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1. Flat Spectra of Energetic Particles in Interplanetary Shock Precursors

   https://doi.org/10.3847/1538-4357/ad631e  

   Malkov, Mikhail; Giacalone, Joe; Guo, Fan (September 2024, The Astrophysical Journal)

   Zank, Gary (Ed.)

   Abstract The observed energy spectra of accelerated particles at interplanetary shocks often do not match the diffusive shock acceleration (DSA) theory predictions. In some cases, the particle flux forms a plateau over a wide range of energies, extendingupstream of the shockfor up to seven fluxe-folds before submerging into the background spectrum. Remarkably, at and downstream of the shock we have studied in detail, the flux falls off in energy asϵ⁻¹, consistent with the DSA prediction for a strong shock. The upstream plateau suggests a particle transport mechanism different from those traditionally employed in DSA models. We show that a standard (linear) DSA solution based on a widely accepted diffusive particle transport with an underlying resonant wave–particle interaction is inconsistent with the plateau in the particle flux. To resolve this contradiction, we modify the DSA theory in two ways. First, we include a dependence of the particle diffusivityκon the particle fluxF(nonlinear particle transport). Second, we invoke short-scale magnetic perturbations that are self-consistently generated by, but not resonant with, accelerated particles. They lead to the particle diffusivity increasing with the particle energy as ∝ϵ^3/2that simultaneously decreases with the particle flux as 1/F. The combination of these two trends results in the flat spectrum upstream. We speculate that nonmonotonic spatial variations of the upstream spectrum, apart from being time-dependent, may also result from non-DSA acceleration mechanisms at work upstream, such as stochastic Fermi or magnetic pumping acceleration. 

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2. 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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3. Species‐Dependent and Azimuthally‐Directional Flux Changes of Dispersionless Ion Injections Inside Geosynchronous Orbit

   https://doi.org/10.1029/2025JA033757  

   Motoba, T; Ohtani, S (June 2025, Journal of Geophysical Research: Space Physics)

   Abstract Dispersionless injection, involving sudden, simultaneous flux enhancements of energetic particles over a broad range of energy, is a characteristic signature of the particles that are experiencing a significant acceleration and/or rapid inward transport process. To provide clues to the physical processes that lead to the acceleration and transport of energetic ions in the dispersionless injection region, we conduct superposed epoch analyses of 75 dispersionless injection events identified by Van Allen Probes with focus on the species‐ and azimuthal angle‐ (φ) dependent signatures of ∼50–600 keV ions inside geosynchronous orbit. Our analysis shows that, on average, the light (hydrogen and helium) ion fluxes undergo a rapid, transient enhancement, while the heavy (oxygen) ion fluxes exhibit a more gradual, persisting enhancement. Such a species‐dependent behavior could be explained in terms of different gyro‐radius of the ion species. For events where the proton injection onset is 30–60 s earlier than the electron one, proton fluxes initially increase at smallφvalues (i.e., tailward guiding centers) and then at largerφvalues (earthward ones). The initial signatures suggest a result of the earthward transport of injected protons, as seen at the explosive growth phase. For events where both electron and proton fluxes increase simultaneously, on the other hand, proton fluxes isotropically increase with no significantφdependence. Such an isotropic proton flux enhancement may imply a local process in which charged protons are rapidly accelerated to higher energies at the spacecraft location. 

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4. 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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5. Diffusive shock re-acceleration

   https://doi.org/10.1017/S0022377818000478  

   Caprioli, Damiano; Zhang, Horace; Spitkovsky, Anatoly (June 2018, Journal of Plasma Physics)

   We have performed two-dimensional hybrid simulations of non-relativistic collisionless shocks in the presence of pre-existing energetic particles (‘seeds’); such a study applies, for instance, to the re-acceleration of galactic cosmic rays (CRs) in supernova remnant (SNR) shocks and solar wind energetic particles in heliospheric shocks. Energetic particles can be effectively reflected and accelerated regardless of shock inclination via a process that we call diffusive shock re-acceleration. We find that re-accelerated seeds can drive the streaming instability in the shock upstream and produce effective magnetic field amplification. This can eventually trigger the injection of thermal protons even at oblique shocks that ordinarily cannot inject thermal particles. We characterize the current in reflected seeds, finding that it tends to a universal value $$J\simeq en_{\text{CR}}v_{\text{sh}}$$ , where $$en_{\text{CR}}$$ is the seed charge density and $$v_{\text{sh}}$$ is the shock velocity. When applying our results to SNRs, we find that the re-acceleration of galactic CRs can excite the Bell instability to nonlinear levels in less than $${\sim}10~\text{yr}$$ , thereby providing a minimum level of magnetic field amplification for any SNR shock. Finally, we discuss the relevance of diffusive shock re-acceleration also for other environments, such as heliospheric shocks, galactic superbubbles and clusters of galaxies. 

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