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1. Speed-dependent Threshold for Electron Injection into Diffusive Shock Acceleration

   https://doi.org/10.3847/2041-8213/ae1ba9  

   Gupta, Siddhartha; Caprioli, Damiano; Spitkovsky, Anatoly (November 2025, The Astrophysical Journal Letters)

   Abstract Finding the injection threshold for diffusive shock acceleration (DSA) of electrons in collisionless shocks has been a longstanding unsolved problem. Using first-principles kinetic simulations, we identify the conditions for electron injection into DSA and quantify the evolution of the nonthermal tail in self-generated electromagnetic turbulence. By analyzing electron trajectories and their momentum gain during shock-recrossing cycles, we demonstrate that electrons start participating in DSA when their speed is large enough to overrun the shock. We develop a minimal model showing that speed-dependent injection reproduces nonthermal electron spectra observed in kinetic simulations. Our findings establish a new criterion for electron DSA, which has broad implications for the shock-powered nonthermal emission from space/astrophysical systems. 

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2. Shock Acceleration via Idealized Short Large-amplitude Magnetic Structures

   https://doi.org/10.3847/1538-4357/adb7e3  

   Hemler, Zachary; Spitkovsky, Anatoly; Zeković, Vladimir (July 2025, The Astrophysical Journal)

   Abstract To accelerate cosmic rays (CRs) to ∼PeV energies, diffusive shock acceleration (DSA) in Galactic supernova remnants requires amplified magnetic turbulence in the shock to facilitate broadband Bohm diffusion of CRs. Recent particle-in-cell (PIC) shock simulations suggest that diffusion may be driven by short large-amplitude magnetic structures (SLAMS). Persistent SLAMS develop in the upstream of shocks with an Alfvénic Mach numberM_A ≳ 20 via the Bell instability and nonlinear amplification/steepening. We employ test-particle simulations to examine particle transport and acceleration in model shocks populated by analytically prescribed, idealized SLAMS that approximate the magnetic structures of PIC shock simulations. We demonstrate that SLAMS drive broadband Bohm diffusion of magnetized electrons (i.e., electron Larmor radiusr_L ≪  magnetic-structure lengthλ_AM) and unmagnetized electrons (i.e.,r_L ≫ λ_AM). We show that SLAMS accelerate unmagnetized electrons via DSA, and magnetized electrons via shock drift acceleration (SDA) and quasi-periodic shock acceleration (QSA). QSA, a novel Fermi-type mechanism, proceeds via rapid scattering in the converging flow between the first upstream magnetic structure and the near-downstream, shock-amplified field. QSA becomes vital for maintaining electron acceleration in shocks with superluminal SLAMS, which strongly advect magnetized electrons due to high inclination between field lines and the flow. We find that test-electron spectra are consistent with spectra from PIC simulations, indicating that the test-particle method can be used to extrapolate PIC results to longer spatial and temporal scales. Overall, our results suggest that SLAMS inM_A ≳ 20 shocks may play an important role in facilitating shock acceleration. 

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3. SLAMS-propelled Electron Acceleration at High-Mach-number Astrophysical Shocks

   https://doi.org/10.3847/1538-4357/ade05f  

   Zeković, Vladimir; Spitkovsky, Anatoly; Hemler, Zachary (July 2025, The Astrophysical Journal)

   Abstract Short large-amplitude magnetic structures (SLAMS) are frequently detected during spacecraft crossings over Earth's bow shock. We investigate the existence of such structures at astrophysical shocks, where they could result from the steepening of cosmic-ray (CR) driven waves. Using kinetic particle-in-cell simulations, we study the growth of SLAMS and the appearance of associated transient shocks in the upstream region of parallel, nonrelativistic, high-Mach-number collisionless shocks. We find that high-energy CRs significantly enhance the transverse magnetic field within SLAMS, producing highly inclined field lines. As SLAMS are advected toward the shock, these field lines form an intermittent superluminal configuration that traps magnetized electrons at fast shocks. Due to their oscillatory nature, SLAMS are periodically separated by subluminal gaps with lower transverse magnetic field strength. In these regions, electrons diffuse and accelerate by bouncing between the shock and the approaching SLAMS' region through a mechanism that we call quasi-periodic shock acceleration (QSA). We analytically derive the distribution of electrons accelerated via QSA,f(p) ∼p^{[−4.7,−5.7]}, which agrees well with the simulation spectra. We find that the electron power law remains steep until the end of our longest runs, providing a possible explanation for the steep electron spectra observed at least up to GeV energies in young and fast supernova remnants. 

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4. Electron Acceleration at Quasi-parallel Nonrelativistic Shocks: A 1D Kinetic Survey

   https://doi.org/10.3847/1538-4357/ad7c4c  

   Gupta, Siddhartha; Caprioli, Damiano; Spitkovsky, Anatoly (November 2024, The Astrophysical Journal)

   Abstract We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel nonrelativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speedsv_sh≈ 0.067–0.267c, Alfvén Mach numbers ${\mathcal{M}}_{\mathrm{A}}=5–40$ , sonic Mach numbers ${\mathcal{M}}_{\mathrm{s}}=5–160$ , as well as the proton-to-electron mass ratiosm_i/m_e= 16–1836. We find that high Alfvén Mach number shocks can channel a large fraction of their kinetic energy into nonthermal particles, self-sustaining magnetic turbulence and acceleration to larger and larger energies. The fraction of injected particles is ≲0.5% for electrons and ≈1% for protons, and the corresponding energy efficiencies are ≲2% and ≈10%, respectively. The extent of the nonthermal tail is sensitive to the Alfvén Mach number; when ${\mathcal{M}}_{\mathrm{A}}\lesssim 10$ , the nonthermal electron distribution exhibits minimal growth beyond the average momentum of the downstream thermal protons, independently of the proton-to-electron mass ratio. Acceleration is slow for shocks with low sonic Mach numbers, yet nonthermal electrons still achieve momenta exceeding the downstream thermal proton momentum when the shock Alfvén Mach number is large enough. We provide simulation-based parameterizations of the transition from thermal to nonthermal distribution in the downstream (found at a momentum around $p_{\mathrm{i},\mathrm{e}}/m_{\mathrm{i}}{v}_{\mathrm{sh}}\approx 3\sqrt{m_{\mathrm{i},\mathrm{e}}/m_{\mathrm{i}}}$ ), as well as the ratio of nonthermal electron to proton number density. The results are applicable to many different environments and are important for modeling shock-powered nonthermal radiation. 

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5. The Role of Three-dimensional Effects on Ion Injection and Acceleration in Perpendicular Shocks

   https://doi.org/10.3847/1538-4357/ae563e  

   Orusa, Luca; Caprioli, Damiano; Sironi, Lorenzo; Spitkovsky, Anatoly (April 2026, The Astrophysical Journal)

   Abstract Understanding the conditions that enable particle acceleration at nonrelativistic collisionless shocks is essential to unveil the origin of cosmic rays. We employ 2D and 3D hybrid simulations (with kinetic ions and fluid electrons) to explore particle acceleration and magnetic field amplification in nonrelativistic perpendicular shocks, focusing on the role of shock drift acceleration and its dependence on the shock Mach number. We perform an analysis of the ion injection process and demonstrate why efficient acceleration is only observed in 3D. In particular, we show that ion injection critically depends on the “porosity” of the magnetic turbulence in the downstream region near the shock, a property describing how easily the postshock region allows particles to traverse it and return upstream without being trapped. This effect can only be properly captured in 3D. Additionally, we explore the impact of numerical resolution on ion energization, highlighting how resolving small-scale turbulence—on scales below the thermal ion gyroradius—is essential for accurately modeling particle injection. Overall, our results emphasize the necessity of high-resolution 3D simulations to capture the fundamental microphysics driving particle acceleration at perpendicular shocks. 

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