Collisional implicit particle-in-cell methods for fully kinetic simulations of dynamically compressing plasmas
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Physics - Plasma physics↗
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Results for “particle-in-cell methods”
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A deterministic verification strategy for multidimensional gyrokinetic particle-in-cell algorithms using the method of manufactured solutions
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Mathematics and Computing↗
Verification of an energy-conserving semi-implicit electrostatic particle-in-cell scheme for modeling high-density plasma at scale
A verification study of a semi-implicit energy-conserving electrostatic particle-in-cell algorithm is presented. The algorithm relaxes the time-step and mesh-size constraints that require resolution of the plasma period and Debye length associated with traditional explicit momentum-conserving particle-in-cell algorithms. Physical implications and applicability of using the semi-implicit scheme for modeling high-density plasmas are discussed. Where possible, numerical results are compared against analytical solutions. The simulation results indicate that the algorithm is stable at time steps larger than twice the inverse plasma frequency and cell sizes larger than the Debye length. It is found that the algorithm gives adequate results, provided that the distribution function and the spatiotemporal scales dictating the physics of the problem are resolved. As such, the algorithm may provide a robust method for kinetic modeling of high-density plasmas at scale.
Cyclotron resonance↗
Plasma gradient effect on direct laser acceleration
The transfer of a high-intensity laser pulse energy to a high-energy electron beam via the direct laser acceleration mechanism is shown to be significantly enhanced through control of the plasma density gradient. Experiments performed using the OMEGA EP facility's high-intensity beams altered the plasma density and gradients by changing the Mach number and the angle of the gas-jet nozzle to the laser axis. When a long density gradient at the rear of the target is used, the total high-energy electron number measured was enhanced by 4.5 times compared to a shorter rear gradient. Complementary two-dimensional simulations, which follow the laser field evolution and the corresponding electron dynamics, strongly support the key trends observed in the experiment. The effect is twofold, the long density gradient provides the longest acceleration distance while it minimizes the formation of the sheath field as the electron beam exits into the vacuum. This study shows the importance of tailoring the plasma density.
Laser plasma interactions↗
Scalings of laser-driven MeV electron sources with relativistic multi-picosecond laser pulses
We investigate the generation of MeV electrons in relativistic multi-picosecond laser–solid interactions, using two-dimensional particle-in-cell simulations. Scanning a parameter space of intensities from 10 18 to 10 20 W/cm 2 and pulse durations between 100 fs and 10 ps, we discuss scalings of the effective hot electron temperature and MeV electron dose relevant to applications, as well as the direct laser acceleration mechanism that drives electrons to energies much higher than the ponderomotive potential of the laser pulse.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Saturation of the kinetic ballooning instability due to the electron parallel nonlinearity
The electron parallel nonlinearity (EPN) is implemented in the gyrokinetic particle-in-cell turbulence code GEM [Y. Chen and S. E. Parker, J. Comp. Phys. 220, 839 (2007)]. Application to the Cyclone Base Case reveals a strong effect of EPN on the saturated heat transport above the kinetic ballooning mode (KBM) threshold. Evidence is provided to show that the strong effect is associated with the electron radial motion due to magnetic fluttering, which turns fine structures of the KBM eigenmode in radius into fine structures in velocity and increases the magnitude of the EPN term in the kinetic equation.
Gyrokinetic simulations↗
Accelerating kinetic plasma simulations with machine-learning-generated initial conditions
Computational models of plasma technologies often solve for the system operating conditions by time-stepping an initial value problem to a quasi-steady solution. However, the strongly nonlinear and multi-timescale nature of plasma dynamics often necessitate millions, or even hundreds of millions, of steps to reach convergence, reducing the effectiveness of these simulations for computer-aided engineering. We consider acceleration of kinetic plasma simulations via data-driven machine-learning-generated initial conditions, which initialize the simulations close to their final quasi-steady-state, thereby reducing the number of steps to reach convergence. Three machine-learning models are developed to predict the density and ion kinetic profiles of capacitively coupled plasma discharges relevant to the microelectronics industry. The models are trained on kinetic simulations over a range of device operating frequencies and pressures. Best performance was observed when simulations were initialized with ion kinetic profiles generated by a convolutional neural network, reducing the mean number of steps to reach convergence by 17.1× when compared to initialization with a zero-dimensional global model. We also outline a workflow for continuous data-driven model improvement and simulation speedup, with the aim of generating sufficient data for full device digital twins.
Artificial neural networks↗
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↗
Flying focus with arbitrary directionality for spatiotemporal control of laser intensity
Flying focus techniques produce laser pulses whose focal points travel at arbitrary, controllable velocities. While this flexibility can enhance a broad range of laser-based applications, existing techniques constrain the motion of the focal point to the propagation direction of the pulse. Here, we introduce a flying focus configuration that decouples the motion of the focus from the propagation direction. Here, a chirped laser pulse focused and diffracted by a diffractive lens and grating creates a focal point that can move both along and transverse to the propagation direction. The focal length of the lens, grating period, and chirp can be tuned to control the direction and velocity of the focus. Simulations demonstrate this control for a holographic configuration suited to high-power pulses, in which two off-axis pump beams with different focal lengths encode the equivalent phase of a chromatic lens and grating in a gas or plasma. For low-power pulses, conventional solid-state or adaptive optics can be used instead. Multi-dimensional control over the focal trajectory enables new configurations for applications, including laser wakefield acceleration of ions, nonlinear Thomson scattering, and surface-plasmon emission of THz radiation.
Classical optics↗
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↗
Velocity-space Origins of the Pressure–Strain Interaction in Multipopulation Distributions and Its Application to Magnetic Reconnection
A forefront research question is how energy evolves in weakly collisional plasmas for which departures from local thermodynamic equilibrium (LTE) are significant. The standard approach is studying the terms in the non-LTE energy evolution equation derived by taking the second moment of the Boltzmann equation, but the resultant fluid metrics do not retain information about which particles at which velocities drive energy evolution. A widely studied channel for internal energy density evolution is the pressure–strain interaction. Here, we employ the kinetic pressure–strain, a phase-space diagnostic whose velocity-space integral recovers the pressure–strain interaction to disambiguate the contributions to the pressure–strain interaction from disparate particle populations in composite phase-space densities. We develop phase-space analogs of the pressure–strain interaction decompositions to provide the phase-space origins of normal versus sheared flow. We introduce the “kinetic strain-rate” tensor, the phase-space analog of the strain-rate tensor, which we argue is needed to interpret the phase-space origins of the pressure–strain interaction. To demonstrate the utility of these quantities, we investigate them for composite electron distributions near the electron diffusion region in two-dimensional particle-in-cell simulations of antiparallel symmetric magnetic reconnection. We find that the phase-space-based diagnostics isolate the roles of distinct populations. These results contribute to a growing body of work providing new methods for quantifying phase-space energy evolution for a broad array of processes, from magnetic reconnection to collisionless shocks and turbulence, opening new pathways for answering longstanding problems of particle energization in weakly collisional plasmas.
79 ASTRONOMY AND ASTROPHYSICS↗
Entity—Hardware-agnostic Particle-in-cell Code for Plasma Astrophysics. II. General Relativistic Module
Black hole (BH) environments often host plasmas that are fully collisionless or contain intrinsically collisionless regions, including relativistic jets and coronae, where particle energization is ubiquitous. Capturing the physics of these systems requires numerical methods capable of modeling relativistic, magnetized, collisionless plasmas in strong gravitational fields. In this work, we introduce the general relativistic module for Entity—the first open-source, coordinate-agnostic, performance-portable, particle-in-cell code. The code enables fast axisymmetric simulations of collisionless plasmas around BHs on any modern high-performance computing architecture (both GPUs and CPUs).
Galishnikova, Alisa [Flatiron Institute, New York,↗
Intrinsic nonlocality of spin- and polarization-resolved probabilities in strong-field quantum electrodynamics
Spin and polarization are central to precision tests of fundamental physics and for interpreting radiation from astrophysical sources and ultraintense laser-matter experiments. Here, focusing on the fundamental process of nonlinear Compton scattering, we demonstrate that a key assumption underlying current strong-field quantum electrodynamics models, i.e., that emission can be treated as an instantaneous random event sampled from a local differential rate, is inconsistent once emission angles, electron spin, and/or photon polarization are resolved. Namely, even in strictly constant and uniform fields , the resulting fully differential distribution is sign indefinite, yielding negative inferred probabilities. The physical reason is that the photon emission probability builds up over a finite length of the electron trajectory, the formation region, during which the electron direction changes by roughly the same small angle that defines the radiation cone. Therefore, we put forward a new method where we integrate over this formation region analytically to obtain a physically consistent electron spin and photon polarization model. We show that the implementation of our model is compatible with existing Monte Carlo and particle-in-cell workflows. Simulations of a GeV-class electron-laser collision accessible at current petawatt facilities and of emission in a pulsarlike magnetic field are shown to reveal spin and polarization patterns that differ even qualitatively from state-of-the-art local models. In particular, our new model predicts substantial angle-dependent circular photon polarization where the well-known collinear-emission approach yields none, and a pronounced helicity bias in the recoiling electrons absent from current predictions. These findings have direct implications for upcoming strong-field QED experiments and for interpreting polarized radiation from extreme astrophysical environments.
astrophysical electromagnetic fields↗
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↗
The Verification and Validation of a Magnetic Plasma Fluid Model Utilizing the MOOSE (Multiphysics Object Oriented Simulation Environment) Framework
As the goal of achieving fusion power on the grid comes closer to fruition, fully coupled multiphysics models of fusion devices will be crucial. Currently, there are two main approaches to developing these platforms: (1) loosely coupled, where one couples existing codes and solvers together through input and output parameters and data, and (2) tightly coupled, where one develops the necessary models within a singular, integrated framework. This work focuses on the latter approach for magnetically confined fusion devices by developing a fluid-based plasma-edge model within the Multiphysics Object Oriented Simulation Environment (MOOSE) Framework. This effort is coordinated with other efforts to develop, test, demonstrate, and deploy fusion relevant multiphysics capabilities including electromagnetics, particle-in-cell plasma, tritium transport, and fusion blanket design. This new model is an expansion of the MOOSE-based plasma application, Zapdos, which was originally formulated to model low-temperature, non-magnetized plasma processes. Verification, benchmarking, and validation studies have been conducted. Verification studies involved utilizing the method of manufactured solutions and comparing the convergence slope of a known solution to the theoretical slope. Benchmarking consists of comparisons to existing edge codes, namely BOUT++ and SOLEDGE3X. Validation efforts focused on comparisons against open-source data from the TCV tokamak.
70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A Monte-Carlo method for Coulomb collisions in moderately coupled plasmas
Here, we introduce a new approach for coupling cumulative and single-scattering distributions, extending Monte Carlo methods for Coulomb collisions in weakly coupled plasmas into the moderately coupled regime. Using time steps typical of cumulative-scattering methods, we show that this approach not only recovers leading-order corrections proportional to the inverse Coulomb logarithm but also solves the full Boltzmann collision integral. A key feature of the method is its simplicity: it can be integrated into cumulative-scattering methods for weakly coupled plasmas with only ~ 10 additional lines of code.
Boltzmann collision integral↗
Demonstration of a Novel Phase-Space Painting Method in a Coupled Lattice to Mitigate Space Charge in High-Intensity Hadron Beams
Multiturn charge-exchange injection is the primary method of creating high-intensity hadron beams in circular accelerators, and phase space painting during injection enables tailoring of the accumulated phase space distribution. A technique we call eigenpainting allows injection of particles into a single mode of a coupled ring, providing full four-dimensional control of the phase space distribution. Under ideal conditions, uniform eigenpainting generates a linear-force equilibrium distribution in the transverse plane, with zero volume in four-dimensional transverse phase space, even including space charge. Here, we have implemented eigenpainting for the first time in the spallation neutron source accumulator ring. Injecting 8.8 μC of an 800 MeV beam, we obtain a final ratio of intrinsic transverse emittances of ≈2.4. We analyze the effect of space charge on the final distribution through comparison of the reconstructed phase space to particle-in-cell simulations.
Evans, Nicholas J. [Oak Ridge National Laboratory ↗
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↗