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1. 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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2. Steep Cosmic-Ray Spectra with Revised Diffusive Shock Acceleration

   https://doi.org/10.3847/1538-4357/ac22fe  

   Diesing, Rebecca; Caprioli, Damiano (November 2021, The Astrophysical Journal)

   Abstract Galactic cosmic rays (CRs) are accelerated at the forward shocks of supernova remnants (SNRs) via diffusive shock acceleration (DSA), an efficient acceleration mechanism that predicts power-law energy distributions of CRs. However, observations of nonthermal SNR emission imply CR energy distributions that are generally steeper than E −2 , the standard DSA prediction. Recent results from kinetic hybrid simulations suggest that such steep spectra may arise from the drift of magnetic structures with respect to the thermal plasma downstream of the shock. Using a semi-analytic model of nonlinear DSA, we investigate the implications that these results have on the phenomenology of a wide range of SNRs. By accounting for the motion of magnetic structures in the downstream, we produce CR energy distributions that are substantially steeper than E −2 and consistent with observations. Our formalism reproduces both modestly steep spectra of Galactic SNRs (∝ E −2.2 ) and the very steep spectra of young radio supernovae (∝ E −3 ). 

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3. 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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4. Criteria for ion acceleration in laboratory magnetized quasi-perpendicular collisionless shocks: When are 2D simulations enough?

   https://doi.org/10.1063/5.0269035  

   Orusa, Luca; Valenzuela-Villaseca, Vicente (May 2025, Physics of Plasmas)

   The study of collisionless shocks and their role in cosmic ray acceleration has gained importance through observations and simulations, driving interest in reproducing these conditions in laboratory experiments using high-power lasers. In this work, we examine the role of three-dimensional (3D) effects in ion acceleration in quasi-perpendicular shocks under laboratory-relevant conditions. Using hybrid particle-in-cell (PIC) simulations (kinetic ions and fluid electrons), we explore how the Alfvénic and sonic Mach numbers, along with plasma beta, influence ion energization, unlocked only in 3D, and establish scaling criteria for when conducting 3D simulations is necessary. Our results show that efficient ion acceleration requires Alfvénic Mach numbers ≥25 and sonic Mach numbers ≥13, with plasma-β≤5. We theoretically found that, while two-dimensional (2D) simulations suffice for current laboratory-accessible shock conditions, 3D effects become crucial for shock velocities exceeding 1000 km/s and experiments sustaining the shock for at least 10 ns. We surveyed previous laboratory experiments on collisionless shocks and found that 3D effects are unimportant under those conditions, implying that one-dimensional and 2D simulations should be enough to model the accelerated ion spectra. However, we do find that the same experiments are realistically close to accessing the regime relevant to 3D effects, an exciting prospect for future laboratory efforts. We propose modifications to past experimental configurations to optimize and control 3D effects on ion acceleration. These proposed experiments could be used to benchmark plasma astrophysics kinetic codes and/or employed as controllable sources of energetic particles. 

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5. Evidence of Electron Acceleration via Nonlinear Resonant Interactions with Whistler-mode Waves at Foreshock Transients

   https://doi.org/10.3847/1538-4357/acd9ab  

   Shi, Xiaofei; Artemyev, Anton; Angelopoulos, Vassilis; Liu, Terry; Zhang, Xiao-Jia (July 2023, The Astrophysical Journal)

   Abstract Shock waves are sites of intense plasma heating and charged particle acceleration. In collisionless solar wind plasmas, such acceleration is attributed to shock drift or Fermi acceleration but also to wave–particle resonant interactions. We examine the latter for the case of electrons interacting with one of the most commonly observed wave modes in shock environments, the whistler mode. Such waves are particularly intense in dynamic, localized regions upstream of shocks, arising from the kinetic interaction of the shock with solar wind discontinuities. These regions, known as foreshock transients, are also sites of significant electron acceleration by mechanisms not fully understood. Using in situ observations of such transients in the Earth’s foreshock, we demonstrate that intense whistler-mode waves can resonate nonlinearly with >25 eV solar wind electrons and accelerate them to ∼100–500 eV. This acceleration is mostly effective for the 50–250 eV energy range, where the accelerated electron population exhibits a characteristic butterfly pitch-angle distribution consistent with theoretical predictions. Such nonlinear resonant acceleration is very fast, implying that this mechanism may be important for injecting suprathermal electrons of solar wind origin into the shock region, where they can undergo further, efficient shock-drift acceleration to even higher energies. 

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