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1. Phase-space Energization of Ions in Oblique Shocks

   https://doi.org/10.3847/1538-4357/acaf53  

   Juno, James; Brown, Collin R.; Howes, Gregory G.; Haggerty, Colby C.; TenBarge, Jason M.; Wilson III, Lynn B.; Caprioli, Damiano; Klein, Kristopher G. (February 2023, The Astrophysical Journal)

   Abstract Examining energization of kinetic plasmas in phase space is a growing topic of interest, owing to the wealth of data in phase space compared to traditional bulk energization diagnostics. Via the field-particle correlation (FPC) technique and using multiple means of numerically integrating the plasma kinetic equation, we have studied the energization of ions in phase space within oblique collisionless shocks. The perspective afforded to us with this analysis in phase space allows us to characterize distinct populations of energized ions. In particular, we focus on ions that reflect multiple times off the shock front through shock-drift acceleration, and how to distinguish these different reflected populations in phase space using the FPC technique. We further extend our analysis to simulations of three-dimensional shocks undergoing more complicated dynamics, such as shock ripple, to demonstrate the ability to recover the phase-space signatures of this energization process in a more general system. This work thus extends previous applications of the FPC technique to more realistic collisionless shock environments, providing stronger evidence of the technique’s utility for simulation, laboratory, and spacecraft analysis. 

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2. Velocity-space signatures of shock-drift acceleration at quasi-perpendicular collisionless shocks

   https://doi.org/10.1063/5.0269528  

   Howes, Gregory G; Felix, Alberto; Brown, Collin R; Haggerty, Colby C; Juno, James; TenBarge, Jason M; Wilson, Lynn B; Caprioli, Damiano (June 2025, Physics of Plasmas)

   The shock-drift acceleration of ions at quasi-perpendicular shocks is a well-known kinetic mechanism for the acceleration of a small fraction of incoming ions to high energy. Here, we use a suite of sixteen hybrid simulations of quasi-perpendicular collisionless shocks over the range of Alfvén Mach number 4.3≤MA≤15.8 (corresponding to a range of fast magnetosonic Mach numbers 2.6≤Mf≤9.4) and shock-normal angle 45°≤θBn≤90° to identify the velocity-space signature of shock-drift acceleration using the field-particle correlation technique. We show that the features of the ion velocity distribution in the shock foot and ramp regions can be clearly interpreted by analysis of the single-particle trajectory of a reflected ion through the full 3D-3V phase space. The characteristic features of the velocity-space signature of shock-drift acceleration remain qualitatively robust over the full parameter range of our simulations, providing a potential means for its identification using single-point spacecraft measurements. At higher Alfvén Mach numbers MA≳8 (Mf≳5), kinetic instabilities generate fluctuations of the electromagnetic fields within the shock transition region, leading to fluctuations in and smearing out of the resulting velocity-space signatures, but the signature remains generally robust and identifiable. The results on the shock-drift acceleration of ions presented here represent a novel means to determine more completely the partitioning of upstream bulk flow kinetic energy into plasma heating, particle acceleration, and electromagnetic fields in collisionless shocks. 

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3. A field–particle correlation analysis of a perpendicular magnetized collisionless shock

   https://doi.org/10.1017/S0022377821000623  

   Juno, James; Howes, Gregory G.; TenBarge, Jason M.; Wilson, Lynn B.; Spitkovsky, Anatoly; Caprioli, Damiano; Klein, Kristopher G.; Hakim, Ammar (August 2021, Journal of Plasma Physics)

   null (Ed.)

   Using the field–particle correlation technique, we examine the particle energization in a three-dimensional (one spatial dimension and two velocity dimensions; 1D-2V) continuum Vlasov–Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field–particle correlation technique with the high-fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons arising from the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov–Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field–particle correlation technique to spacecraft measurements of collisionless shocks. 

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4. 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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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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