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PPPL Laboratory Directed Research and Development (Project Final Reports, FY2018 - FY2020)

The U.S. Department of Energy’s (DOE) Princeton Plasma Physics Laboratory (PPPL) is a collaborative national center for fusion energy science, basic sciences, and advanced technology. The Laboratory has three major missions: (1) to develop the scientific knowledge and advanced engineering to enable fusion to power the U.S. and the world; (2) to advance the science of nanoscale fabrication for technologies of tomorrow; and (3) to further the development of the scientific understanding of the plasma universe from laboratory to astrophysical scales. PPPL’s Laboratory Directed Research and Development (LDRD) program supports and encourages creativity and innovation and contributes to its long-term viability. New scientific and technical research areas emerge and are nurtured through the program. Furthermore, new capabilities are developed to enable the Laboratory to meet its and DOE’s missions. The program is used to systematically diversify the Laboratory’s programs and mission. In the last few years, the program has started projects in nanomaterial synthesis, microelectronics, advanced x-ray spectroscopy, high-energy-density physics, superconducting magnet technology, machine learning and artificial intelligence, 3D magnetic fields to optimize fusion plasmas, integration of permanent magnets with simple high-field magnets to reduce the cost of producing complex 3D magnetic fields, advanced computational methods for predictive understanding and control of fusion plasma, development of quantum computing algorithms for plasma physics, liquid metal plasma-facing components for fusion reactors, virtual engineering, and plasma-based space propulsion. The program is also the vehicle to recruit and train talented scientists and engineers with the new skills needed to perform the Laboratory’s mission. Many of the new hires through the program go on to become world-class scientists and engineers in their fields. This report provides descriptions and accomplishments of those LDRD projects that were completed during fiscal years 2018 through 2020.

36 MATERIALS SCIENCE↗

Parameterized anomalous transport model for current-carrying collisionless plasmas in pulsed power inertial confinement fusion

Current delivery in pulsed power inertial confinement fusion is influenced by collisionless current-carrying microturbulent plasmas, which are sourced from electrode surfaces. In this setting, the lower hybrid drift instability—triggered by plasma acceleration—is a leading candidate driver of difficult-to-predict momentum and energy transport. To characterize the nonlinear state of the microturbulent plasma, a parameterized anomalous transport model is developed for the instability, with analytic formulas for anomalous collision frequency, resistivity, and species heating rates. The formulas are expressed in terms of linear-theory variables and four dimensionless parameters that characterize the macroscopic plasma state. The model is built on linear theory analysis, power law analysis, and quasilinear theory analysis, and is validated using a series of nonlinear continuum kinetic Vlasov–Poisson simulations. The theoretical and computational investigation demonstrates that the anomalous collision frequency associated with the instability can be reliably approximated, within about a factor of five or better, by the unscaled linear theory growth rate of the fastest-growing wavenumber mode. This finding enables efficient calculation of anomalous resistivity and species heating rates over a wide range of plasma conditions, resulting in improved predictive capabilities.

Complex functions↗

Ideal MHD Limited Electron Temperature in Spherical Tokamaks

It is well documented that the central electron temperature in the national spherical torus experiment (NSTX) remains largely unchanged as the external heating power, and hence the normalized volume averaged plasma pressure β increases [Stutman, Phys. Rev. Lett. 102, 115002 (2009)]. Herein we present a hypothesis that low n, pressure driven ideal magnetohydrodynamic (MHD) instabilities that are nondisruptive, can break magnetic surfaces in the central region and thereby flatten the electron temperature profiles. We demonstrate this mechanism in a 3D resistive MHD simulation of a NSTX discharge. By varying the toroidal magnetic field strength, and/or the heating power, we show that there is a critical value of β, above which the central temperature profile no longer peaks on axis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

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↗

Error field identification through torque balance on a saturated island in DIII-D

Measurement of the electromagnetic torque on a magnetic island could be an attractive method for error field identification in the early phase of ITER operation. Previous DIII-D experiments (Strait 2014 Nucl. Fusion 54 073004; Shiraki et al 2015 Plasma Phys. Control. Fusion 57 025016) have demonstrated the principle of this approach using a stationary or slowly rotating island, while recent developments in magnetic data analysis (Sweeney and Strait 2019 Phys. Plasmas 26 012509) allow the field of a rapidly rotating island to be readily distinguished from that of the wall currents induced by its rotation. In a recent experiment, a rotating n = 1 magnetic perturbation forced a saturated magnetic island to rotate, thus sampling all toroidal phases periodically in a single discharge. The phase and amplitude of the error field are inferred from analysis of the time-dependent torque balance on the island, including torques from the error field, the applied magnetic perturbation, and the wall currents induced by rotation of the applied perturbation and the island. Furthermore, results agree well with those from more conventional methods.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Preface to the Proceedings of the 25th Topical Conference on High-Temperature Plasma Diagnostics

The 25th Topical Conference on High-Temperature Plasma Diagnostics (HTPD 2024) was held in Asheville, NC, USA, at the Renaissance Asheville Downtown Hotel from 21 to 25 April 2024. This biennial conference brings together scientists and engineers from a variety of fields, including magnetic confinement fusion, inertial confinement fusion, space plasmas, astrophysics, and industrial applications, to discuss mutual problems in the development of instrumentation and experimental techniques for the characterization of high-temperature plasmas. As the 25th meeting, HTPD 2024 represents ∼50 years of ongoing international collaboration on these topics.

Biewer, Theodore [ORNL] (ORCID:0000000174563509)↗

Collision operator for electron runaway in cold weakly ionised plasmas

In cold weakly ionised plasmas, the Dreicer generation mechanism can be non-diffusive as demonstrated in a recent study. By expanding the previous letter, we present the detailed description of a proper collision operator to precisely account for the non-diffusive electron kinetics. The operator appropriately combines the Fokker–Planck operator and Boltzmann operator where free-bound collision cross-sections are valid in the low-energy region. The proposed operator is envisaged to predict runaway electron generation in cold weakly ionised plasmas, particularly to design a runaway-free reactor tokamak start-up.

fusion plasma↗

Plasma confinement state classification in fusion power plants: Profile reflectometer and ensemble diagnostics

As Fusion Pilot Plants (FPPs) are increasingly viewed as within reach, many engineering challenges remain. Not many diagnostics are expected to be available in a reactor environment. Survivability, maintainability, and limited port space substantially restrict the number of FPP-relevant diagnostics. One remaining challenge is developing tools and devices to extract plasma state information necessary for controlling an FPP from a limited subset of diagnostics. This work is part of an overarching project to address this challenge. The specific diagnostic subset to be used in FPPs is still under debate. We take the approach of developing machine-learning-based tools for different significant plasma state parameters, using already known FPP-viable diagnostics. Previously we developed a plasma confinement mode classifier utilizing the Electron Cyclotron Emission (ECE) diagnostic. Here, we expand on this by developing a Profile Reflectometer (PR) based classifier with 97% test accuracy, and an ensemble model that combines the ECE and PR models into a single model, achieving 99% test accuracy.

Clark, Randall [Univ. of California, San Diego, CA↗

Fast ion stabilization of tilt in large radius FRCs

The field reversed configuration (FRC) has been a curious case in plasma physics research in that early MHD analysis suggested FRCs should be grossly unstable, while experimental results contradicted that prediction. Later, this theory was able to resolve this contradiction by understanding that finite Larmor radius effects largely negated the MHD predictions. Similarly, previous theoretical studies of beam driven FRCs predicted that such system would be unstable to beam driven modes while, again, experimental results indicated the contradiction. In this paper, we reconcile the theoretical understanding of beam driven modes with experimental observations of stability in these systems. By self-consistently capturing fast ion generation from neutral beam injection and its impact on the plasma equilibrium, we show that low amplitude perturbations in the magnetic field, driven by betatron particles, modify the precession frequencies of the betatron particles such that the drive for compressional Alfvén waves in the thermal plasma is reduced. Finally, we are able to demonstrate, for the first time, stable beam driven FRC evolution at high S*/E in 3D kinetic simulations.

Betatrons↗

Fueling method for small, steady-state, aneutronic FRC fusion reactors

A system and method for fueling a fusion reactor. The system includes a reactor chamber containing a stable plasma including a fusion fuel; a heating system configured to heat the plasma and increase an ion energy of the plasma to a level sufficient for producing net power from fusion reactions in the stable plasma; a plurality of magnets coaxial to the reactor chamber, the plurality of magnets producing a magnetic field sufficient to confine the stable plasma and promote rapid loss of fusion products into a scrape off layer; and a neutral beam injection system configured to inject additional quantities of the fusion fuel to sustain the power output of the fusion reaction.

Cohen, Samuel A.↗

Fast electron transport dynamics and energy deposition in magnetized, imploded cylindrical plasma

Inertial confinement fusion approaches involve the creation of high-energy-density states through compression. High gain scenarios may be enabled by the beneficial heating from fast electrons produced with an intense laser and by energy containment with a high-strength magnetic field. Here, we report experimental measurements from a configuration integrating a magnetized, imploded cylindrical plasma and intense laser-driven electrons as well as multi-stage simulations that show fast electrons transport pathways at different times during the implosion and quantify their energy deposition contribution. The experiment consisted of a CH foam cylinder, inside an external coaxial magnetic field of 5 T, that was imploded using 36 OMEGA laser beams. Two-dimensional (2D) hydrodynamic modelling predicts the CH density reaches 9.0 g cm − 3 , the temperature reaches 920 eV and the external B-field is amplified at maximum compression to 580 T. At pre-determined times during the compression, the intense OMEGA EP laser irradiated one end of the cylinder to accelerate relativistic electrons into the dense imploded plasma providing additional heating. The relativistic electron beam generation was simulated using a 2D particle-in-cell (PIC) code. Finally, three-dimensional hybrid-PIC simulations calculated the electron propagation and energy deposition inside the target and revealed the roles the compressed and self-generated B-fields play in transport. During a time window before the maximum compression time, the self-generated B-field on the compression front confines the injected electrons inside the target, increasing the temperature through Joule heating. For a stronger B-field seed of 20 T, the electrons are predicted to be guided into the compressed target and provide additional collisional heating. This article is part of a discussion meeting issue ‘Prospects for high gain inertial fusion energy (part 2)’.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The shear Alfvén continuum of quasisymmetric stellarators

The shear Alfvén wave (SAW) continuum plays a critical role in the stability of energetic particle-driven Alfvén eigenmodes. We develop a theoretical framework to analyze the SAW continuum in three-dimensional (3-D) quasisymmetric magnetic fields, focusing on its implications for stellarator design. By employing a near-axis model and degenerate perturbation theory, the continuum equation is solved, highlighting unique features in 3-D configurations, such as the interactions between spectral gaps. Numerical examples validate the theory, demonstrating the impact of flux-surface shaping and quasisymmetric field properties on continuum structure. The results provide insights into optimizing stellarator configurations to minimize resonance-driven losses of energetic particles. This work establishes a basis for incorporating Alfvénic stability considerations into the stellarator design process, demonstrated through optimization of a quasihelical configuration to avoid high-frequency spectral gaps.

fusion plasma↗

Alfvén mode spectrum in the advanced steady-state tokamak scenario with negative triangularity

In the earlier studies [Zheng et al. Fundam. Plasma Phys. 10, 100051 (2024)], the negative triangularity tokamak was shown to have a unique and outstanding feature for the steady-state confinement. In addition to relieving the divertor heat load concern, it can reach a much higher beta limit in the nearly steady-state confinement, about twice the Troyon limit in the positive triangularity case. In this work, we extend the investigation to the Alfvén spectrum and toroidal Alfvén eigenmodes (TAEs). This helps to evaluate the property of energetic particle confinement in this advanced scenario of a negative triangularity tokamak. We found that, because of the large safety factor and reversed magnetic shear in the core plasma region near the magnetic axis, the TAE gap tends to be closed or have only a short radial extension between the continua. in the on-axis core region and open primarily in the off-axis region, where TAEs are shown to be present. This indicates that energetic particle confinement in the core region near the magnetic axis, where nuclear fusion reactions prevail, is not seriously affected by the excitation of TAEs in this scenario. The configuration with off-axis TAEs helps the confinement of energetic particles as compared to the configuration with near-axis TAEs. The results show that the advanced steady-state tokamak scenario with negative triangularity, because of the rapid variation of the safety factor, also has a favorable feature for energetic particle confinement.

Fourier analysis↗

Bootstrap current modeling in M3D-C1

Bootstrap current plays a crucial role in the equilibrium of magnetically confined plasmas, particularly in quasi-symmetric stellarators and in tokamaks, where it can represent bulk of the electric current density. Accurate modeling of this current is essential for understanding the magnetohydrodynamic (MHD) equilibrium and stability of these configurations. This study expands the modeling capabilities of M3D-C1, an extended-MHD code, by implementing self-consistent physics models for bootstrap current. It employs two analytical frameworks: a generalized Sauter model (Sauter et al. 1999 Phys. Plasmas vol. 6, no. 7, pp. 2834–2839), and a revised Sauter-like model (Redl et al. 2021 Phys. Plasmas vol. 28, no. 2, pp. 022502). The isomorphism described by Landreman et al. (2022 Phys. Rev. Lett. vol. 128, pp. 035001) is employed to apply these models to quasi-symmetric stellarators. The implementation in M3D-C1 is benchmarked against neoclassical codes, including NEO, XGCa and SFINCS, showing excellent agreement. These improvements allow M3D-C1 to self-consistently calculate the neoclassical contributions to plasma current in axisymmetric and quasi-symmetric configurations, providing a more accurate representation of the plasma behavior in these configurations. A workflow for evaluating the neoclassical transport using SFINCS with arbitrary toroidal equilibria calculated using M3D-C1 is also presented. This workflow enables a quantitative evaluation of the error in the Sauter-like model in cases that deviate from axi- or quasi-symmetry (e.g. through the development of an MHD instability).

fusion plasma↗

Direct comparison of gyrokinetic and fluid scrape-off layer simulations

Typically, fluid simulations are used for tokamak divertor design. However, fluid models are only valid if the scrape-off layer (SOL) is highly collisional. This assumption is valid in many present-day experiments but is questionable in the upstream SOL of some high-power scenarios envisioned for burning plasmas and fusion pilot plants. This paper reports on comparisons between fluid and kinetic simulations of the SOL for upstream parameters and geometry representative of the Spherical Tokamak for Energy Production fusion pilot plant. The SOLPS-ITER (fluid) and Gkeyll (gyrokinetic) codes are operated in a two-dimensional axisymmetric mode, which replaces turbulence with ad-hoc diffusivities. In kinetic simulations, we observe that the ions in the upstream SOL experience significant mirror trapping. This substantially increases the upstream temperature and has important implications for impurity dynamics. We show that the mirror force, which is excluded in SOLPS’s fluid equations, enhances the electrostatic potential drop along the field line in the SOL. We also show that the assumption of equal main ion and impurity temperatures, which is made in commonly used fluid codes, is invalid for the regimes explored here. The combination of these effects results in superior confinement of impurities to the divertor region in kinetic simulations, consistent with our earlier predictions [Kotschenreuther et al., in 29th IAEA 29 Fusion Energy Conference (IAEA, London, UK, 2023)]. This effect can be dramatic, reducing the midplane impurity density by orders of magnitude. These results indicate that in lower collisionality SOL’s the tolerable downstream impurity densities may be higher than would be predicted by fluid simulations, allowing for higher radiated power while avoiding unacceptable core contamination. Our results highlight the importance of kinetic simulations for divertor design and optimization for fusion pilot plants.

Computational fluid dynamics↗

Free-Surface Liquid Lithium Flow Modeling and Stability Analysis for Fusion Applications

Liquid metal plasma facing components are considered an attractive design choice for fusion devices including pilot plants. Virtual prototyping of such devices includes modeling of free-surface flow of the electrically conductive liquid, which requires computational fluid dynamics (CFD) and magnetohydrodynamics (MHD) simulations. Numerical tools capable of simulating flows and heat transfer in the free-surface MHD flow were developed at PPPL based on the customized ANSYS CFX. Here, MHD is introduced using a magnetic vector potential approach. Free-surface flow capabilities are available in the code and were tested. Special stabilization procedures were derived and applied to improve convergence of the momentum equations with the source terms due to the Lorentz force and surface tension. Important characteristics of the fusion-relevant liquid metal flow is free surface smoothness and stability. Heat flux from the plasma impacts the liquid surface at a very acute angle, so any change of the free surface from axisymmetry can dramatically increase the local heat flux density and thus create excessive evaporation of liquid lithium into the plasma, which is detrimental to operations. Stability analysis of the liquid metal film flow was performed to determine applicable flow regimes. Thin film flow along horizontal wall is considered. Effects of gravity, magnetic field, and surface tension are included in the analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Evaluation of the Abel inversion integral in O-mode plasma reflectometry using Chebyshev–Gauss quadrature

The Abel transform is often used to reconstruct plasma density profiles from O-Mode polarized reflectometry diagnostics. However, standard numerical trapezoidal evaluation of the Abel inversion integral can be computationally expensive for a large number of evaluation points, and an endpoint singularity exists on the upper-bound of the integral, which can result in an increased error. In this work, Chebyshev–Gauss quadrature is introduced as a new method to evaluate the Abel inversion integral for the problem of O-Mode plasma reflectometry. Here, the method does not require numerical evaluation of an integral singularity and is shown to have similar accuracy compared to existing methods while being computationally efficient.

47 OTHER INSTRUMENTATION↗