from active galactic nuclei (AGN). The successful launch of the Imaging X-ray Polarimetry Explorer (IXPE) on 9 December 2021 has expanded the previously restricted scope of polarimetry into the X-ray domain, enabling X-ray polarimetric studies of AGN. Over a span of two years, IXPE has observed various AGN populations, including blazars and radio-quiet AGN. In this paper, we summarize the remarkable discoveries achieved thanks to the opening of the new window of X-ray polarimetry of AGN through IXPE observations. We will delve into two primary areas of interest: first, the magnetic field geometry and particle acceleration mechanisms in the jets of radio-loud AGN, such as blazars, where the relativistic acceleration process dominates the spectral energy distribution; and second, the geometry of the hot corona in radio-quiet AGN. Thus far, the IXPE results from blazars favor the energy-stratified shock acceleration model, and they provide evidence of helical magnetic fields inside the jet. Concerning the corona geometry, the IXPE results are consistent with a disk-originated slab-like or wedge-like shape, as could result from Comptonization around the accretion disk.

New constraints on the gamma-ray and high energy neutrino fluxes from the circumstellar interaction of SN 2023ixf

The recent supernova, SN 2023ixf, one of the closest observed type II SNe has revealed the presence of a dense circumstellar material (CSM). Interaction of the SN ejecta with this dense CSM might create high energy protons of PeV energies through shock acceleration. These accelerated protons then colliding with the CSM (inelastic pp collision) can produce secondaries such as high energy gamma-rays and neutrinos. However, no gamma-rays and neutrinos have been detected by Fermi-LAT and IceCube from this event. Fermi-LAT has placed an upper limit on the gamma-ray flux above 100 MeV to be 2.6 × 10-11 erg cm-2 s-1. On the other hand, IceCube's upper limit on muon neutrino flux is 7.3 × 10-2 GeV cm-2. Taking these limits into account and using the shock-CSM properties derived from multi-wavelength observations, we obtain new upper limits on the gamma-ray (10-11 erg cm-2 s-1) and neutrino (10-3 GeV cm-2) fluxes from SN 2023ixf produced via the pp interaction channel. While we found the gamma-ray flux to be consistent with Fermi-LAT's upper limit, the neutrino flux is found to be about 2 orders of magnitude smaller than the IceCube's upper limit. We further analyse the detection prospects of such secondary signals from future SN 2023 like events with upcoming detectors, CTA and IceCube-Gen2 and found to have great discovery potential, if any similar event occurs within 7 Mpc.

Likely Common Coronal Source of Solar Wind and 3He-enriched Energetic Particles: Uncoupled Transport from the Low Corona to 0.2 au

Parker Solar Probe (PSP) observations of a small dispersive event on 2022 February 27 and 28 indicate scatter-free propagation as the dominant transport mechanism between the low corona and greater than 35 solar radii. The event occurred during unique orbital conditions that prevailed along specific flux tubes that PSP encountered repeatedly between 25 and 35 Rs during outbound orbit 11. This segment of the PSP orbit exhibits almost stationary angular motion relative to the rotating solar surface, such that in the rotating frame, PSP’s motion is essentially radial. The time dispersion often observed in impulsive solar energetic particle (SEP) events continues in this case down to velocities including the core solar-wind ion velocities. Especially at the onset of this event, the 3He content is much larger than the usual SEP abundances seen in the energy range from ∼100 keV to several MeV for helium. Later in the event, iron is enhanced. The compositional signatures suggest this to be an example of an acceleration mechanism for generating the seed energetic particles required by shock (or compression) acceleration models in SEP events to account for the enrichment of various species above solar abundances in such events. A preliminary search of similar orbital conditions over the PSP mission has not revealed additional such events, although favorable conditions (isolated impulsive acceleration and well-ordered magnetic field connection with minimal magnetic field fluctuation) that would be required are infrequently realized, given the small fraction of the PSP trajectory that meets these observation conditions.

Statistical analysis of high-frequency whistler waves at Earth's bow shock: Further support for stochastic shock drift acceleration

We statistically investigate high-frequency whistler waves (with frequencies higher than ∼10% of the local electron cyclotron frequency) at Earth's bow shock using magnetospheric multi-scale (MMS) spacecraft observations. We focus specifically on the wave power within the shock transition layer, where we expect electron acceleration via stochastic shock drift acceleration (SSDA) to occur associated with efficient pitch-angle scattering by whistler waves. We find that the wave power is positively correlated with both the Alfvén Mach number in the normal incidence frame MA and in the de Hoffmann–Teller frame MA/cos θBn. The empirical relation with MA/cos θBn is compared with the theory of SSDA that predicts a threshold wave power proportional to (MA/cos θBn)−2. The result suggests that the wave power exceeds the theoretical threshold for MA/cos θBn≳30–60, beyond which efficient electron acceleration is expected. This aligns very well with previous statistical analysis of electron acceleration at Earth's bow shock [Oka et al., Geophys. Res. Lett. 33, 5–6 (2006)]. Therefore, we consider that this study provides further support for SSDA as the mechanism of electron acceleration at Earth's bow shock. At higher-Mach-number astrophysical shocks, SSDA will be able to inject electrons into the diffusive shock acceleration process for subsequent acceleration to cosmic-ray energies.

Bell Instability–mediated Diffusive Shock Acceleration at Supernova Blast Wave Shock Propagating in the Interstellar Medium

Supernova blast wave shock is a very important site of cosmic-ray acceleration. However, the detailed physical process of acceleration, in particular, nonlinear interplay between cosmic-ray streaming and magnetic field amplification, has not been studied under a realistic environment. In this paper, using a unique and novel numerical method, we study cosmic-ray acceleration at supernova blast wave shock propagating in the interstellar medium with well-resolved magnetic field amplification by nonresonant hybrid instability (or Bell instability). We find that the magnetic field is mildly amplified under typical interstellar medium conditions that leads to maximum cosmic-ray energy ≃30 TeV for supernova remnants with age ≃1000 yr consistent with gamma-ray observations. The strength of the amplified magnetic field does not reach the so-called saturation level because the cosmic-ray electric current toward the shock upstream has a finite spatial extent, by which Bell instability cannot experience many e-folding times.

Proton acceleration from optically tailored high-density gas jet targets

Laser-driven ion acceleration is well established using solid targets mainly in the target normal sheath acceleration regime. To follow the increasing repetition rate available on high-intensity lasers, the use of high-density gas targets has been explored in the past decade. When interacting with targets reaching densities close to the critical one, the laser pulse can trigger different acceleration mechanisms such as Collisionless Shock Acceleration (CSA) or hole boring. Particle-in-cell simulations using ideal target profiles show that CSA can accelerate a collimated, narrow energy spread and few hundreds of megaelectronvolts ion beam on the laser axis. Nevertheless, in real experiments, the laser will not only interact with an overcritical, thin plasma slab with sharp density gradients, but also with lower density regions surrounding the core of the gas jet, extending to several hundreds of micrometres. The interaction of the laser with these lower density wings will lead to nonlinear effects that will reduce the available energy to drive the shock in the high-density region of the target. Optically tailoring this target could mitigate that issue. Recent experiments conducted on different laser facilities aimed at testing several tailoring configurations. We first tested a scheme with a copropagating picosecond prepulse to create a lower density plasma channel to facilitate the propagation of the main pulse, while the second one was a transverse tailoring driven by nanosecond laser pulses to generate blast waves and form a high-density plasma slab. The main results will be presented here and the methods compared.

Spin-polarized 3He shock waves from a solid-gas composite target at high laser intensities

We investigate collisionless shock acceleration of spin-polarized 3 He for laser pulses with normalized vector potentials in the range a0=100−200 . The setup utilized in the 2D-particle-in-cell simulations consists of a solid carbon foil that is placed in front of the main Helium target. The foil is heated by the laser pulse and shields the Helium from the highly oscillating fields. In turn, a shock wave with more homogeneous fields is induced, leading to highly polarized ion beams. We observe that the inclusion of radiation reaction into our simulations leads to a higher beam charge without affecting the polarization degree to a significant extent.

Interactions between elementary waves and weak discontinuity in two-layer blood flow through artery

Blood flow through arterial circulation can be characterized by fluid transport in flexible tubes and modeled mathematically using the conservation of mass and momentum. A one-dimensional model for two-layer blood flow with different blood velocities and the same constant density in each layer derived from the Euler equations of gas dynamics by taking the vertical average across each layer. This work presents interactions of elementary waves with a weak discontinuity for the quasilinear 3 × 3 system of conservation laws governing the two-layer blood flow in arteries. Exploiting elementary waves as a single-parameter curve, we study the Riemann solution uniquely and consequently establish the condition on initial data for the existence of a solution to the Riemann problem. Furthermore, we discuss the evolution of weak discontinuity waves and subsequently derive their amplitudes; in what follows, we investigate the interactions of weak discontinuity with contact discontinuity and shocks. Finally, a series of numerical tests have been performed to understand the impact of shock strength and the initial data on the amplitudes of reflected and transmitted waves and the jumps in shock acceleration.