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DOE OSTI2025

Particle collisionality in scaled kinetic plasma simulations

Kinetic plasma processes, such as magnetic reconnection, collisionless shocks, and turbulence, are fundamental to the dynamics of astrophysical and laboratory plasmas. Simulating these processes often requires particle-in-cell (PIC) methods, but the computational cost of fully kinetic simulations can necessitate the use of artificial parameters, such as a reduced speed of light and ion-to-electron mass ratio, to decrease expense. While these approximations can preserve overall dynamics under specific conditions, they introduce nontrivial impacts on particle collisionality that are not yet well understood. In this work, we develop a method to scale particle collisionality in simulations employing an artificial speed of light and/or an artificial ion-to-electron mass ratio. By introducing species-dependent scaling factors, we independently adjust inter- and intra-species collision rates to better replicate the collisional properties of the physical system. Our approach maintains the fidelity of electron and ion transport properties while preserving critical relaxation rates, such as energy exchange timescales, within the limits of weakly collisional plasma theory. Furthermore, we demonstrate the accuracy of this scaling method through benchmarking tests against theoretical relaxation rates and connecting to fluid theory, highlighting its ability to retain key transport properties. Existing collisional PIC implementations can be easily modified to include this scaling, which will enable deeper insights into the behavior of marginally collisional plasmas across various contexts.

Totorica, S. R. [Princeton Univ., NJ (United State↗

DOE OSTI2026

Machine learning surrogates for ion energy–angle distributions in thermal and RF plasma sheaths

Ion energy–angle distributions (IEADs) at material surfaces are a critical input for plasma–material interaction (PMI) studies in fusion devices, yet they are computationally expensive to obtain using particle-in-cell (PIC) simulations. In this work, we develop a machine learning surrogate based on a deep deconvolutional neural network (DDeCNN) trained on large databases generated with the hPIC2 code. The surrogate is capable of reconstructing IEADs from sheath parameters for both thermal and radio-frequency (RF) plasmas, including cases with multiple ion species. Across thousands of test cases, the model achieves high accuracy, with over 97 % of predictions classified as good or average based on standard error metrics (MAE, MSE, L2). Even in the more challenging RF and multi-species regimes, the surrogate reliably captures the multi-peak structure of PIC results. Once trained, the surrogate produces IEADs in milliseconds on a common workstation, yielding speedups of six to seven orders of magnitude compared with running a full PIC simulation. This computational gain enables dense parameter scans and direct coupling of IEAD predictions with PMI and erosion models on whole-device scales in fusion-relevant conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Calculating the space-charge-limited current density for nonplanar geometries by simulating the charge-free electric field

Calculating the space-charge-limited-current density (SCLCD) for a complicated diode geometry often requires computationally expensive particle-in-cell (PIC) codes. Here, this paper addresses this issue by using the charge-free electric field $E_0$ calculated using COMSOL Multiphysics to determine local and global SCLCD. The SCLCD obtained by using the surface average of $|E_0|^2$ on the cathode recovers theoretical results for one-dimensional (1D) planar, cylindrical, and tip-to-tip geometries in appropriate limits. We next compared tip-to-tip calculations with the SCLCD obtained using the PIC code Empire. The SCLCD calculated using COMSOL agreed well with Empire for flatter 1D tip-to-tip geometries and diverged with increasing sharpness. Physically, Empire predicts lower SCLCD than COMSOL because the electrons spread due to concentrated space-charge at the tip, whereas theory assumes that the electrons follow the charge-free electric field lines. We further assess the behavior of the SCLCD for tips protruding from the centers of flat, circular plates of various areas. Larger plate areas with constant tip size recover the 1D planar SCLCD globally and 1D tip-to-tip SCLCD locally, while reducing the difference between Empire and COMSOL calculations since larger plates capture more of the emitted electrons, reducing SCLCD suppression due to beam spreading. These results show that charge-free electric field simulations can be used to determine the SCLCD without needing to simulate particle dynamics in PIC.

Wright, Jack K. [Purdue Univ., West Lafayette, IN ↗

DOE OSTI2026

Collider-quality electron bunches from an all-optical plasma photoinjector

We present an approach for generating collider-quality electron bunches using a plasma photoinjector. The approach leverages recently developed techniques for the spatiotemporal control of laser pulses to produce a moving ionization front in a nonlinear plasma wave. The moving ionization front generates an electron bunch with a current profile that balances the longitudinal electric field of an electron beam-driven plasma wave, creating a uniform accelerating field across the bunch. Particle-in-cell (PIC) simulations of the ionization stage show the formation of an electron bunch with 220 pC charge and low emittance (ɛ 𝑥 = 171 nm rad, ɛ 𝑦 = 76 nm rad). Quasistatic PIC simulations of the acceleration stage show that the bunch is efficiently accelerated to 24 GeV over 2 m with a final energy spread of less than 1% and emittances of ɛ 𝑥 = 189 nm rad and ɛ 𝑦 = 80 nm rad. This high-quality electron bunch meets the requirements outlined by the Snowmass process for intermediate-energy colliders and compares favorably to the beam quality of proposed and existing accelerator facilities. The results establish the feasibility of plasma photoinjectors for future collider applications making a significant step toward the realization of high-luminosity, compact accelerators for particle physics research.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Expansion-Driven Self-Magnetization of High-Energy-Density Plasmas

Understanding plasma self-magnetization is one of the fundamental challenges in both laboratory and astrophysical plasmas. Self-magnetization can modify plasma transport properties, altering the dynamical evolution of plasmas. Multiple high-energy-density (HED) experiments have observed the formation of ion-scale magnetic filaments of megagauss strength, though their origin remains debated. Here, in this study, we conduct 2D collisional particle-in-cell (PIC) simulations with a laser ray-tracing module for a fully self-consistent simulation of the plasma ablation, expansion, and magnetization. The simulations use a planar geometry, effectively suppressing the Biermann magnetic fields, to focus on anisotropy-driven instabilities. The laser intensity is varied between 10 13 and 10 14 W/cm 2 , which is relevant to HED and inertial fusion experiments where collisions must be considered. We find that, above a critical intensity, the plasma rapidly self-magnetizes via an expansion-driven Weibel process, producing a plasma beta of 100 (𝛽 = 8⁢𝜋⁢𝑘 𝐵 ⁢𝑛 𝑒 ⁢𝑇 𝑒 /𝐵 2 ) and Hall parameter 𝜔 ce ⁢𝜏 𝑒 >1 within the first few hundred picoseconds. The magnetic field is sufficiently strong to modify plasma heat transport, and simulations with an artificially suppressed magnetic field show noticeably different temperature profiles.

Lezhnin, K. V. [Princeton Plasma Physics Laborator↗

DOE OSTI2025

Addressing key physics problems in high-energy-density plasmas with a novel kinetic simulation capability

Many important physical processes in inertial confinement fusion (ICF) and dense Z-pinch (DZP) experiments require a kinetic (velocity-space-dependent) description. Conventional particle-in-cell (PIC) methods are poorly suited for high-energy-density (HED) plasmas, due to restrictive time-step constraints and the inability to conserve energy. In a previous LDRD (21-FS-048), we demonstrated that a fully implicit PIC formulation overcomes these limitations: it conserves energy even when coupled with Coulomb collision models and can be solved efficiently with large grid cells and large time steps. Thus, it is feasible to use this method to study kinetic effects in ICF and DZP plasmas on hydro-like time and spatial scales. In this follow-on LDRD, we advanced this methodology into a high-fidelity tool for production-scale simulations and used it to answer key questions relevant to ICF and DZP experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

The Effect of Inverse Compton Losses on Particle Acceleration in Three-dimensional Relativistic Reconnection

Relativistic magnetic reconnection is a key mechanism for dissipating magnetic energy and accelerating particles in astrophysics. In the absence of radiative cooling, recent particle-in-cell (PIC) simulations have shown that high-energy particles gain most of their energy in the upstream region, during a short-lived “free phase” where they meander between the two sides of the layer; when they get captured/trapped by the downstream flux ropes, they undergo a “trapped phase,” where no significant energization occurs. Here, we perform a suite of 3D PIC simulations of relativistic reconnection, including inverse Compton (IC) losses in the weakly cooled regime in which the radiation-reaction-limited Lorentz factor γrad exceeds the magnetization σ. We show that electron cooling losses do not appreciably alter the reconnection rate, the structure of the layer, and the physics of particle acceleration in the free phase, so the spectrum of free electrons is dN free /dγ ∝ γ −1 , as in the uncooled case. The spectrum of trapped electrons above the cooling break γcool (in the range γ cool < γ < γ rad ) is dN/dγ ∝ γ −3 , steeper than the scaling dN/dγ ∝ γ −2 of uncooled simulations. This confirms that no significant particle energization occurs during the trapped phase. Our results validate the model by Zhang et al. for particle acceleration in 3D relativistic reconnection, and imply that radiative emission models of reconnection-powered astrophysical sources should employ a two-zone structure that differentiates between free, rapidly accelerating particles and trapped, passively cooling particles.

79 ASTRONOMY AND ASTROPHYSICS↗

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 OSTI2026

Entity—Hardware-agnostic Particle-in-cell Code for Plasma Astrophysics. I. Curvilinear Special Relativistic Module

Entity is a new-generation, fully open-source particle-in-cell (PIC) code developed to overcome key limitations in astrophysical plasma modeling, particularly the extreme separation of scales and the performance challenges associated with evolving, GPU-centric computing infrastructures. It achieves hardware-agnostic performance portability across various GPU and CPU architectures using the Kokkos library. Crucially, Entity maintains a high standard for usability, clarity, and customizability, offering a robust and easy-to-use framework for developing new algorithms and grid geometries, which allows extensive control without requiring edits to the core source code. This paper details the core general-coordinate special relativistic module. Entity is the first PIC code designed to solve the Vlasov–Maxwell system in general coordinates, enabling a coordinate-agnostic framework that provides the foundational structure for straightforward extension to arbitrary coordinate geometries. The core methodology achieves numerical stability by solving particle equations of motion in the global orthonormal Cartesian basis, despite using generalized coordinates like Cartesian, axisymmetric spherical, and quasi-spherical grids. Charge conservation is ensured via a specialized current deposition technique using conformal currents. The code exhibits robust scalability and performance portability on major GPU platforms (AMD MI250X, NVIDIA A100, and Intel Max Series), with the 3D particle pusher and the current deposition operating efficiently at about 2 ns per particle per time step. Functionality is validated through a comprehensive suite of standard Cartesian plasma tests and the accurate modeling of relativistic magnetospheres in curvilinear axisymmetric geometries.

Hakobyan, Hayk [Flatiron Institute, New York, NY (↗

DOE OSTI2026

The effect of inverse Compton losses on particle acceleration in three-dimensional relativistic reconnection

Relativistic magnetic reconnection is a key mechanism for dissipating magnetic energy and accelerating particles in astrophysics. In the absence of radiative cooling, recent particle-in-cell (PIC) simulations have shown that high-energy particles gain most of their energy in the upstream region, during a short-lived "free phase" where they meander between the two sides of the layer; when they get captured/trapped by the downstream flux ropes, they undergo a "trapped phase", where no significant energization occurs. Here, we perform a suite of 3D PIC simulations of relativistic reconnection including inverse Compton (IC) losses in the weakly cooled regime in which the radiation-reaction-limited Lorentz factor $γ_{\rm rad}$ exceeds the magnetization $σ$. We show that electron cooling losses do not appreciably alter the reconnection rate, the structure of the layer, and the physics of particle acceleration in the free phase, so the spectrum of free electrons is $dN_{\rm free}/dγ\propto γ^{-1}$, as in the uncooled case. The spectrum of trapped electrons above the cooling break $γ_{\rm cool}$ (in the range $γ_{\rm cool}<γ<γ_{\rm rad}$) is $dN/dγ\propto γ^{-3}$, steeper than the scaling $dN/dγ\propto γ^{-2}$ of uncooled simulations. This confirms that no significant particle energization occurs during the trapped phase. Our results validate the model by arXiv:2302.12269 for particle acceleration in 3D relativistic reconnection, and imply that radiative emission models of reconnection-powered astrophysical sources should employ a two-zone structure, that differentiates between free, rapidly accelerating particles and trapped, passively cooling particles.

FOS: Physical sciences↗

DOE OSTI2026

A Structure-Preserving Decorated Particle Method for the Vlasov-Poisson System

We revisit the Scovel-Weinstein framework (Scovel & Weinstein, CPAM 1994) for reducing the Vlasov-Poisson system while preserving its Hamiltonian structure. Standard particle-in-cell (PIC) algorithms approximate the distribution function by macro-particles with position and velocity. In contrast, Scovel-Weinstein decorated particles involve additional shape degrees of freedom, while maintaining a finite-dimensional reduction with Hamiltonian structure inherited from the continuum model. Although the original work established this structure three decades ago, its computational potential has remained largely unexplored. We present a practical implementation of the Scovel-Weinstein model and compare it with a standard PIC algorithm. Numerical experiments demonstrate that macro-particles in standard PIC can be replaced by far fewer decorated particles while retaining comparable accuracy. This decorated particle approach offers a new structure-preserving paradigm for kinetic plasma simulation.

65M75, 70H05, 70G65↗

DOE OSTI2026

Machine Learning for Multipactor Susceptibility Prediction in Planar RF Gaps

Multipactor discharge is a nonlinear electron avalanche that limits the performance of high-power radio-frequency (RF) and vacuum electronic devices. Predicting multipactor susceptibility traditionally relies on Monte Carlo or particle-in-cell (PIC) simulations, which become computationally expensive for large parametric studies. In this work, we present a supervised machine-learning (ML) framework for prediction of multipactor susceptibility in a two-surface planar geometry. The models are trained using high-fidelity PIC simulation generated susceptibility data and learn the relationship between operational parameters, geometry, and material-dependent secondary electron emission properties. The proposed approach enables rapid reconstruction of susceptibility charts while preserving the physical structure of multipactor growth regions.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Two-Frequency RF Fields Induced Multipactor in Coaxial Transmission Lines

Multipactor is a nonlinear discharge phenomenon that occurs in vacuum RF systems, potentially leading to signal distortion, power loss, and even permanent damage to high-power components. This study presents a detailed investigation of two-surface multipactor in coaxial transmission lines under two-frequency excitation, using one-dimensional (1D) Monte Carlo simulations validated by three-dimensional (3D) Particle-in-Cell (PIC) results and experimental data. Introducing a second carrier mode is shown to suppress multipactor by reshaping and shrinking the susceptibility region, with the extent and location of suppression strongly dependent on the device aspect ratio and the relative phase of the second mode. Distinct suppression patterns emerge across different frequency–gap distance (fd) regimes, and in certain cases, susceptibility expansion is also observed. The study identifies and distinguishes pure and mixed multipactor modes in coaxial geometry, where analytical mode boundaries are not readily defined. Unlike planar systems, pure-mode regions in coaxial structures overlap with mixed-mode domains, complicating classification. Image charge forces are found to have minimal effect on susceptibility thresholds but do influence electron growth rates. These findings provide new insights into waveform-driven control of multipactor in high-power RF systems.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Machine Learning for Predicting Multipactor Susceptibility in Planar RF Structures

Multipactor discharge is a persistent challenge in high-power microwave (HPM) and accelerator systems, where secondary electron avalanches can cause heating, vacuum degradation, and failure. This work presents the first supervised machine learning (ML) framework for multipactor prediction, trained on high-fidelity 3D Particle-in-Cell (PIC) simulation data in planar geometries. The model maps operational, geometric, and material-dependent secondary electron yield (SEY) parameters to the time-averaged electron growth rate, enabling rapid reconstruction of susceptibility charts. Among the models evaluated, tree-based ensemble methods such as Random Forest and Extra Trees demonstrate superior generalization to unseen materials compared to neural networks such as multilayer perceptron (MLP). Performance metrics, including Intersection over Union (IoU), Structural Similarity Index Measure (SSIM), and Pearson correlation, show close agreement with simulation benchmarks. Principal Component Analysis attributes generalization limits to material feature-space disjointedness.

43 PARTICLE ACCELERATORS↗

DOE OSTI2026

Onset of Fluidization in MP-PIC Simulations using MFIX-Exa

Fluidized bed reactors are used across a variety of industries, including for energy processes like pyrolysis that result in low-cost energy products. Design and scale-up of fluidized beds is de-risked by modeling and simulation, utilizing tools like NETL’s MFIX-Exa High-Performance Computing (HPC) code for reacting multiphase flow. This report summarizes an investigation into the breadth of problems to which MFIX-Exa may be applied, specifically with regard to low fluid velocities and the onset of fluidization. A simple fluidization study is conducted both experimentally and numerically for particles of interest, then reactor simulations are compared to cold flow experiments for uniform distributor plates. Approaches for modeling bubble caps are also presented.

discrete particle method↗

DOE OSTI2026

Numerical-heating effects in atmospheric pressure streamer discharges simulated with a PIC code

Artificial heating in plasma simulations is a well-known phenomenon which occurs when, among other things, the Debye length is poorly resolved by the simulation mesh. Here, in this work, the degree to which numerical-heating occurs during a simulation of a nanosecond atmospheric pressure streamer discharge is examined. The streamer is simulated using a two-dimensional finite-element, particle-in-cell code Empire, which uses direct simulation Monte Carlo for binary particle interactions. Initially, an estimate of the numerical-heating rate applied to Empire is performed using a simple plasma model. Second, a positive atmospheric pressure streamer discharge simulation is performed to study the effects of numerical heating on plasma density, electron temperature, and streamer velocity. The nominal Debye length is approximately 1 μm and the amount of numerical heating introduced in the simulation is varied by using mesh sizes ranging from 2 μm to 20 μm. A measurable numerical heating quantity is proposed that can be used to estimate the appropriate element size and quantify the numerical-heating that can be expected over the simulation time for an atmospheric pressure streamer. In conclusion while Δx/λ D violations can be an issue it is not likely to be an issue with streamer discharges that are temporally short and occur in environments where collision frequencies are high. This result validates the rationale of grid size choices for a large amount of previously published works where Δx/λ D violation was not clearly addressed. Primary finding of this work is that numerical heating is of minor concern for plasma simulations where electron–neutral collisions are numerous such that multiple collisions can occur within a single plasma period.

Nikic, Dejan [University of New Mexico, Albuquerqu↗

DOE OSTI2025

Azimuthal and axial structures in 3D particle-in-cell simulation of Penning discharge

We report the results of a 3D particle-in-cell simulation of cylindrical Penning discharge with the axial magnetic field in the so-called reflex configuration, where the cathode and anti-cathode are biased to the same negative potential. The discharge is supported by thermal electron emission from the cathode. Electron and ion collisions, including ionization, are fully accounted for. The emphasis is on a specific regime in which the plasma potential at the center of the discharge is positive with respect to the chamber walls, serving as an anode. Spatial and temporal scales of the observed azimuthal and axial fluctuations and structures are characterized. It is suggested that azimuthal structures are caused by the dissipative gradient-drift instability. We find that the axial fluctuations related to the plasma-beam instabilities are weakly correlated with the azimuthal perturbations of the density, so that the azimuthal modes rotate as a whole and do not show any axial shear. The behavior of the electric potential is more involved, demonstrating intermittent standing wave and propagating structures in the axial direction that modulate the electron transport, producing the standing wave pattern (along the z-direction) in the radial electron flux.

3D PIC simulation of discharge↗

DOE OSTI2026

Proton beam enhancements from ultrafast laser interactions with compound parabolic concentrators

Target normal sheath acceleration (TNSA) is among the most widely studied laser–plasma ion acceleration mechanisms. In this Letter, we report on studies of proton acceleration from flat Cu targets with cone-like focusing structures called compound parabolic concentrators (CPCs) coupled to their front surface. The CPC acts as a non-imaging focusing optic that enhances the laser intensity at the target's front surface by ∼2×, from 9 × 10 18 to 2 × 10 19 W/cm 2 . This effect drives a reduction in the particle source size from the typical laser spot size of 120 μm to the CPC tip size of 65 μm and significant enhancements in the peak energy and temperature (2.6 × increase) of the resulting TNSA proton beam. We also observe increased opening angle of the beam. 2D PIC simulations have been conducted and replicate the experimental behavior. These increases have implications for long focal length facilities that require higher energy proton beams, which now can be achieved without significant infrastructure changes.

3D printing↗