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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Planar Collisionless Shock Simulations with the Semi-implicit Particle-in-cell Model FLEKS

This study investigates the applicability of the semi-implicit particle-in-cell code FLexible Exascale Kinetic Simulator (FLEKS) to heliospheric shock simulations. We examine one- and two-dimensional local planar shock simulations, initialized using MHD states with upstream conditions representative of plasmas in the hypersonic, β ∼ 1 regime, for both quasi-perpendicular and quasi-parallel configurations. The refined algorithm in FLEKS proves robust, enabling accurate shock simulations with a grid resolution on the order of the electron inertial length d e . Our simulations successfully capture key shock features, including shock structures (foot, ramp, overshoot, and undershoot), upstream and downstream waves (fast magnetosonic, whistler, Alfvén ion-cyclotron, and mirror modes), and non-Maxwellian particle distributions. Crucially, we find that at least two spatial dimensions are critical for accurately reproducing downstream-wave physics in quasi-perpendicular shocks and capturing the complex dynamics of quasi-parallel shocks, including surface rippling, shocklets, short, large-amplitude magnetic structures, magnetic reconnection, and jets. Furthermore, our parameter studies demonstrate the impact of mass ratio and grid resolution on shock physics. This work provides valuable guidance for selecting appropriate physical and numerical parameters for shock simulations using a semi-implicit PIC method, paving the way for incorporating kinetic shock processes into large-scale collisionless plasma simulations with the MHD-AEPIC model.

plasma astrophysics↗
DOE OSTI2020

Laser-driven collisionless shock acceleration of ions from near-critical plasmas

Here, this paper overviews experimental and numerical results on acceleration of narrow energy spread ion beams by an electrostatic collisionless shockwave driven by 1 μm (Omega EP) and 10 μm (UCLA Neptune Laboratory) lasers in near critical density CH and He plasmas, respectively. Shock waves in CH targets produced high-energy ~50 MeV protons (ΔE/E of ≤30%) and 314 MeV C 6+ ions (ΔE/E of ≤10%). Observation of acceleration of both protons and carbon ions to similar velocities is consistent with reflection of particles off the moving potential of a shock front. For shocks driven by CO 2 laser in a gas jet, ~30 MeV peak in He ion spectrum was detected. Particle-in-cell simulations indicate that regardless of the target further control over its density profile is needed for optimization of accelerated ion beams in part of energy spread, yield and maximum kinetic energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Electron–Ion Temperature Ratio in Astrophysical Shocks

Collisionless shock waves in supernova remnants and the solar wind heat electrons less effectively than they heat ions, as is predicted by kinetic simulations. However, the values of T e /T p inferred from the Hα profiles of supernova remnant shocks behave differently as a function of Mach number or Alfvén Mach number than what is measured in the solar wind or predicted by simulations. Here we determine T e /T p for supernova remnant shocks using Hα profiles, shock speeds from proper motions, and electron temperatures from X-ray spectra. We also improve the estimates of sound speed and Alfvén speed used to determine Mach numbers. We find that the Hα determinations are robust and that the discrepancies among supernova remnant shocks, solar wind shocks, and computer-simulated shocks remain. We discuss some possible contributing factors, including shock precursors, turbulence, and varying preshock conditions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Electron energization dynamics in interaction of self-generated magnetic vortices in upstream of collisionless electron/ion shocks

Abstract Relativistic collisionless shocks are considered responsible for particle energization mechanisms leading to particle acceleration. While electron energization in shock front region of electron/ion collisionless shocks are the most studied, the mechanism of electron energization in interaction with self-generated magnetic vortices (MVs) in the upstream region is still unclear. We investigate electron energization mechanism in the upstream region of electron/ion relativistic collisionless shocks, using two dimensional particle-in-cell (PIC) simulations. We discuss mechanism of electron energization which takes place in the upstream region of the shock, where the counter stream particles interact with incoming flow. The energy gain of electrons happens during their interaction with evolving fields of self-generated magnetic vortices in this region. Three Fermi-like electron energization scenarios are discussed. Stochastic acceleration of electrons in interaction with fields of MV leads to anisotropic heating of fast electrons due to diffusion in the momentum space of electrons and, finally, synergetic effect of evolving fields of MVs leads to the formation of a power-law tail of supra-thermal particles.

Naseri, N.↗
DOE OSTI2021

Fermi acceleration in relativistic collisionless plasma shocks correlates with anisotropic energy gains

Collisionless shocks generated by two colliding relativistic electron-positron plasma shells are studied using particle-in-cell simulations. Shocks are mediated by the Weibel instability (WI), and the kinetic energy of the fastest accelerated particles is found to be anisotropically modified by WI-induced electric fields. Specifically, we show that all particles interacting with the shock bifurcate into two groups based on their final relativistic Lorentz factor γ: slow (γ < γ bf ) and fast (γ < γ bf ), where γ bf is the bifurcation Lorentz factor that was found to be approximately twice the initial (upstream) Lorentz factor γ0. We have found that the kinetic energies of the slow particles are equally affected by the longitudinal and transverse components of the shock electric field, whereas the fast particles are primarily accelerated by the transverse field component.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

The structure of cluster merger shocks: turbulent width and the electron heating time-scale

We present a new 2MsChandra observation of the cluster merger Abell 2146, which hosts two huge M ~ 2 shock fronts each ~500 kpc across. For the first time, we resolve and measure the width of cluster merger shocks. The best-fitting width for the bow shock is 17 ± 1kpc and for the upstream shock is 10.7 ± 0.3 kpc. A narrow collisionless shock will appear broader in projection if its smooth shape is warped by local gas motions. We show that both shock widths are consistent with collisionless shocks blurred by local gas motions of 290 ± 30 km s –1 . The upstream shock forms later on in the merger than the bow shock and is therefore expected to be significantly narrower. From the electron temperature profile behind the bow shock, we measure the time-scale for the electrons and ions to come back into thermal equilibrium. We rule out rapid thermal equilibration of the electrons with the shock-heated ions at the 6σ level. The observed temperature profile instead favours collisional equilibration. For these cluster merger shocks, which have low sonic Mach numbers and propagate through a high β plasma, we find no evidence for electron heating over that produced by adiabatic compression. Our findings are expected to be valid for collisionless shocks with similar parameters in other environments and support the existing picture from the solar wind and supernova remnants. Furthermore, the upstream shock is consistent with this result but has a more complex structure, including a ~2ke V increase in temperature ~50 kpc ahead of the shock.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Flux Ropes, Turbulence, and Collisionless Perpendicular Shock Waves: High Plasma Beta Case

With the onset of solar maximum and the expected increased prevalence of interplanetary shock waves, Parker Solar Probe is likely to observe numerous shocks in the next few years. An outstanding question that has received surprisingly little attention has been how turbulence interacts with collisionless shock waves. Turbulence in the supersonic solar wind is described frequently as a superposition of a majority 2D and a minority slab component. Here we formulate a collisional perpendicular shock-turbulence transmission problem in a way that enables investigation of the interaction and transmission of quasi-perpendicular fluctuations such as magnetic flux ropes/islands and vortices as well as entropy and acoustic modes in the large plasma beta regime. We focus on the transmission of an upstream spectrum of these modes, finding that the downstream spectral amplitude is typically increased significantly (a factor of 10 or more), and that the upstream spectral index of the inertial range, and indeed the general spectral shape, is unchanged for the downstream magnetic variance, kinetic energy, and density variance. A comparison of the theoretically predicted downstream magnetic variance, kinetic energy, and density variance spectra with those observed at 1, 5, and 84 au by Wind, Ulysses, and Voyager 2 shows excellent agreement. The overall theoretically predicted characteristics of the transmission of turbulence across shocks observed in the solar wind appear to be largely consistent with recent observational studies by Pitňa et al. and Borovsky.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Collaborative Research: Vlasov-Maxwell Simulations to Resolve Electron Heating and Dissipation, in Quasi-Perpendicular Shocks (Final Report)

Collisionless shocks are a grand challenge problem in plasma physics and have been the subject of study for more than six decades. Shocks are ubiquitous phenomena in the universe and are responsible for transforming high energy and momentum flows into thermal energy and energetic particles. Understanding how shocks operate is of primary importance to understand the sun-earth coupling, protecting manned missions and spacecrafts from high energy particles, inertial confinement fusion, and radiation observed from astrophysical plasmas, such as supernova remnants and astrophysical jets. A major unanswered question on this frontier is, how does a collisionless plasma transform flow energy and momentum into electron thermal energy? Many potential mechanisms have been proposed to perform the conversion between flow and thermal energy in a collisionless plasma, but the answer has been elusive. To solve the mystery, non-relativistic perpendicular and quasi-perpendicular shocks are studied via a coordinated approach employing cutting-edge numerical simulations with the continuum kinetic code Gkeyll and spacecraft observations supplied by NASA's Magnetospheric Multiscale (MMS) mission. In both sets of data, we employ novel techniques to identify how and where energy is exchanged between electromagnetic fields and plasma particles. By combining cutting-edge spacecraft data and numerical simulations with these diagnostics, we have been able to identify some of the primary mechanisms responsible electron heating and dissipation in heliospheric shocks. In addition to electron dynamics, we have complete access to proton simulation and in situ data, enabling us to characterize proton heating and acceleration in quasi-perpendicular shocks. Many astrophysical quasi-perpendicular shocks have similar parameters to those in this study, including supernova remnants and shocks in galaxy clusters. Additionally, the simulation code, Gkeyll, and associated analysis scripts are openly available for community use. This award has supported a collaborative effort between Princeton University, the University of Arizona - Tucson, and the University of Maryland - College Park. The award funded three early career scientists, including the funding and training of one female postdoctoral researcher, who was involved in all aspects of the MMS data analysis and some portions of the simulation analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Maximum Energy of Particles Accelerated in Gamma-Ray Burst Afterglow Shocks

Particle acceleration in relativistic collisionless shocks remains an open problem in high-energy astrophysics. Particle-in-cell (PIC) simulations predict that electron acceleration in weakly magnetized shocks proceeds via small-angle scattering, leading to a maximum electron energy significantly below the Bohm limit. This upper bound on electron energy manifests observationally as a characteristic synchrotron cutoff, providing a direct probe of the underlying acceleration physics. Gamma-ray burst (GRB) afterglows offer an exceptional laboratory for testing these predictions. Here, we model the spectral evolution of GRB afterglows during the relativistic deceleration phase, incorporating PIC-motivated acceleration prescriptions and self-consistently computing synchrotron and synchrotron self-Compton emission. We find that low-energy bursts in low-density environments, typical of short GRBs, exhibit a pronounced synchrotron cutoff in the GeV band within minutes to hours after the trigger. Applying our framework to GRB 190114C and GRB 130427A, we find that current observations are insufficient to discriminate between PIC-motivated acceleration and the Bohm limit, primarily due to poor photon statistics in the Fermi-Large Area Telescope band. Nevertheless, future MeV–TeV afterglow observations can break model degeneracies and place substantially tighter constraints on the mechanisms responsible for particle acceleration in relativistic shocks. To this end, we simulate a fiducial nearby short GRB as a promising probe of the cutoff location, for which the two acceleration scenarios are cleanly distinguishable and the detection of such an event in the near future remains feasible.

Wu, Zhao-Feng [Purdue University, West Lafayette, ↗
DOE OSTI2023

Phase-space Energization of Ions in Oblique Shocks

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.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

The Role of Three-dimensional Effects on Ion Injection and Acceleration in Perpendicular Shocks

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.

Orusa, Luca [Princeton Univ., NJ (United States); ↗
DOE OSTI2023

Particle-in-cell Simulations of Mildly Relativistic Outflows in Kilonova Emissions

Abstract The electromagnetic emission from neutron star mergers is comprised of multiple components. Synchrotron emission from the disk-powered jet and thermal emission from the merger ejecta (powered by a variety of sources) are among the most studied sources. The low masses and high velocities of the merger ejecta quickly develop conditions where emission from collisionless shocks becomes critical and synchrotron emission from the merger ejecta constitutes a third component to the observed signal. The aim of this project is to examine shock development, magnetic field generation, and particle acceleration in the case of mildly relativistic shocks, which are expected when the tidal ejecta of neutron star mergers drive a shock into the external medium. Using LANL’s vector particle-in-cell (VPIC) code, we have run simulations of such mildly relativistic, collisionless, weakly magnetized plasmas and computed the resultant magnetic fields and particle energy spectra. We show the effects of varying plasma conditions, as well as explore the validity of using different proton-to-electron mass ratios in VPIC. Our results have implications for observing late-time electromagnetic counterparts to gravitational wave detections of neutron star mergers.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Electron cyclotron drift instability and anomalous transport: two-fluid moment theory and modeling

In the presence of a strong electric field perpendicular to the magnetic field, the electron cross-field (E × B) flow relative to the unmagnetized ions can cause the so-called electron cyclotron drift instability (ECDI) due to resonances of the ion acoustic mode and the electron cyclotron harmonics. This occurs in, for example, collisionless shock ramps in space, and in E × B discharge devices such as Hall thrusters. A prominent feature of ECDI is its capability to induce an electron flow parallel to the background >E field at a speed greatly exceeding predictions by classical collision theory. Such anomalous transport is important due to its role in particle thermalization at space shocks, and in causing plasma flows towards the walls of E × B devices, leading to unfavorable erosion and performance degradation, etc. The development of ECDI and anomalous transport is often considered requiring a fully kinetic treatment. In this work, however, we demonstrate that a reduced variant of this instability, and more importantly, the associated anomalous transport, can be treated self-consistently in a collisionless two-fluid framework without any adjustable collision parameter. By treating both electron and ion species on an equal footing, the free energy due to the inter-species velocity shear allows the growth of an anomalous electron flow parallel to the background E field. We will first present linear analyses of the instability in the two-fluid five- and ten-moment models, and compare them against the fully-kinetic theory. At low temperatures, the two-fluid models predict the fastest-growing mode in good agreement with the kinetic result. Also, by including more (> = 10) moments, secondary (and possibly higher) unstable branches can be recovered. The dependence of the instability on ion-to-electron mass ratio, plasma temperature, and background B field strength is also thoroughly explored. We then carry out direct numerical simulations of the cross-field setup using the five-moment model. The development of the instability, as well as the anomalous transport, is confirmed and in excellent agreement with theoretical predictions. The force balance properties are also studied using the five-moment simulation data. Here this work casts new insights into the nature of ECDI and the associated anomalous transport and demonstrates the potential of the two-fluid moment model in efficient modeling of E × B plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗