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DOE OSTI2025

Drift-cyclotron loss-cone instability in 3-D simulations of a sloshing-ion simple mirror

The kinetic stability of collisionless, sloshing beam-ion (45° pitch angle) plasma is studied in a three-dimensional (3-D) simple magnetic mirror, mimicking the Wisconsin high-temperature superconductor axisymmetric mirror experiment. The collisional Fokker–Planck code CQL3D-m provides a slowing-down beam-ion distribution to initialize the kinetic-ion/fluid-electron code Hybrid-VPIC, which then simulates free plasma decay without external heating or fuelling. Over 1 – 10 μs, drift-cyclotron loss-cone (DCLC) modes grow and saturate in amplitude. The DCLC scatters ions to a marginally stable distribution with gas-dynamic rather than classical-mirror confinement. Sloshing ions can trap cool (low-energy) ions in an electrostatic potential well to stabilize DCLC, but DCLC itself does not scatter sloshing beam-ions into the said well. Instead, cool ions must come from external sources such as charge-exchange collisions with a low-density neutral population. Manually adding cool ∼1keV ions improves beam-ion confinement several-fold in Hybrid-VPIC simulations, which qualitatively corroborates prior measurements from real mirror devices with sloshing ions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Quasilinear modelling of collisional trapped electron modes

The simplification of collision operators is necessary for quasilinear turbulence modelling used with integrated modelling frameworks, such as the gyrokinetic code QuaLiKiz. The treatment of collisions greatly impacts the accuracy of trapped electron mode (TEM) modelling, which is necessary to predict the electron heat flux and the balance between inward and outward particle fluxes. In particular, accurate particle flux predictions are necessary to successfully model density peaking in the tokamak core. We explored two ways of improving collisional TEM model reduction for tokamak core plasmas. First, we carried out linear GENE simulations to study the complex interplay between collisions and trapped electrons. We then used these simulations to define an effective trapped fraction to characterize the collisional TEM based on two key parameters, the local inverse-aspect ratio $\epsilon$ and the collisionality $\nu ^\ast$. One aspect missing from analytical TEM research is that the collisional frequency and the bounce-transit frequency are both velocity dependent; this effective trapped fraction takes both into account. In doing so, we determined that two parameters are not enough to model the collisional TEM, as an additional third free parameter was necessary. We determined that this model, as currently formulated, is not suitable for integrated modelling purposes. Second, we directly improved QuaLiKiz's Krook operator, which relies on two free parameters. We determined that these parameters required adjustments against higher-fidelity collisional models. In order to improve density profile predictions when paired with integrated models, we refined the Krook operator by using GENE simulations as a higher-fidelity point of comparison. We then demonstrate strong improvement of density peaking predictions of QuaLiKiz within the integrated modelling framework JETTO.

fusion plasma↗

DOE OSTI2025

Plasma instabilities dominate radioactive transients magnetic fields: the self-confinement of leptons in Type Ia and core-collapse supernovae, and kilonovae

The light curves of radioactive transients, such as supernovae and kilonovae, are powered by the decay of radioisotopes, which release high-energy leptons through $\beta ^+$ and $\beta ^-$ decays. These leptons deposit energy into the expanding ejecta. As the ejecta density decreases during expansion, the plasma becomes collisionless, with particle motion governed by electromagnetic forces. In such environments, strong or turbulent magnetic fields are thought to confine particles, though the origin of these fields and the confinement mechanism have remained unclear. Using fully kinetic particle-in-cell (PIC) simulations, we demonstrate that plasma instabilities can naturally confine high-energy leptons. These leptons generate magnetic fields through plasma streaming instabilities, even in the absence of pre-existing fields. The self-generated magnetic fields slow lepton diffusion, enabling confinement, and transferring energy to thermal electrons and ions. Our results naturally explain the positron trapping inferred from late-time observations of thermonuclear and core-collapse supernovae. Furthermore, they suggest potential implications for electron dynamics in the ejecta of kilonovae. We also estimate synchrotron radio luminosities from positrons for Type Ia supernovae and find that such emission could only be detectable with next-generation radio observatories from a Galactic or local-group supernova in an environment without any circumstellar material.

instabilities↗

DOE OSTI2024

Modeling of Macroscopic Dynamics in Three-Dimensional Plasma Configurations (Final Technical Report)

A numerical simulation-based study to investigate the stability properties of inherently three-dimensional plasma magnetic configurations is presented. These configurations, called stellarators and heliotrons, use external helical coils to provide the twisting magnetic field that is required to confine ionized plasma particles. In contrast to the tokamak configuration, which nominally has the property of axisymmetry, electrical current does not need to be induced in stellarator and heliotron plasma. Experiments have shown that these three-dimensional configurations are remarkably robust to macroscopic instability, even when driven to relatively high levels of plasma pressure. Our understanding of how the plasma is able to withstand macroscopic instability will be enhanced by the work proposed here. The effort will generalize existing numerical modeling capability, and it will apply the new capability to model macroscopic dynamics in these three-dimensional configurations. The development work has been applied to the NIMROD simulation code (https://nimrodteam.org) that was originally based on axisymmetric problem domains. It has been generalized to accommodate the three-dimensional shaping of the plasma volume in stellarators and heliotrons. Its use of equilibrium data has also been generalized, and the implementation allows different numerical representation of the magnetic field. Analysis has been performed to inform the selection of numerical methods, and a method to accelerate the iterative solution of the necessary algebraic systems has been developed and implemented. Verification of the new NIMSTELL code on benchmark problems has also been an important part of the effort.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Reconnection-driven Flares in M87*: Proton–Synchrotron-powered GeV Emission

Magnetic reconnection in current layers that form intermittently in radiatively inefficient accretion flows onto black holes is a promising mechanism for particle acceleration and high-energy emission. It has been recently proposed that such layers, arising during flux eruption events, can power the rapid TeV flares observed from the core of M87. In this scenario, inverse-Compton scattering of soft radiation from the accretion flow by energetic electron–positron pairs produced near the reconnection layer was suggested as the primary emission mechanism. However, detailed calculations show that radiation from pairs alone cannot account for the GeV emission detected by the Fermi observatory. In this work, we combine analytic estimates with 3D radiative particle-in-cell simulations of pair–proton plasmas to show that the GeV emission can be naturally explained by synchrotron radiation from protons accelerated in the current sheet. Although the exact proton content of the layer is uncertain, our model remains robust across a broad range of proton-to-pair number density ratios. While protons are subdominant in number compared to pairs, our simulations demonstrate that they can be accelerated more efficiently, leading to a self-regulated steady state in which protons dominate the energy budget. Ultimately, proton synchrotron emission accounts for approximately 5%–20% of the total dissipation power. The majority is radiated as MeV photons via pair synchrotron emission, with a smaller fraction emitted as TeV photons through inverse-Compton scattering.

Active galactic nuclei↗

DOE OSTI2026

Connect microstructure evolution to property degradation with validated simulation

Reliable material performance is required for plasma-facing material (PFM) candidates. Previous research has shown that plasma and neutron radiation exposure induces microstructural changes in PFMs; changes in thermal and electrical conductivities and in material hardening and embrittlement were also observed after neutron irradiation. These material property changes will negatively impact the performance of the PFMs in a fusion reactor. Despite the well-known connection between material microstructure, properties, and performance, there is a need for validated modeling capabilities connecting PFM property degradation with microstructural evolution under fusion-relevant conditions. We are developing a simulation capability to couple plasma-induced microstructural evolution to material property degradation. Our approach relies on deliberate mapping between individual simulation models and experimental characterization for validation. The open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) software was used for this simulation capability development. A MOOSE phase-field model was coupled with the cluster dynamics code, Xolotl, to predict microstructural evolution. Microstructure characterization techniques, including scanning electron microscopy (SEM), transmission electron microscopy (TEM), and laser scanning confocal microscopy (LSCM) are used to validate these microstructural evolution simulations. Calculation of thermal and electrical conductivities with first principles simulations was performed for bulk material and for grain boundaries; these results are used within MOOSE models to calculate effective thermal and electrical conductivities as a function of grain characteristics. Thermoreflectance and four-probe techniques were employed to measure the thermal and electrical conductivities, respectively. A MOOSE crystal plasticity model was adapted to predict microstructure-sensitive deformation behavior, and X-ray diffraction (XRD) was used to collect bulk dislocation density data for validation. After individual simulation validation, these models are coupled to predict material property changes resulting from plasma exposure. We focused here on an experimental design to emphasize the separate effects of moderate thermal loads and plasma exposure using tungsten. Annealing of tungsten was performed under a protective environment for temperatures ranging from 500$^o$C to 1500$^o$C. The plasma exposure was completed in the Tritium Plasma Experiment at Idaho National Laboratory under a deuterium flux of 1e22 $\frac{D}{m^2s}$. This incremental approach is employed to build confidence in the modeling capability: separate-effects tests ensure that the models capture key mechanisms from single environmental conditions before predicting PFM property degradation under combined loads. We will show our early results from coupling these simulation models to predict PFM property changes from microstructural evolution. Comparisons of the simulation results with preliminary validation data will be discussed.

36 - MATERIALS SCIENCE↗

DOE OSTI2025

Role of perturbed parallel magnetic field effects in predicting turbulent transport in NSTX

This study presents analysis of gyrokinetic simulations on the National Spherical Torus Experiment (NSTX) to investigate the effects of electromagnetic fields on plasma turbulence and transport. The simulations, performed with varying levels of fidelity using the gyrokinetic CGYRO code, include electrostatic (ES), single-field electromagnetic (EM1), and two-field electromagnetic (EM2) models. A detailed comparison across the simulation database reveals that electromagnetic effects increase both predicted growth rates and quasilinear fluxes, with EM2 simulations producing stronger turbulence than ES and EM1 cases. Quasilinear modeling using QLGYRO demonstrates that while the perturbed parallel magnetic field (δB ∥ ) does not drastically affect the total flux at experimental gradients, it leads to a shift in the dominant instability, altering mode structures from microtearing to kinetic ballooning modes (KBMs). The proximity of the plasma profiles to the KBM threshold is explored, with the experimental conditions being near the onset of KBM-driven transport. The KBM, with its large growth rates, is identified as a potential driver of electron temperature flattening, as it can rapidly transport heat across flux surfaces. Performing stability analysis shows core-localized unstable a low- mode that could contribute to the flattening at the early times of the discharge. TGYRO predictive modeling, incorporating both TGLF and QLGYRO, indicates that the inclusion of δB ∥ significantly improves the accuracy of temperature profile predictions in NSTX high-beta plasmas, although challenges remain in modeling the sharp flux discontinuities caused by KBM-driven instabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

FENIX: An Open-Source Multiphysics Integrated Framework Enabling Collaborative Development of Plasma Facing Component Modeling Capabilities

Advanced modeling and simulation tools have a crucial role to play in accelerating fusion energy deployment as a sustainable power source. Multiphysics, high-fidelity computational tools can help understand, model, and quantify the complex interactions between materials performance, plasma and neutron exposure, and engineering processes. As a result, they accelerate the design, safety analysis, and performance evaluation of fusion systems. This webinar introduces the Fusion ENergy Integrated multiphys-X (FENIX) framework, an open-source multiphysics tool for plasma facing component modeling. FENIX leverages the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework, which has been developed by the United States Department of Energy Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. FENIX couples various MOOSE capabilities such as heat transfer, thermomechanics, thermal hydraulics, electromagnetics, and plasma kinetics with the MOOSE-based applications Cardinal (neutronics) and TMAP8 (tritium transport). During the webinar, we will present FENIX and discuss how its modularity, openness, software quality assurance processes, and licensing approach supports effective collaborations, including public-private partnerships.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2024

FENIX: Towards a Fully Integrated Multiphysics Framework for Plasma Facing Component Modeling

Computational tools have a crucial role to play in accelerating the deployment of fusion as a clean, reliable, abundant, and sustainable energy source. Multiphysics, high-fidelity simulation capabilities can help model, study, and predict intricate interactions between materials performance, plasma exposure, neutron irradiation, and engineering processes. As such, they can assist in the resolution of scientific and engineering challenges underpinning design, construction, and commission of fusion power plants. To address these needs, ongoing efforts are leveraging the Multiphysics Object-Oriented Simulation Environment (MOOSE) framework and delivering new computational tools for the fusion community. These tools inherit crucial attributes from MOOSE. They are open-source, modular, integrated with nuclear industry-standard software quality assurance processes, and enable multiphysics, multi-fidelity, fully integrated, zero- to three-dimensional, and massively parallel simulations. After a short overview of these capabilities, we will present the development of Fusion ENergy Integrated multiphys-X (FENIX), a MOOSE-based application designed to enable plasma facing component design and performance evaluation. Throughout their lifetime, plasma facing components are exposed to extreme thermal loads, repeated thermal shocks, and irradiation by plasma ions, neutral particles, and high-energy neutrons. Consequently, designing a plasma facing component with acceptable lifetime degradation is extremely challenging. FENIX aims to model the multiphysics environment in which plasma facing components evolve to accelerate their design studies. To that end, FENIX couples existing MOOSE capabilities such as heat transfer, thermomechanics, and thermal hydraulics, with tritium transport via the MOOSE-based Tritium Migration Analysis Program, Version 8 (TMAP8), with neutronics via the MOOSE-based high-fidelity neutron-photon transport and fluid dynamics code Cardinal, and finally with Particle-in-Cell plasma simulation capabilities being developed in this project. In this study, we present the current FENIX capabilities and preliminary results of its application to model the Tritium Plasma Experiment set up at Idaho National Laboratory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Learning plasma dynamics and robust rampdown trajectories with predict-first experiments at TCV

The rampdown phase of a tokamak pulse is difficult to simulate and often exacerbates multiple plasma instabilities. To reduce the risk of disrupting operations, we leverage advances in Scientific Machine Learning (SciML) to combine physics with data-driven models, developing a neural state-space model (NSSM) that predicts plasma dynamics during Tokamak à Configuration Variable (TCV) rampdowns. The NSSM efficiently learns dynamics from a modest dataset of 311 pulses with only five pulses in a reactor-relevant high-performance regime. The NSSM is parallelized across uncertainties, and reinforcement learning (RL) is applied to design trajectories that avoid instability limits. High-performance experiments at TCV show statistically significant improvements in relevant metrics. A predict-first experiment, increasing plasma current by 20% from baseline, demonstrates the NSSM’s ability to make small extrapolations. The developed approach paves the way for designing tokamak controls with robustness to considerable uncertainty and demonstrates the relevance of SciML for fusion experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Advanced Simulation of ITER Core X-ray Crystal Spectroscopy

X-Ray Simulation Analysis (XRSA) is an analytical ray-tracing mixed code developed specifically for the ITER Core X-Ray Crystal Spectroscopy (XRCS-Core) diagnostic, which employs a dual-reflection configuration incorporating multiple pre-reflectors made of Highly Oriented Pyrolytic Graphite (HOPG) and spherically curved analyzing crystals. The ITER XRCS-Core is designed for high spectral resolution measurement in specific wavelength ranges, including narrow bands around 1.354 Å for W 64+ , 2.19 Å for Xe 51+ , and 2.555 Å for Xe 44+ and Xe 47+ , enabling diagnostic capability across a broad electron temperature range in the ITER plasma. XRSA facilitates efficient simulation of the spectral performance of this complex X-ray spectroscopic system. Recent updates to the XRSA code have incorporated two critical effects: auto-focusing, which specifically applies to HOPG, and polarization. These two effects are particularly important in the dual-reflection configuration used in the ITER XRCS-Core system to provide more accurate modeling results. Here, simulations conducted with the updated code demonstrate that polarization has a substantial impact on the performance of the dual-reflection system. Additionally, the combined influence of polarization and system layout introduces performance variations across channels through the same crystal.

Computer graphics↗

DOE OSTI2024

Pseudospectral particle-in-cell formulation with arbitrary charge and current-density time dependencies for the modeling of relativistic plasmas

This paper introduces a formulation of the particle-in-cell (PIC) method for the modeling of relativistic plasmas, that leverages the ability of the pseudospectral analytical time-domain solver (PSATD) to handle arbitrary time dependencies of the charge and current densities during one PIC cycle (applied to second-order polynomial dependencies here). Here, the formulation is applied to a modified set of Maxwell's equations that was proposed earlier in the context of divergence cleaning, and to recently proposed extensions of the PSATD-PIC algorithm. Detailed analysis and testings revealed that, under some condition, the formulation can expand the range of numerical parameters under which PIC simulations are stable and accurate when modeling relativistic plasmas such as, e.g., plasma-based particle accelerators.

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Generation of Large-Volume High-Pressure Plasma by Spatio-Temporal Control of Space Charge

Due to the fundamental limitations of scaling, very little progress has been made towards achieving a large-volume dense non-equilibrium plasma near atmospheric pressures. Commercially available state-of-the art glow-like atmospheric plasma devices for industrial applications are either narrow tubes or wide slits with narrow openings. Often multiple sources are put together in various configurations to process larger surfaces. The traditional methods of exciting electrodes create spatially fixed electric fields. As a result, the space charge at atmospheric pressure tends to be spatially confined resulting in non-uniformity which eventually leads to instability as the discharge is scaled. Theoretical work done under this project showed that it is possible to generate a spatially rotating electric field by exciting a set of electrodes with phase staggered sinusoidal waveforms. The modeling and simulations were done using plasma fluid models. It was shown that such a field can produce a uniform plasma. At the conclusion of the project, experimental proof of concept with an eight-electrode system in various gases (Air, Helium and Argon) was demonstrated. Power measurements and spectral investigation show that the concept can be used to generate a uniform stable plasma. This plasma source has the potential of opening new applications of nonthermal plasma including combustion of carbon-free fuel. The current limitation of the proposed method in scaling to higher volume and pressure is the need for multiple high voltage amplifiers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Optical diagnostic design for measuring the radiation front with a mid-leg pumped divertor on DIII-D

The design of an optical diagnostic system to localize the radiation front in a mid-leg pumped divertor configuration on DIII-D is presented. Divertor detachment is a key mechanism for handling power exhaust in tokamaks, and mid-leg pumping offers a promising approach to radiatively dissipate power while maintaining acceptable core performance. To predict the location of the radiation front and design a spectroscopic diagnostic to measure its position, a database of SOLPS-ITER simulations across a range of input powers and gas puffing rates representative of DIII-D operation was employed. These simulations provide self-consistent plasma backgrounds for a Cherab-Raysect synthetic diagnostic framework, which incorporates detailed tokamak geometry and physically accurate ray-tracing. Synthetic simulations of optical sightlines and viewing cone geometry were used to calculate line-integrated emission from the plasma, particularly of the C III 465 nm line, to serve as a proxy for the T e ≈ 7 − 10 eV temperature region associated with the onset and evolution of divertor detachment. Neutral deuterium emission is also evaluated for comparison. The synthetic diagnostic is used to assess the performance of existing DIII-D optical systems, including filterscopes and the Multichord Divertor Spectrometer, and to optimize line-of-sight placement within mechanical and installation constraints. The results provide quantitative guidance for diagnostic implementation on DIII-D and demonstrate the advantage of integrated synthetic diagnostics for divertor design studies and future advanced divertor concepts.

Cherab↗

DOE OSTI2026

Validation of Hermes-3 turbulence simulations against the TCV-X21 diverted L-mode reference case

Electrostatic flux-driven turbulence simulations with the Hermes-3 code are performed in TCV L-mode conditions in forward and reversed toroidal field configurations, and compared to the TCV-X21 reference dataset (Oliveira et al 2022 Nucl. Fusion 62 096001) qualitatively and with a quantitative methodology. Using only the magnetic equilibrium, total power across the separatrix (120 kW) and total particle flux to the targets (3 x 10 21 s −1 ) as inputs, the simulations produce time-averaged plasma profiles in good agreement with experiment. Shifts in the target peak location when the toroidal field direction is reversed are reproduced in simulation, including the experimentally observed splitting of the outer strike point into two density peaks. The overall normalized discrepancy between simulation and observation is better than any previously reported in the reversed field configuration, and matches the best previously reported in forward field configuration. Differences between simulation and experiment include density profiles inside the separatrix and at the inner target in forward (favorable $\bigtriangledown B$) field configuration. These differences in target temperature in forward field configuration lead to differences in the balance of current to the inner and outer divertor in the private flux region. The cause of these differences is most likely the lack of neutral gas in these simulations, indicating that even in low recycling regimes neutral gas plays an important role in determining edge plasma profiles. These conclusions are consistent with findings in Oliveira et al (2022 https://github.com/SPCData/TCV-X21).

Physics - Plasma physics↗

DOE OSTI2025

Deep potential molecular dynamics simulations of ion-enhanced etching of silicon by atomic chlorine

The continued development of plasma-assisted processing techniques requires a fundamental understanding of plasma-surface interactions. Molecular dynamics (MD) simulations have been employed to complement experimental studies and better understand the properties of such systems. Recently, machine learning (ML) methods have enabled the development of ab initio-based interatomic potentials, which can be generalized to complex combinations of multiple atom types. In this work, we use ML potentials developed using the Deep Potential Molecular Dynamics (DeepMD) framework to provide a model of ion-enhanced etching of Si by Cl atoms. We demonstrate the importance of proper selection of the training data set to the accuracy of the DeepMD model and compare our results to MD results using empirical potentials, as well as to experimental measurements. Exposure of undoped Si at 300 K to thermal Cl atoms yields a steady-state Cl coverage of 1.25 monolayers, which is slightly lower than the value obtained in previous experimental studies. Predictions of Si etch yields by simultaneous Cl atom and Ar + ion impacts as a function of ion energy, neutral to ion flux ratio, and angle of incidence of the ions are in reasonably good agreement with classical MD results and experimental measurements. Finally, etch yields and SiCl x mixed layer thicknesses during simultaneous bombardment of the Si(100) surface by Cl atoms and Cl + ions are in good agreement with experimental data. In conclusion, the present work is a necessary condition for the extension of the DeepMD procedure to more complex systems of interest in plasma-surface interactions.

Artificial neural networks↗

DOE OSTI2025

Surrogate Modeling of Landau Damping with Deep Operator Networks

Kinetic simulations excel at capturing microscale plasma physics phenomena with high accuracy, but their computational demands make them impractical for modeling large-scale space and astrophysical systems. In this context, we build a surrogate model, using Deep Operator Networks (DeepONets), based upon the Vlasov–Poisson simulation data to model the dynamical evolution of plasmas, focusing on the Landau damping process—a fundamental kinetic phenomenon in space and astrophysical plasmas. The trained DeepONets are able to capture the evolution of electric field energy in both linear and nonlinear regimes under various conditions. Extensive validation highlights DeepONets’ robust performance in reproducing complex plasma behaviors with high accuracy, paving the way for large-scale modeling of space and astrophysical plasmas.

plasma astrophysics↗

DOE OSTI2025

Reconstruction of beam parameters and betatron radiation spectra measured with a Compton spectrometer

The photon flux resulting from high-energy electron beam interactions with high-field systems, such as those found in the upcoming FACET-II experiments at the SLAC National Accelerator Laboratory, yields deep insight into the electron beam’s underlying dynamics during the interaction. However, extracting this information is an intricate process. To demonstrate how to approach this challenge using modern methods, this paper utilizes simulated data that models plasma wakefield acceleration-derived betatron radiation in experiments to determine reliable methods of reconstructing key beam and beam-plasma interaction properties. For betatron radiation measurements, translating the observed 200⁢ keV to 30⁢ MeV photon double-differential energy-angle spectra obtained from an advanced Compton spectrometer requires testing multiple methods to optimize the pipeline from its response to incident electron beam information. The paper compares maximum likelihood estimation and machine learning to refine the translation of photon spectra into precise electron beam metrics, such as spot size, energy, and emittance, enhancing the understanding of beam behavior within these dense, high-field environments. We also introduce machine learning and the expected maximization algorithm to reconstruct the primary photon spectrum, employing a multilayer neural network for regression analysis of the energy and angle spectra. With appropriate modifications, the advanced methods reproduce relevant incident beam parameters with high accuracy, even for beam sizes in the <10 μ⁢m range. This capacity is critical to understanding intense beam propagation and its optimization in plasma.

Beam code development & simulation techniques↗