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1. 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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2. In Situ Measurement of the Energy Fraction in Suprathermal and Energetic Particles at ACE, Wind, and PSP Interplanetary Shocks

   https://doi.org/10.3847/1538-4357/ac54af  

   David, Liam; Fraschetti, Federico; Giacalone, Joe; Wimmer-Schweingruber, Robert F.; Berger, Lars; Lario, David (March 2022, The Astrophysical Journal)

   Abstract The acceleration of charged particles by interplanetary shocks (IPs) can drain a nonnegligible fraction of the plasma pressure. In this study, we have selected 17 IPs observed in situ at 1 au by the Advanced Composition Explorer and the Wind spacecraft, and 1 shock at 0.8 au observed by Parker Solar Probe. We have calculated the time-dependent partial pressure of suprathermal and energetic particles (smaller and greater than 50 keV for protons and 30 keV for electrons, respectively) in both the upstream and downstream regions. The particle fluxes were averaged for 1 hr before and 1 hr after the shock time to remove short timescale effects. Using the MHD Rankine–Hugoniot jump conditions, we find that the fraction of the total upstream energy flux transferred to suprathermal and energetic downstream particles is typically ≲16%, in agreement with previous observations and simulations. Notably, by accounting for errors on all measured shock parameters, we have found that for any given fast magnetosonic Mach number, M f < 7, the angle between the shock normal and average upstream magnetic field, θ Bn , is not correlated with the energetic particle pressure; in particular, the partial pressure of energized particles does not decrease for θ Bn ≳ 45°. The downstream electron-to-proton energy ratio in the range ≳ 140 eV for electrons and ≳ 70 keV for protons exceeds the expected ∼1% and nears equipartition (>0.1) for the Wind events. 

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3. 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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4. Deep learning analysis of ions accelerated at shocks

   https://doi.org/10.1088/1475-7516/2026/06/071  

   Swierc, P; Caprioli, D; Orusa, L; Cernetic, M (June 2026, Journal of Cosmology and Astroparticle Physics)

   Abstract We study the application of deep learning techniques to the analysis and classification of ions accelerated at collisionless shocks in hybrid (kinetic ions-fluid electrons) simulations.Ions were classified as thermal, suprathermal, or non-thermal, depending on the energy they achieved and the acceleration regime they fell under. These classifications were used to train deep learning models to predict which particles are injected into the acceleration process with high accuracy (>90%), using only time series ofthe localmagnetic or electric field they experienced during their initial interaction with the shock.An autoencoder architecture was also tested, for which time series of various parameters were reconstructed from encoded representations.This study shows the potential of applying machine learning techniques to extract physical insights from kinetic plasma simulations and sets the groundwork for future applications, including the construction of sub-grid models in fluid approaches. 

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5. The Importance of Heat Flux in Low-Mach-number, Quasi-parallel Collisionless Shocks

   https://doi.org/10.3847/1538-4357/ae2acc  

   Haggerty, Colby C; Caprioli, Damiano; Cassak, Paul A; Barbhuiya, M Hasan; Wilson, Lynn; Turner, Drew L (February 2026, The Astrophysical Journal)

   Abstract Collisionless plasma shocks are a common feature of many space and astrophysical systems. They are sources of high-energy particles and nonthermal emission, channeling as much as 20% of the shock’s energy into nonthermal particles. The generation and acceleration of these nonthermal particles have been previously studied and shown to affect shock hydrodynamics to the zeroth order. In this work, we use self-consistent hybrid particle-in-cell simulations to examine the effect of self-generated nonthermal ion populations on the nature of collisionless, quasi-parallel shocks. Accelerated nonthermal particles downstream of the shock diffuse into the upstream region, taking energy away from the shock, which increases the compression ratio, slows the shock down, and flattens the nonthermal population’s spectral index for lower-Mach-number shocks. We show that this enhances shock compressibility when the heat flux is included in the Rankine–Hugoniot jump conditions, results that are roughly consistent with previous theories of “cosmic-ray-modified shocks.” Additionally, the simulation data show that heat flux and enthalpy flux cancels out in the upstream region, yielding a relatively simple, alternative closure for the jump conditions which accurately predict for the shock speed and compression ratio. The results have the potential to explain discrepancies between predictions and observations in a wide range of systems, such as inaccuracies in predictions of the arrival times of coronal mass ejections and the conflicting radio and X-ray observations of intracluster shocks. These effects will likely need to be included in fluid modeling to predict shock evolution accurately. 

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