Recent Publications

Deuterium retention of boron powder from deuterium gas or ion exposure

Shota Abe, Adam Q. Kuang, Christopher P Chrobak, Alessandro Bortolon, Camilo Jaramillo-Correa, Bruce E Koel

Princeton Plasma Physics Laboratory, Princeton University, Commonwealth Fusion Systems LLC

We report retention of deuterium (D), a proxy for tritium (T), from D2 neutral gas and D+ ion exposures on commercial boron (B) powder, a proxy for B dust potentially formed in fusion reactors. D removal behavior from B powder is reported as a means of estimating a potential T inventory in B dust in advanced fusion reactors, such as SPARC and ITER, the latter currently plans to employ B wall conditioning by glow-discharge boronization. B wall conditioning forms surface coatings of chemical compounds on tungsten (W) plasma-facing components (PFCs), thus suppressing plasma contamination by impurities such as oxygen, carbon, and tungsten. However, B-based slag or dust particles are expected to form. Such B dust particles can retain hydrogen isotope species, thereby causing a T inventory issue. In this work, the commercial B powder was exposed to D2 neutral gas or D+ ions and analyzed by temperature-programmed desorption to quantify D retention and the desorption temperature. The experiment confirmed D retention from D2 neutral gas exposure. A strong D2 desorption peak at 700 K, corresponding to B-D bonding, was observed for all D2 gas and D+ ion exposure cases. For D2 gas exposures, D retention was significantly enhanced at a B powder temperature of 550 K. B powder bakeout under vacuum at 600 K for 22 hours after D2 exposure exhibited efficient D removal. In contrast, the B powder bakeout at 420 K, even for 1 day, did not remove D efficiently. D retention yields from D+ ion exposure, emulating charge-exchange involving D atoms, were determined. Experiments confirmed that D retention was suppressed by oxidation of the B powder surface, which naturally occurs in reactor environments.

Machine learning methods to fit interatomic potentials for plasma–surface interactions: A C–H–O–Ar example

Jack S. Draney, Athanassios Z. Panagiotopoulos, David B. Graves

Princeton University

At the core of molecular dynamics (MD) simulations of plasma–surface interactions is the interatomic potential that predicts the energy and forces of atomic configurations. Recently, machine-learned interatomic potentials (MLIPs) have become popular in related fields. These MLIPs, developed for near-equilibrium calculations, are challenged when used for the relatively high-energy, chaotic conditions of plasma–surface interactions. In this paper, active learning is used to produce a large dataset of density functional theory calculations featuring C, H, O, and Ar in configurations relevant to simulations of plasma–surface interactions. These data are then used to train both an MLIP and a classical interatomic potential (reactive force field, ReaxFF) for direct comparison. Both potentials are trained using typical machine learning methods, namely, optimization of a loss function via automatic differentiation with respect to the interatomic potential parameters. Both models performed well on a test dataset, producing comparable errors. However, MD simulations using the MLIP were not consistent with published experiments. In contrast, the trained ReaxFF potential appears to perform well on these tasks. Active learning accompanied by machine-learning-style parameter fitting appears promising as a method for producing transferable interatomic potentials for simulations of plasma–surface interactions.

Nonlinear saturation of ballooning modes in stellarators

X. Chu, S.C. Cowley, N. Ferraro, Y. Zhou, F.I. Parra

Princeton Plasma Physics Laboratory, Princeton University, Shanghai Jiao Tong University

Ballooning mode saturation is investigated in realistic stellarator configurations using the flux tube approach of Ham et al (2018 Plasma Phys. Control. Fusion 60 075017), Ham et al (2016 Phys. Rev. Lett. 116 235001). The method is adapted to account for the lack of exact force balance in stellarator equilibrium solvers that assume existence of nested flux surfaces. A variational approach for calculating flux tube energy is developed to overcome this force error problem in stellarator numerical equilibria. Saturated (equilibrium) flux tube states that cross 10%–20% of the plasma minor radius are shown to exist for linearly ballooning unstable profiles. It is shown that several features of the displaced flux tube structure in a full nonlinear MHD simulation of Wendelstein 7X are reproduced by our model. Saturated states are found in a compact stellarator equilibrium close but below the marginal ballooning linear instability, i.e. the unperturbed equilibrium is metastable. This suggests that edge-localized-mode-like explosive MHD behavior may be possible in stellarators.

Hot Spot Evolution Measured by High-Resolution X-Ray Spectroscopy at the National Ignition Facility

Lan Gao, B. F. Kraus, K. W. Hill, M. B. Schneider, A. Christopherson, B. Bachmann, M. Bitter, P. Efthimion, N. Pablant, R. Betti, et al.

Lawrence Livermore National Laboratory, Princeton Plasma Physics Laboratory, Princeton University, Laboratory for Laser Energetics, University of Rochester

Evolution of the hot spot plasma conditions was measured using high-resolution x-ray spectroscopy at the National Ignition Facility (NIF). The capsules were filled with DD gas with trace levels of Kr, and had either a high-density-carbon (HDC) ablator or a tungsten (W)-doped HDC ablator. Time-resolved measurement of the Kr He$β$ spectra, absolutely calibrated by a simultaneous time-integrated measurement, allows inference of the electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. By matching the calculated hot spot emission using a collisional-radiative code to experimental observations, the hot spot size and areal density are determined. These advanced spectroscopy techniques further reveal the effect of W dopant in the ablator on the hot spot parameters for their improved implosion performance.

Absolute Calibration of a Time-Resolved High Resolution X-ray Spectrometer for the National Ignition Facility (invited)

Lan Gao, B. F. Kraus, K. W. Hill, M. Bitter, P. Efthimion, M. B. Schneider, A. G. MacPhee, D. B. Thorn, J. Kilkenny, J. Ayers, et al.

Lawrence Livermore National Laboratory, Princeton Plasma Physics Laboratory, Princeton University, Laboratory for Laser Energetics, University of Rochester

A high resolution, Diagnostic Instrument Manipulator (DIM)-based x-ray Bragg crystal spectrometer has been calibrated for and deployed at the National Ignition Facility (NIF) to diagnose plasma conditions in ignition capsules near stagnation times. The spectrometer has two conical crystals in the Hall geometry focusing rays from the Kr He$α$, Ly$α$, and He$β$ complexes onto a streak camera, with the physics objectives of measuring time-resolved electron density and temperature through observing Stark broadening and the relative intensities of dielectronic satellites. A third von Hámos crystal that time-integrates the Kr He$α$, He$β$ and intervening energy range provides in-situ calibration for the streak camera signals. The spectrometer has been absolutely calibrated using a microfocus x-ray source, an array of CCD and single-photon-counting detectors, and multiple K- and L-absorption edge filters at the Princeton Plasma Physics Laboratory (PPPL) x-ray laboratory. Measurements of the integrated reflectivity, energy range, and energy resolution for each crystal are discussed. These calibration data provide absolute x-ray signal levels for NIF measurements, enabling precise filter selection and comparisons to simulations.

Velocity-space Origins of the Pressure–Strain Interaction in Multipopulation Distributions and Its Application to Magnetic Reconnection

M. Hasan Barbhuiya, Paul A. Cassak, Sarah Conley, Julia E. Stawarz, Emily Lichko, Jason M. TenBarge, James Juno, Jason R. Shuster, Gregory G. Howes, Subash Adhikari

Clemson University, Bates College, Northumbria University, Princeton University, Princeton Plasma Physics Laboratory

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.

Ion Weibel instability in the hybrid framework: The optimal resolution

Luca Orusa, Taiki Jikei

Columbia University, Princeton University, The University of Tokyo

The study of collisionless shocks and their role in cosmic-ray acceleration has gained increasing importance through both observations and simulations. Accurately modeling the shock transition region, where particle injection and energization occur, requires a proper description of the microinstabilities governing its structure. In high-Mach-number astrophysical shocks, such as those associated with supernova remnants, the ion Weibel instability is believed to provide the dominant dissipation mechanism. In this work, we investigate the ion Weibel instability driven by counterstreaming beams in the presence of an external perpendicular magnetic field, with beam velocities significantly exceeding the local Alfvén speed. We employ hybrid simulations, in which ions are treated kinetically while electrons are modeled as a charge-neutralizing fluid. Although hybrid models are widely employed to study collisionless shocks, the resolution requirements needed to accurately capture ion-scale instabilities remain poorly understood. We address this issue by developing a linear theory of the ion Weibel instability tailored to the massless-electron assumption of hybrid models and validating it with one- and two-dimensional simulations over a wide range of Alfvénic Mach numbers. We show that hybrid simulations can reliably reproduce the growth, saturation, and polarization of Weibel-generated magnetic fields in weakly magnetized regimes, provided that the relevant ion-scale modes are properly resolved. From the scaling of the dominant mode, we derive a minimum spatial resolution required as a function of Alfvénic Mach number. We also demonstrate that excessive resolution introduces unphysical small-scale whistler modes inherent to the massless-electron approximation. We validate the analysis by comparing the results with full particle-in-cell simulations. Together, these results provide practical guidance for hybrid simulations of collisionless shocks and beam-driven plasma systems.

Phase-space energy transfer of wave–particle interactions using the field–particle correlation technique and linear plasma theory with JET-PLUME

Collin R. Brown, Gregory G. Howes, Kristopher G. Klein, Jason M. TenBarge

University of Iowa, Naval Research Laboratory, University of Arizona, Princeton University

The collisionless transfer of energy between fields and particles through wave–particle interactions is a fundamental process in space plasmas but remains incompletely characterized because many mechanisms operate across a wide parameter range and diverse plasma conditions. The field–particle correlation (FPC) technique reveals velocity-space signatures of particle energization by correlating measured electric field fluctuations with changes in the velocity distribution. Fully mapping these signatures across plasma parameters requires an impractically large number of kinetic simulations or observations. To address this challenge, we introduce JET-PLUME (Judging Energy Transfer in a Plasma in a Linear Uniform Magnetized Environment), an extension of the PLUME Vlasov–Maxwell dispersion solver. JET-PLUME uses PLUME's ability to model parallel drifting bi-Maxwellian distributions to examine phase-space energy transfer by adding an analytic Fourier-space formulation of the FPC. This approach isolates the contribution of individual resonances, separates degenerate entropy mode components, and allows systematic analysis of unstable, growing modes. Dimensionless expressions extend the results across a broad parameter range and highlight the role of off-diagonal elements of the susceptibility tensor in coupling electric field and current response. We show that during kinetic Alfvén wave damping, the perpendicular field can drive parallel ion currents among particles with large v⊥, reducing the net Landau damping. The resulting velocity-space signatures, accessible through JET-PLUME, demonstrate how analytic formulations of phase-space energy transfer can reveal novel physics of wave–particle interactions across diverse plasma environments.

Real-time plasma monitoring framework for advanced plasma control and ML-research in DIII-D

SangKyeun Kim, Keith Erickson, Azarakhsh Jalalvand, Ramon Reed, Ricardo Shousha, Andy Rothstein, Jalal Butt, Filippo Scotti, Steve Allen, Semin Joung, et al.

Princeton Plasma Physics Laboratory, Princeton University, University of Wisconsin-Madison, SLAC National Accelerator Laboratory, Lawrence Livermore National Laboratory

Estimating coil features from an equilibrium

E. Rodríguez, W. Sengupta

Max Planck Institute for Plasma Physics, Princeton University

We present an explicit theoretical framework for constructing artificial modular coils for vacuum stellarator fields based solely on equilibrium properties, achieved through the formulation of a current potential defined on flux surfaces. Contours of constant Boozer toroidal angle can be directly interpreted as proxy coils, and so we demonstrate that key measures of coil complexity—particularly coil non-planarity—are strongly governed by local magnetic-field properties. This approach shows promise as predictor for more realistic coil configurations, providing both a pathway toward deeper understanding of equilibrium–coil relationships and a potential practical proxy for coil design.

Asymptotic behavior of the shear flow reactivity enhancement effect

Henry Fetsch, Nathaniel J. Fisch

Princeton University

Fusion reactivity is enhanced in the vicinity of strongly sheared flow due to the tendency of fast ions near the Gamow peak to travel long distances between collisions, thereby sometimes crossing gradients in the background flow and attaining a velocity boost relative to the thermal background. This “shear flow reactivity enhancement effect” (SFRE) allows turbulent kinetic energy on fine spatial scales to contribute to fusion reactivity before thermalizing, which, remarkably, enables ignition of some inertial confinement fusion hot spots under conditions where fully thermalized plasma would fail to ignite. The size of the SFRE is a consequence of the dramatic scale separations distinguishing thermal ions, which govern fluid quantities, and fast ions, which govern fusion reactivity. It is demonstrated in this work that, as the Gamow energy increases relative to the thermal energy, the SFRE in unmagnetized plasma becomes asymptotically large compared to hydrodynamic effects such as viscous dissipation. An asymptotic formula is derived in this limit, quantifying the SFRE for reactants of disparate masses and charge states.

Enabling integrated AI control on DIII-D: a control system design with state-of-the-art experiments

A. Rothstein, H.J. Farre-Kaga, J. Butt, R. Shousha, K. Erickson, T. Wakatsuki, P. Steiner, S.K. Kim, A. Jalalvand, E. Kolemen

Princeton University, Princeton Plasma Physics Laboratory, National Institutes for Quantum and Radiological Science and Technology

We present the design and application of a general algorithm for Prediction And Control using MAchiNe learning ( PACMAN ) in DIII-D. Machine learning (ML)-based predictors and controllers have shown great promise in achieving regimes in which traditional controllers fail, such as tearing mode (TM) free scenarios, ELM-free scenarios and stable advanced tokamak conditions. The architecture presented here was deployed on DIII-D to facilitate the end-to-end implementation of advanced control experiments, from diagnostic processing to final actuation commands. This paper describes the detailed design of the algorithm and explains the motivation behind each design point. We also describe several successful ML control experiments in DIII-D using this algorithm, including a reinforcement learning controller targeting advanced non-inductive plasmas, a wide-pedestal quiescent H-mode ELM predictor, an Alfvén Eigenmode controller, a Model Predictive Control plasma profile controller and a state-machine TM predictor-controller. There is also discussion on guiding principles for real-time ML controller design and implementation.

The impact of kinetic and global effects on ideal ballooning 2nd stable pedestals of conventional and low aspect-ratio tokamaks

M.S. Anastopoulos Tzanis, M. Yang, A. Kleiner, J.F. Parisi, G.M. Staebler, P.B. Snyder

Oak Ridge National Laboratory, Princeton University, Marathon Fusion, Commonwealth Fusion Systems

The EPED model (Snyder et al 2011 Nucl. Fusion 51 103016) has had success in describing the pedestal structure of Type-I ELM and QH-mode plasmas in tokamaks, by combining kinetic ballooning mode (KBM) and peeling–ballooning (PB) constraints. Within EPED, the KBM constraint is often approximated by a technique using calculated ideal ballooning mode (IBM) thresholds, fit to a functional form designed to capture non-local effects. It has been noted that quantitative differences between local ideal MHD and gyro-kinetic (GK) ballooning stability can be larger at low aspect ratio. KBM critical pedestals are consistent with observations in initial studies on conventional and spherical tokamaks. In this work, the application of a reduced model for the calculation of the kinetic ballooning stability boundary is presented based on a novel and newly developed gyro-fluid system (GFS) code (Staebler et al 2023 Phys. Plasmas 30 102501). GFS is observed to capture KBMs in DIII-D as well as the NSTX pedestals, opening a route to integrating this model into EPED. Finally, high but finite n global ballooning modes are observed to limit the access to the local 2nd stability and thus provide a transport mechanism that constrains the pedestal evolution with β p , ped . The high n global ballooning stability is approximated by its ideal MHD analog using ELITE. It is shown that nearly-local high n modes with k y ρ s ∼ 0.25 − 0.5 can provide a proxy for the critical β p , ped when a 2nd stable access exists on DIII-D plasmas. The use of GFS and ELITE scaling in EPED provides improved agreement to EPED1 in an initial comparison with DIII-D pedestal data.