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1. Electron Injection via Modified Diffusive Shock Acceleration in High-Mach-number Collisionless Shocks

   https://doi.org/10.3847/2041-8213/ad0cf9  

   Grassi, A.; Rinderknecht, H. G.; Swadling, G. F.; Higginson, D. P.; Park, H.-S.; Spitkovsky, A.; Fiuza, F. (November 2023, The Astrophysical Journal Letters)

   Abstract The ability of collisionless shocks to efficiently accelerate nonthermal electrons via diffusive shock acceleration (DSA) is thought to require an injection mechanism capable of preaccelerating electrons to high enough energy where they can start crossing the shock front potential. We propose, and show via fully kinetic plasma simulations, that in high-Mach-number shocks electrons can be effectively injected by scattering in kinetic-scale magnetic turbulence produced near the shock transition by the ion Weibel, or current filamentation, instability. We describe this process as a modified DSA mechanism where initially thermal electrons experience the flow velocity gradient in the shock transition and are accelerated via a first-order Fermi process as they scatter back and forth. The electron energization rate, diffusion coefficient, and acceleration time obtained in the model are consistent with particle-in-cell simulations and with the results of recent laboratory experiments where nonthermal electron acceleration was observed. This injection model represents a natural extension of DSA and could account for electron injection in high-Mach-number astrophysical shocks, such as those associated with young supernova remnants and accretion shocks in galaxy clusters. 

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2. Return Currents in Collisionless Shocks

   https://doi.org/10.3847/1538-4357/ad3e75  

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

   Abstract 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. 

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3. 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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4. Magnitude of Short-wavelength Electric Field Fluctuations in Simulations of Collisionless Plasma Shocks

   https://doi.org/10.3847/1538-4357/ae06a9  

   Roytershteyn, Vadim; Wilson, Lynn B; Chen, Li-Jen; Gedalin, Michael; Pogorelov, Nikolai (October 2025, The Astrophysical Journal)

   Large-amplitude electrostatic fluctuations are routinely observed by spacecraft upon traversal of collisionless shocks in the heliosphere. Kinetic simulations of shocks have struggled to reproduce the amplitude of such fluctuations, complicating efforts to un- derstand their influence on energy dissipation and shock structure. In this paper, 1D particle-in-cell simulations with realistic proton-to-electron mass ratio are used to show that in cases with upstream electron temperature Te exceeding the ion temperature Ti, the magnitude of the fluctuations increases with the electron plasma-to-cyclotron frequency ratio ωpe/Ωce, reaching realistic values at ωpe/Ωce ≳ 30. The large-amplitude fluctuations in the simulations are shown to be associated with electrostatic solitary structures, such as ion phase-space holes. In the cases where upstream temperature ratio is reversed, the magnitude of the fluctuations remains small. 

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5. Electrostatic Waves and Electron Holes in Simulations of Low-Mach Quasi-perpendicular Shocks

   https://doi.org/10.3847/1538-4357/ad6b0c  

   Bohdan, Artem; Tran, Aaron; Sironi, Lorenzo; Wilson, Lynn B (October 2024, The Astrophysical Journal)

   Abstract Collisionless low-Mach-number shocks are abundant in astrophysical and space plasma environments, exhibiting complex wave activity and wave–particle interactions. In this paper, we present 2D Particle-in-Cell (PIC) simulations of quasi-perpendicular nonrelativistic (v_sh≈ (5500–22000) km s⁻¹) low-Mach-number shocks, with a specific focus on studying electrostatic waves in the shock ramp and precursor regions. In these shocks, an ion-scale oblique whistler wave creates a configuration with two hot counterstreaming electron beams, which drive unstable electron acoustic waves (EAWs) that can turn into electrostatic solitary waves (ESWs) at the late stage of their evolution. By conducting simulations with periodic boundaries, we show that the EAW properties agree with linear dispersion analysis. The characteristics of ESWs in shock simulations, including their wavelength and amplitude, depend on the shock velocity. When extrapolated to shocks with realistic velocities (v_sh≈ 300 km s⁻¹), the ESW wavelength is reduced to one-tenth of the electron skin depth and the ESW amplitude is anticipated to surpass that of the quasi-static electric field by more than a factor of 100. These theoretical predictions may explain a discrepancy, between PIC and satellite measurements, in the relative amplitude of high- and low-frequency electric field fluctuations. 

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