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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

LLNL FESP Theory Highlights: August 2024

The 2024 ABOUND SciDAC and BOUT++ combined workshop was held August 5-9 th 2024 at the University of California Livermore Collaboration Center (UCLC) in Livermore. Bringing together leading scientists and researchers from across the globe, this pivotal event focused on advancing plasma physics and boundary plasma dynamics within the context of fusion energy research. Key discussions throughout the meeting highlighted significant advancements in the BOUT++ framework, including enhanced simulations of small Edge Localized Modes (ELMs) and the initiation of integrating the integration of the 5D GEM gyrokinetic turbulence core code with the 2D SOLPS-ITER boundary transport code. These developments are crucial for managing heat loads in fusion reactors and supporting the longevity of plasma-facing components. The event also featured a session on Inter-SciDAC Collaborations, where principal investigators from multiple U.S. FES SciDAC tokamak projects explored opportunities for cross-collaboration. Additionally, the meeting showcased cutting-edge advancements in GPU acceleration and AI/ML technologies, poised to drive the next generation of fusion research. In his closing remarks, Dr. Xueqiao Xu emphasized the importance of the collaborative efforts and discussions that took place, noting their potential to shape future breakthroughs in fusion energy. The event underscored the global nature of the BOUT++ collaboration, with contributions from over 57 institutions worldwide. The 2024 BOUT++ and ABOUND Joint Hybrid Meeting continues to drive forward the research and innovations needed to achieve fusion energy, setting the stage for future collaboration and discovery.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

A review of low-rank methods for time-dependent kinetic simulations

Time-dependent kinetic models are ubiquitous in computational science and engineering. The underlying integro-differential equations in these models are high-dimensional, comprised of a six–dimensional phase space, making simulations of such phenomena extremely expensive. In this article we demonstrate that in many situations, the solution to kinetics problems lives on a low dimensional manifold that can be described by a low-rank matrix or tensor approximation. We then review the recent development of so-called low-rank methods that evolve the solution on this manifold. The two classes of methods we review are the dynamical low-rank (DLR) method, which derives differential equations for the low-rank factors, and a Step-and-Truncate (SAT) approach, which projects the solution onto the low-rank representation after each time step. Thorough discussions of time integrators, tensor decompositions, and method properties such as structure preservation and computational efficiency are included. We further show examples of low-rank methods as applied to particle transport and plasma dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

An open-source hybrid unstructured mesh - CAD fusion multiphysics analysis workflow in SALAMANDER

Plasma facing components in fusion devices will endure extreme neutron and heat fluxes. To facilitate their design using simulation tools, the open-source Fusion Module, Fusion ENergy Integrated multiphys-X (FENIX) framework is being developed to model these components with a high-fidelity multi-physics multi-dimensional approach. It can iteratively resolve couplings between all the physics at play, from neutron radiation, to thermomechanics, to near-wall plasma dynamics. This framework is based on the Multiphysics Object Oriented Simulation Environment (MOOSE), which is developed by a collaboration of US National Laboratories since 2008, for advanced nuclear, geomechanics simulations and other applications. FENIX couples numerous simulation tools, including OpenMC, the Tritium Migration Analysis Program v8, the NekRS CFD software, and most MOOSE modules. For the coupling of radiation transport and other physics, FENIX supports a hybrid workflow between Computer Assisted Design (CAD) and unstructured mesh geometries. The CAD can be generated from skinning the unstructured mesh, to enable a coarse geometry for efficient particle transport, but still resolving the local material compositions and temperature gradients. Neutron transport is performed using DAGMC on the CAD, and Cardinal, integrated in FENIX, maps tallied quantities, such as the heat deposition or the tritium generation rates, from a tally volumetric mesh to the other physics’ unstructured mesh. This coupling was exercised on a simplified tokamak geometry, coupling neutron transport with the heat conduction equation, and on a monoblock divertor problem, coupling additionally with tritium migration. Mesh convergence studies highlight the importance of the mapping conservativeness. Coupling with thermo-mechanics is further enabled by the generalization of the approach to moving meshes. The presentation will include these coupled analysis as well as an update on status of the FENIX framework.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗
DOE OSTI2026

Disruption modelling for engineering and physics design of ST-E1 fusion power plant

Plasma disruptions represent a critical challenge for high-performance tokamak operations, as they can compromise machine integrity and reduce operational availability. Although future fusion devices essentially need to incorporate strategies to minimise disruption occurrence, complete avoidance remains unattainable. Consequently, assessing and characterising unmitigated disruption consequences is fundamental for the design and qualification of next-generation fusion power plants. This work supports the pre-conceptual design of ST-E1, a low aspect-ratio Tokamak Fusion Power Plant developed by Tokamak Energy Ltd., by presenting a comprehensive disruption modelling approach applied across different design stages. The methodology integrates both physics and engineering considerations to evaluate the impact of disruptions on machine performance and structural integrity. From an engineering perspective, several ST-E1 layout options were analysed to investigate the electromagnetic response of key components under disruption-induced loads, enabling comparison between alternative design solutions. On the physics side, a broad set of disruption scenarios was explored, scanning operational space parameters, plasma-material interactions, and associated thermal loads. Furthermore, the study examined variations in disruption behaviour arising from different reference equilibria, focusing on a range starting from Double Null to Single Null configurations, reflecting the increasing up-down asymmetry consequences. The results reveal significant contrasts in plasma dynamics and structures electromagnetic behaviour between configurations, highlighting the importance of disruption modelling in guiding design choices. These analyses have proven instrumental in shaping ST-E1 development, offering critical insights for mitigating risks and optimising future fusion power plant designs.

Borowiec, Katarzyna [ORNL] (ORCID:0000000335911739↗
DOE OSTI2026

Structure preservation using discrete gradients in the Vlasov-Poisson-Landau system

We present a novel structure-preserving framework for solving the Vlasov-Poisson-Landau system of equations using a particle in cell (PIC) discretization combined with discrete gradient time integrators. The Vlasov-Poisson-Landau system is an accurate model for studying hot plasma dynamics at a kinetic scale where small-angle Coulomb collisions dominate. Our scheme guarantees conservation of mass, momentum and energy as well as preservation of the monotonicity of entropy production in both the time-continuous and discrete systems. We employ the conservative integrator for both the Hamiltonian Vlasov-Poisson equations and the dissipative Landau equation using the PETSc library (www.mcs.anl.gov/petsc) to showcase structure-preserving properties.

Discrete gradients↗
DOE OSTI2024

Plasma potential shaping using end-electrodes in the Large Plasma Device

We perform experiments in the Large Plasma Device at the University of California, Los Angeles, studying how different end-electrode biasing schemes modify the radial potential profile in the machine. We impose biasing profiles of different polarities and gradient signs on a set of five concentric electrodes placed 12 m downstream from the plasma source. We find that imposing concave-down profiles (negative potential radial gradient) on the electrodes creates radial potential profiles halfway up the plasma column that are comparable to those imposed on the electrodes and a few electron temperature in height, regardless of the biasing polarity. On the other hand, imposing concave-up profiles (positive potential radial gradient) leads to non-monotonic radial potential profiles. This observation can be explained by the current drawn through the electrodes and the parallel plasma resistivity, highlighting their important role in controlling the rotation of plasma. Concave-down plasma potential profiles, obtained by drawing electrons on the axis, are predicted to drive azimuthal drift velocities that can approach significant fractions of the ion sound speed in the central region of the plasma column.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2025

X-point effects on the ideal MHD modes in tokamaks in the description of dual-poloidal-region safety factor

The flux coordinates with dual-region safety factor (q) in the poloidal direction are developed in this work. The X-point effects on the ideal MHD modes in tokamaks are then analyzed using this coordinate system. Since the X-point effects mainly affect the edge region, the modes localized at the tokamak edge are particularly examined. Two types of modes are studied. The first is related to the conventional peeling or peeling-ballooning modes. The mode existence aligned with the local magnetic field in the poloidally core region as observed experimentally is confirmed. The X points are shown to contribute to a stabilizing effect for the conventionally treated modes with the surface-averaged q and with the tokamak edge portion truncated. The other is the axisymmetric modes localized in the vicinity of X points, which can affect the cross-field-line transport near the X points. The existence of axisymmetric modes points to the possibility of applying a toroidally axisymmetric resonant magnetic perturbation (RMP) in the X-point area for mitigating the edge localized modes, which can be an alternative to the current RMP design. The dual q description also has important implications for the existing non-axisymmetric RMP concept. It helps to understand why the RMP suppression of edge localized modes is difficult to achieve in the double-null tokamak configurations and points to the possibility of further improving the current RMP concept by considering the alignment to the local q.

Fourier analysis↗
DOE OSTI2025

Effect of self-generated magnetic fields on x-ray emission in Kr-filled targets at the National Ignition Facility

We examine the effects of self-generated magnetic fields in a Kr gas pipe x-ray source platform. X-ray emission from Kr plasma is dependent on the plasma conditions, as the ionization state is largely a function of temperature. Magnetic fields are known to limit heat conduction, which increases temperature. We show that the emission in simulations of the gas pipe x-ray source is dependent on how self-generated magnetic fields are modeled. The inclusion of self-generated magnetic fields in simulations more accurately captures the emission of lower energy x-ray emission (L-shell), bringing results closer to experiments. The modeled x-ray emission and self-generated magnetic fields are shown to be particularly sensitive to the inclusion of the Nernst effect in simulations. Severely limiting the Nernst effect leads to a hotter Kr plasma, which can account for the discrepancy seen in earlier studies. By modifying the Nernst effect multiplier, we can achieve better experimental agreement in x-ray emission from gas pipes; the value of the multiplier that leads to the best agreement is dependent on the laser power of the drive. Currently, the suppression factor of the Nernst effect needed for high power drives (PL>200 TW) is more restrictive than what is currently put forward by non-local models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Effects of oxidation and impurities in lithium surfaces on the emitting wall plasma sheath

The use of lithium as a surface coating in fusion devices improves the plasma performance, but the change in the wall properties affects the secondary electron emission properties of the material. Lithium oxidizes easily, which drives the emission yield well above unity. We present here simulations demonstrating the change in the sheath structure from monotonic to the nonmonotonic space-charge limited sheath using an energy-dependent data-driven emission model, which self-consistently captures both secondary emission and backscattering populations. Increased secondary electron emission from the material has ramifications for the degradation and erosion of the wall. The results show that the oxidation leads to an increased electron energy flux into the wall and a reduced ion energy flux. The net transfer of energy to the surface is significantly greater for the oxidized case than for the pure lithium case. High backscattering rates of low-energy particles lead to a high re-emission rate at the wall.

Fusion reactors↗
DOE OSTI2025

Taylor limit studies for local helicity injection plasma startup

Solenoid-free tokamak startup techniques can simplify the design and reduce the cost of tokamak-based fusion energy systems. The newly commissioned Pegasus-III spherical tokamak provides a dedicated platform for developing a scalable solenoid-free startup approach. Local helicity injection (LHI) is one promising technique being developed on Pegasus-III, which uses compact edge current sources to drive open field line current I inj that is redistributed via helicity-conserving instabilities to initiate tokamak plasmas. These instabilities relax the system toward a minimum energy state described by Taylor relaxation theory. This relaxation process imposes a global current limit for LHI plasmas, referred to as the Taylor limit I TL ⁠, which can dictate the plasma current I p evolution. Experiments on Pegasus and Pegasus-III show that increasing this limit leads to more effective utilization of the available helicity input and higher I p plasmas. Initial Pegasus-III experiments have verified the expected I TL $\varpropto$ ( I inj B T ) 1/2 scaling holds for B T and I inj up to 0.3 T on axis and 12 kA ⁠, respectively. Additionally, data from different injector arrays show that the width of the injector aperture directly alters I TL and can be leveraged for future injector design optimization. Throughout these scaling studies, discharges were overdriven at I p = I TL by providing excess helicity input. Intermittent bursts of n = 1 magnetic activity consistent with large-scale reconnection events occurred more often as the system was increasingly overdriven leading to a flattening of the λ = μ 0 J ∥ / |B| profile, where J ∥ is the parallel current density.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Latent space mapping: Revolutionizing predictive models for divertor plasma detachment control

The inherent complexity of boundary plasma, characterized by multi-scale and multi-physics challenges, has historically restricted high-fidelity simulations to scientific research due to their intensive computational demands. Consequently, routine applications such as discharge control and scenario development have relied on faster but less accurate empirical methods. This work introduces DivControlNN, a novel machine-learning-based surrogate model designed to address these limitations by enabling quasi-real-time predictions (i.e., ~ 0.2 ms) of boundary and divertor plasma behavior. Trained on over 70,000 2D UEDGE simulations from KSTAR tokamak equilibria, DivControlNN employs latent space mapping to efficiently represent complex divertor plasma states, achieving a computational speed-up of over 10 8 compared to traditional simulations while maintaining a relative error below 20% for key plasma property predictions. During the 2024 KSTAR experimental campaign, a prototype detachment control system powered by DivControlNN successfully demonstrated detachment control on its first attempt, even for a new tungsten divertor configuration and without any fine-tuning. These results highlight the transformative potential of DivControlNN in overcoming diagnostic challenges in future fusion reactors by providing fast, robust, and reliable predictions for advanced integrated control systems.

Artificial neural networks↗
DOE OSTI2025

Guiding center equations for the magnetic dipole

Since the discovery of Van Allen radiation belts in the 1960s, observations of energetic ions trapped in the Earth's dipole magnetic field have illustrated the remarkable confinement properties of this configuration. As such, it has been used for confining a hot plasma for nuclear fusion studies, starting from the pioneering work of Bo Lehnert and Akira Hasegawa, in the Levitated Dipole Experiment (LDX) at MIT until 2011 and in the RT-1 experiment at the University of Tokyo. More recently, the dipole has been subject to a renewed interest for fusion studies by a couple of startups and for smaller applications as a cold plasma source. While the equilibrium and magneto-hydrodynamic stability of the dipole have been investigated quite in detail, neoclassical properties of the dipole are comparatively much less known: the dipole is more known in geophysics than in fusion science. For this reason, in this paper, we propose a set of Hamiltonian, guiding-center equations to describe the motion of electrons and ions in a magnetic dipole configuration. We also developed a code, and we show the main features of particle motion, benchmarking our results with the analytical solutions for the bounce and precession motion, which are well documented in the literature. We also draw some general conclusions for the neoclassical transport in usual toroidal confinement schemes, such as the tokamak and the stellarator, pointing out the unique advantages of the dipole in confining energetic particles.

Hamiltonian mechanics↗
DOE OSTI2025

Investigation of resonant layer response in electron viscosity regime

We present a supplementary study of previous work in Waybright and Park [Phys. Plasmas 31, 022502 (2024)] which demonstrates a substantial effect of electron viscosity on the resonant layer response to non-axisymmetric magnetic perturbations. A main refinement is to include a curl element of electron viscosity in the generalized Ohm's law. The refinement reveals a resonant layer response in the electron viscosity regime corresponding to slowly rotating and highly viscous plasmas.

Asymptotic analysis↗
DOE OSTI2025

hhg v1.0

The program simulates the non-linear propagation of a laser pulse through a gas medium and calculates the emission of harmonic radiation. The computational model includes the optical Kerr-effect and multiphoton ionization of the gas resulting in plasma dynamics.

Schroeder, Christian [Lawrence Berkeley National L↗
DOE OSTI2024

Coupled Experimental/Computational Investigation of the Dynamics of Interacting Magnetized Plasmas

The interaction, or interpenetration, of magnetized plasmas of different density and/or pressure occurs in a wide variety of natural and man-made systems. Such systems include extragalactic jets propagating into the intergalactic medium, solar coronal mass ejections into background solar wind, compact toroid (CT) fueling of magnetic fusion plasmas, and jets of capsule shell impurities into DT fusion fuel, which can lead to enhanced impurity mix in inertial fusion implosions. These plasmas may take the form of jets, with open, helical magnetic structure, or plasma “bubbles” with closed magnetic fields (B-fields), such as spheromaks or CT’s. Such structures, both open and closed B-field cases, can transport heat, particles and magnetic flux or magnetic helicity into background plasma regions. For example, the origin of extragalactic magnetic fields may be due, at least in part, to transport by astrophysical jets. The goal of this proposed work was to elucidate the detailed plasma and magnetic field dynamics of high-density plasma jets (open B-field) and bubbles (closed B-field) propagating into lower density background magnetized plasma through controlled laboratory experiments and closely coupled nonlinear MHD modeling. These experiments were conducted in the HelCat (Helicon-Cathode) linear plasma device at the University of New Mexico (UNM). Plasma jets and bubbles were launched via an existing compact coaxial plasma gun, mounted on the HelCat device. This gun produced plasmas tens of cm in scale and lasting tens of microseconds, thereby allowing detailed multipoint, space- and time-resolved measurements to be made routinely. The experiments were directly modeled using the extended magnetohydrodynamic (XMHD) PERSEUS code, developed at Cornell University [23,24]. Both experimental and numerical modeling work are ongoing. The main results to date are reported here. Additional supplemental funding for one year (8/1/2019 – 7/31/2020) supported numerical investigation of photoionization processes important in many low temperature plasmas, including the HelCat device. Initial results of this modeling work is also reported.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Photon phase-space dynamics in a plasma wakefield accelerator

Frequency up-shifting of laser light in a beam-driven plasma wakefield has the potential to provide high-intensity sources of short wavelength radiation. Simulations have demonstrated that a laser pulse can undergo large frequency shifts, limited only by the drive beam energy, when the plasma density is tailored to match the accelerating phase of the wake to the group velocity of the pulse. Here, we study the dynamical evolution of photons in the 1D1P phase-space vicinity of the plasma wake-phase matching condition. Numerical calculations using a photon kinetic model are validated by direct comparison with 1D and quasi-3D particle-in-cell simulations. These calculations form the basis of a linear theory of the photon dynamics which reveals several important results, including scalings for the properties of the witness pulse and a self-similar solution for the photon phase-space dynamics. One prediction of the analytic theory is that the pulse can be compressed indefinitely, though the amount of compression would ultimately be limited by practical constraints. These results suggest that photon acceleration can provide a novel source of sub-femtosecond, short wavelength radiation.

XUV generation↗