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DOE OSTI2018

Final Technical Report Under SC0018278

Work supported by the grant "Stability and Control of Burning Tokamak Plasmas with Resistive Walls" in the period Aug 2017 to Aug 2018 can be cast in three general categories: (1) linear tearing regimes and the effects on the response to error fields and resistive walls: (2) nonlinear tearing modes in the presence of error fields, with locking; and (3) energetic particle effects. In the first category, we have completed a study of tearing mode regimes with extended MHD effects, including parallel dynamics and toroidal effects, notably favorable average curvature. This work has been presented at the 2018 Sherwood Conference in Ref.[1]. This work has been published in the ArXiv in Ref.[2] and is being prepared for publication in Physics of Plasmas. A systematic study of shaping in a tokamak plasma with resistive tearing layers and a resistive wall has been presented in the Ph D dissertation[3] by Dov Rhodes, a student of Andrew Cole at Columbia University. John Finn was on Rhodes's Ph D committee, and was a co-author of a paper published in Physics of Plasmas on that work. A detailed study of nonlinear tearing modes in the presence of finite beta, favorable average curvature, and an error field has been nearly completed. In this study it was found that the response to an error field with real frequency a tearing layer agreed with analytic results, and that tearing mode saturation by flattening of the current profile as well as destabilization due to flattening of the pressure profile were important factors in the locking process. This work was presented at the 2017 APS/DPP Conference and at the 2018 Sherwood Conference. The effects of energetic ions on tearing modes was presented at the 2017 APS/DPP Conference and in the Ph D dissertation of Michael Halfmoon. John Finn served as a committee member on Halfmoon's Ph D committee. Extensions to this work including two-fluid effects were performed and presented at the APS/DPP Conference in 2017.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

ARC physics basis–magnetohydrodynamics

ARC is designed to produce 400 ⁢MW of net electricity and prove the commercial feasibility of a fusion power plant. In order to achieve this goal ARC has to operate with optimal core performance in a stationary scenario that minimises wear on the first wall and divertor. This requires avoiding or mitigating magnetohydrodynamic (MHD) instabilities which have the potential to not only degrade the plasma core but also lead to deleterious transient heat loads on plasma facing components. Therefore, this work aims at characterising the MHD stability of the high performance ARC scenario and inform the design of error field correction coils. Firstly, simulations of vertical displacement events show that an in-vessel coil is not needed and instead the poloidal shaping coils can be used to control vertical stability. These simulations also inform the demands on the corresponding coil power supplies. Stability analysis of the ideal kink mode with or without a conducting wall and kinetic effects suggests that the ARC baseline scenario operates deeply in the stable region. Using RDCON, tearing modes at the 𝑚/𝑛 =2/1 and 3/2 surfaces (with poloidal mode number 𝑚, and toroidal mode number 𝑛) are shown to be linearly stable, and including thermal transport effects in the rational surfaces lead to further stabilisation. However, other transient plasma instabilities can seed neoclassical tearing modes (NTMs). The marginally stable width of NTMs in ARC strongly depends on the internal inductance and can fall below 0.1% of the normalised poloidal flux. Furthermore, an empirical cross-machine model of the 𝑛 =1 error field leading to a disruption predicts a critical error field larger than SPARC but smaller than ITER. Three-dimensional coils can be designed with the Generalised Purturbed Equilbium Code based on a simple model that calculates the maximum correctable error field that is limited by the neoclassical toroidal viscosity torque. Broad scans of different coil geometries identify a set of 2 rows of off-midplane coils to be a suitable solution. It is also determined that such a set of three-dimensional coils is capable of correcting 𝑛 =2 error fields to some degree and creating strong enough 𝑛 =2 or 𝑛 =3 edge resonant perturbation fields for the suppression of edge-localised modes at reasonable coil currents. The final design of the first ARC will be further informed by results from SPARC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Stability and Control of Burning Tokamak Plasmas with Resistive Walls: Final Technical Report

This project is focused on theoretical and computational development for quantitative prediction of the stability and control of the equilibrium state evolution in toroidal burning plasmas, including its interaction with the surrounding resistive wall. The stability of long pulse burning plasmas is highly sensitive to the physics of resonant layers in the plasma, sources of momentum and flow, kinetic effects of energetic particles, and boundary conditions at the wall, including feedback control and error fields. In ITER in particular, the low toroidal flow equilibrium state, sustained primarily by energetic alpha particles from fusion reactions, will require the consideration of all of these key elements to predict quantitatively the stability and evolution. The principal investigators on this project have performed theoretical and computational analyses, guided by analytic modeling, to address this physics in realistic configurations. The overall goal has been to understand the key physics mechanisms that describe stable toroidal burning plasmas under active feedback control. Several relevant achievements have occurred during this project, leading to publications and invited conference presentations. In theoretical efforts, with the physics of the resonant layers, resistive wall, and toroidal momentum transport included, this study has extended from cylindrical resistive plasma - resistive wall models with feedback control to toroidal geometry with strong shaping to study mode coupling effects on the stability. These results have given insight into combined tearing and resistive wall mode behavior in simulations and experiment, while enabling a rapid exploration of plasma parameter space, to identify possible domains of interest for large plasma codes to investigate in more detail. Resonant field amplification and quasilinear torques in the presence of error fields and velocity shear have also been investigated. Here it was found, surprisingly, that the Maxwell torque on resonant layers in the plasma which exhibit finite real frequencies ωr in their response is significantly different from the conventional results based on tearing layers with pure real growth (or damping) rates. This observation suggests the possibility that the torque on the tearing layers can lock the plasma rotation to this finite phase velocity, which may lead to locking in which velocity shear is maintained. More broadly, the sources of all torques driving flows in magnetic confinement experiments is not fully understood, and this theoretical work may shed light on puzzling experimental results. It was also found that real frequencies occur over a wide range of plasma response regimes, and are indeed the norm and not the exception, often leading to profound effects on the locking torque. Also, the influence of trapped energetic ions orbiting over the resistive plasma mode structure, a critical effect in burning plasmas, was investigated through analytic modeling and analysis of simulations and experiment. This effort has shown that energetic ions can drive the development of disruptive instabilities, but also damp and stabilize the instabilities, depending on the details of the shear in the equilibrium magnetic field. This finding could be critical to maintaining stable operations in burning plasmas. In the most recent work, a series of simulations have been conducted to study the effect of differential flow and energetic ion effects on entry to the onset of a disruptive instability in the most realistic conditions possible, with preexisting nonlinearly saturated benign instabilities. Throughout this work, the linear and quasilinear theory of resonant layers with differential flow between them, their interaction with resistive wall and error fields, and energetic ions effects, have been used to understand realistic simulations of mode onset and the experimental discharges they represent. These studies will continue to answer remaining questions about the relation between theoretical results obtained in this project and observations of the onset and evolution of disruptive instabilities in experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2017

Physics and Control of Locked Modes in the DIII-D Tokamak

This Final Technical Report summarizes an investigation, carried out under the auspices of the DOE Early Career Award, of the physics and control of non-rotating magnetic islands (“locked modes”) in tokamak plasmas. Locked modes are one of the main causes of disruptions in present tokamaks, and could be an even bigger concern in ITER, due to its relatively high beta (favoring the formation of Neoclassical Tearing Mode islands) and low rotation (favoring locking). For these reasons, this research had the goal of studying and learning how to control locked modes in the DIII-D National Fusion Facility under ITER-relevant conditions of high pressure and low rotation. Major results included: the first full suppression of locked modes and avoidance of the associated disruptions; the demonstration of error field detection from the interaction between locked modes, applied rotating fields and intrinsic errors; the analysis of a vast database of disruptive locked modes, which led to criteria for disruption prediction and avoidance.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Field quality of the 4.5 m-long MQXFA pre-series magnets for the HL-LHC Upgrade as observed during magnet assembly

We report that the U.S. High-Luminosity LHC Accelerator Upgrade Project (HL-LHC AUP) is developing MQXFA magnets, a series of 4.5 m long 150 mm aperture high-field Nb 3 Sn quadrupole magnets for the HL-LHC upgrade at CERN. Five pre-series magnets, MQXFA03 through MQXFA07, have been developed. During the magnet assembly stage, we perform magnetic measurements on the coil-pack sub-assembly and magnets after loading to track the field quality for two purposes. First, it serves as a quality assurance tool to check if the magnetic field quality is on track to meet the acceptance criteria. Magnetic measurements are used to understand if magnetic shims are needed to compensate low-order field errors and to meet the field quality targets. Second, the measurements during the assembly stage can also help understand the field quality, especially the geometric field errors, for Nb 3 Sn accelerator magnets. Here we summarize the measurement results of the pre-series MQXFA magnets, including the magnetic axis and twist angle. The results will provide useful feedback for the series production of Nb 3 Sn magnets and on the optimization of field quality of accelerator magnets based on the wind-and-react Nb 3 Sn technology.

43 PARTICLE ACCELERATORS↗

DOE OSTI2022

A resistive MHD model and simulation on plasma flow evolution in the presence of resonant magnetic perturbation in a tokamak

Nonaxisymmetric magnetic fields such as the intrinsic error field and the externally applied resonant magnetic perturbation (RMP) in a tokamak are known to influence the plasma momentum transport and flow evolution through plasma response, which itself strongly depends on the plasma flow as well. The nonlinear interaction between plasma response and flow has been previously modeled in the conventional error field theory with the “no-slip” condition, which has been recently extended to allow the “free-slip” condition. In this work, we further target this specific process and numerically simulate the nonlinear plasma response and flow evolution in the presence of a single-helicity RMP in a circular-shaped model tokamak configuration, based on the full resistive MHD model in the initial-value code NIMROD. Time evolution of the parallel (to k) flow or “slip frequency” profile and its asymptotic steady state obtained from the NIMROD simulations are compared with both conventional and extended nonlinear response theories. Here, k is the wave vector of the propagating island. Good agreement with the extended theory with free-slip condition has been achieved for the parallel flow profile evolution in response to RMP in all resistive regimes, whereas the difference from the conventional theory with the no-slip condition tends to diminish as the plasma resistivity approaches zero.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Updated magnetized transport coefficients: impact on laser-plasmas with self-generated or applied magnetic fields

Errors in the Epperlein and Haines (1986 Phys. Fluids ) transport coefficients were recently found at low electron magnetizations, with new magnetic transport coefficients proposed simultaneously by two teams (Sadler et al 2021 Phys. Rev. Lett. and Davies et al 2021 Phys. Plasmas ); these two separate sets of updated coefficients are shown in this paper to be in agreement. Here, the importance of these new coefficients in laser-plasmas with either self-generated or applied magnetic fields is demonstrated. When an external magnetic field is applied, the cross-gradient-Nernst term twists the field structure; this twisting is reduced by the new coefficients in the low magnetization regime. For plasmas where only self-generated magnetic fields are present, the new coefficients are found to result in the magnetic field moving with the Righi–Leduc heat-flow, enhancing the impact of MHD. Simulations of Biermann battery magnetic fields around ICF hot-spot perturbations are presented, with cross-gradient-Nernst transport increasing spike penetration.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

Physics and Control of Locked Modes

Locked Modes (LMs) are non-rotating magnetic islands. They can originate from previously rotating islands (“precursors”) that stop rotating due to interaction with the resistive wall and error fields, or they can directly form as non-rotating islands, without any precursor, by penetration of error fields. LMs tend to be large because they do not benefit from rotational stabilization, and large islands tend to lock because of their strong interaction with the wall and error fields. Like large islands in general, LMs are undesired for they decrease the plasma confinement and plasma beta. Additionally, and more importantly, LMs often cause disruptions. For both of these reasons, the physics of LMs needs to be better understood, and their control further improved over already encouraging results obtained at DIII-D by a combination of magnetic control of the LM toroidal phase and Electron Cyclotron Current Drive (ECCD) control of the LM amplitude.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

National Spherical Torus Experiment Upgrade Collaborative Research on Configuration Optimization of Advanced Operating Scenarios and Control Including Macroscopy Stability EOG for Period 3/1/14 through 2/28/18

General Atomics has collaborated with PPPL since 1999 in support of NSTX and NSXT-U by leveraging DIII-D program expertise. John Ferron was the principal investigator (PI) for the first nine years (to 2008) and Rob La Haye since then. The research effort evolved over a number of three-year grants and originally included both the core (control, stability, resonant error fields) and the boundary (ELMs, divertor, error fields). In 2014 the current and last grant extension was stretched to four years and split into a core grant (advanced scenarios and control, macroscopic plasma stability and extending 3D magnetics diagnostics) and a boundary grant. Todd Evans is the PI for the new boundary grant which while also for four years expires later than the core grant; a separate end of grant (EOG) report for that is due in July 2018.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Probabilistic locked mode predictor in the presence of a resistive wall and finite island saturation in tokamaks

We present a framework for estimating the probability of locking to an error field in a rotating tokamak plasma. This leverages machine learning methods trained on data from a mode-locking model, including an error field, resistive magnetohydrodynamics modeling of the plasma, a resistive wall, and an external vacuum region, leading to a fifth-order ordinary differential equation (ODE) system. It is an extension of the model without a resistive wall introduced by Akçay et al. [Phys. Plasmas 28, 082106 (2021)]. Tearing mode saturation by a finite island width is also modeled. We vary three pairs of control parameters in our studies: the momentum source plus either the error field, the tearing stability index, or the island saturation term. The order parameters are the time-asymptotic values of the five ODE variables. Normalization of them reduces the system to 2D and facilitates the classification into locked (L) or unlocked (U) states, as illustrated by Akçay et al., [Phys. Plasmas 28, 082106 (2021)]. This classification splits the control space into three regions: L̂, with only L states; Û, with only U states; and a hysteresis (hysteretic) region Ĥ, with both L and U states. In regions L̂ and Û, the cubic equation of torque balance yields one real root. Region Ĥ has three roots, allowing bifurcations between the L and U states. The classification of the ODE solutions into L/U is used to estimate the locking probability, conditional on the pair of the control parameters, using a neural network. We also explore estimating the locking probability for a sparse dataset, using a transfer learning method based on a dense model dataset.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2019

Field Quality of HD3—A Nb $_3$ Sn Dipole Magnet Based on Block Design

HD3 is the latest magnet of a series of block-type Nb 3 Sn dipole model magnets developed by the Superconducting Magnet Program at Lawrence Berkeley National Laboratory. The magnet is 1 m long with a clear aperture of 43 mm. As a model magnet designed with accelerator-quality features, each coil has flared ends to provide a clear bore for a beam tube. The magnet design was also optimized to minimize the geometric and saturation field errors. In 2013, HD3b reached a peak dipole field of 13.4 T at 4.4 K. As part of the magnet test, we measured field quality using rotating coils with lengths of 26 and 130 mm developed by Fermi National Accelerator Laboratory. We report and analyze the measured static and dynamic field errors. We discuss the insight provided by the field quality study of HD3, which can be useful for the development of high-field block-type dipole magnets for next-generation circular colliders.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2012

Proton beam lifetime increase with 10- and 12-pole correctors in the Relativistic Heavy Ion Collider

10- and 12-pole correctors were installed in a number of machines and are also considered for future machines. In the Relativistic Heavy Ion Collider (RHIC) 10- and 12-pole correctors exist to correct for the detrimental effects of magnetic field errors in the interaction region magnets. These field errors in conjunction with beam-beam effects and parameter modulations dominate the beam lifetime in polarized proton operation. During the 2009 polarized proton run 10- and 12-pole correctors were set through an iterative procedure, and used for the first time operationally in one of the beams. We report on the procedure to set these high-order multipole correctors, compare the found values with calculated ones, estimate the effect of the new corrector settings on the integrated luminosity, and calculate the effect of both the calculated and experimentally found corrector strengths on the dynamic aperture.

43 PARTICLE ACCELERATORS↗

DOE OSTI2012

Proton beam lifetime increase with 10- and 12-pole correctors in the Relativistic Heavy Ion Collider

43 PARTICLE ACCELERATORS↗

NASA NTRS2018

Reflectance-Based Imaging Spectrometer Error Budget Field Practicum at the Railroad Valley Test Site, Nevada

Calibration and validation determine the quality and integrity of the data provided by sensors and have enormous downstream impacts on the accuracy and reliabilityof the products generated by these sensors. With the imminent launch of the next generation of space borne imaging spectroscopy sensors, the IEEE Geoscience and Remote Sensing Society's (GRSS's) Geoscience Spaceborne Imaging Spectroscopy Technical Committee (GSIS TC) initiated a calibration and validation initiative.This article reports on a recent reflectance-based imaging spectrometer error budget field practicum focused on radiometric calibration of spaceborne imaging spectroscopy sensors. The field exercise, conducted at Railroad Valley in Nevada, provided valuable training for personnel in a variety of Earth observation (EO) areas, from engineers developing future sensors to calibration scientists actively working in the field. Future work in this area will focus on analyzing the data acquired as part of the training to answer numerous scientific questions, e.g., understanding the spatial and spectral homogeneity of the site being measured, identifying the optimal sampling to characterize the site, and optimizating the sampling techniques, including looking into the automation of some measurement protocol aspects. The training exercise was recorded to ensure that the knowledge can be disseminated across the GRSS and wider imaging spectroscopy community.

Ong, Cindy↗

DOE OSTI2021

Machine learning methods for probabilistic locked-mode predictors in tokamak plasmas

A rotating tokamak plasma can interact resonantly with the external helical magnetic perturbations, also known as error fields. This can lead to locking and then to disruptions. We leverage machine learning (ML) methods to predict the locking events. We use a coupled third-order nonlinear ordinary differential equation model to represent the interaction of the magnetic perturbation and the plasma rotation with the error field. This model is sufficient to describe qualitatively the locking and unlocking bifurcations. Here, we explore using ML algorithms with the simulation data and experimental data, focusing on the methods that can be used with sparse datasets. These methods lead to the possibility of the avoidance of locking in real-time operations. We describe the operational space in terms of two control parameters: the magnitude of the error field and the rotation frequency associated with the momentum source that maintains the plasma rotation. The outcomes are quan- tified by order parameters that completely characterize the state, whether locked or unlocked. We use unsupervised ML methods to classify locked/unlocked states and note the usefulness of a certain normalization of the order parameters. Three supervised ML classifiers are used in suite to estimate the probability of locking in the region of control parameter space with hysteresis, i.e., the set of control parameters for which both locked and unlocked states can exist. The results show that a neural network gives the best estimate of the locking probability. An analogy of the present locking model with the van der Waals equation of state is also provided.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

A path to stable low-torque plasma operation in ITER with test blanket modules

New experiments in the low-torque ITER Q = 10 scenario on DIII-D demonstrate that n = 1 magnetic fields from a single row of ex-vessel control coils enable operation at ITER performance metrics in the presence of applied non-axisymmetric magnetic fields from a test blanket module (TBM) mock-up coil. With n = 1 compensation, operation below the ITER-equivalent injected torque is successful at three times the ITER equivalent toroidal magnetic field ripple for a pair of TBMs in one equatorial port, whereas the uncompensated TBM field leads to rotation collapse, loss of H-mode and plasma current disruption. In companion experiments at high plasma beta, where the n = 1 plasma response is enhanced, uncorrected TBM fields degrade energy confinement and the plasma angular momentum while increasing fast ion losses; however, disruptions are not routinely encountered owing to increased levels of injected neutral beam torque. In this regime, n = 1 field compensation leads to recovery of a dominant fraction of the TBM-induced plasma pressure and rotation degradation, and an 80% reduction in the heat load to the first wall. These results show that the n = 1 plasma response plays a dominant role in determining plasma stability, and that n = 1 field compensation alone not only recovers most of the impact on plasma performance of the TBM, but also protects the first wall from potentially damaging heat flux. Despite these benefits, plasma rotation braking from the TBM fields cannot be fully recovered using standard error field control. Lastly, given the uncertainty in extrapolation of these results to the ITER configuration, it is prudent to design the TBMs with as low a ferromagnetic mass as possible without jeopardizing the TBM mission.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

3D modeling of n = 1 RMP driven heat fluxes on the SPARC tokamak PFCs using HEAT

3D heat flux calculations at the lower outer divertor plate of SPARC using the HEAT code show that 3D fields generated from error field correction coils can lead to enhanced peak heat fluxes up to 15 times larger compared to the axisymmetric case. Previously employed to simulate axisymmetric heat flux on 3D plasma facing components, the HEAT code can now predict 3D heat flux generated by non-axisymmetric plasmas. This is achieved via a new HEAT module which leverages the 3D field line tracing capabilities of MAFOT starting from an M3D-C1 (MHD resistive code) perturbed equilibria. The resulting heat flux is assigned using the magnetic footprint and the heat flux layer model, an extension of the 2D heat flux model also known as the Eich, to 3D non-axisymmetric plasmas. For SPARC, the new capabilities of HEAT are used to calculate the 3D heat loads resulting from n = 1 perturbation fields (with n indicating the toroidal periodicity) applied through a toroidal array of six picture frame coils with different amplitude. The comparison with the unperturbed case shows significant changes in shape and intensity of the heat flux profile. The results show that the application of n = 1 3D field leads to a localized enhancement of the heat flux peak, influenced by the wetted area impacted by the magnetic footprint, and the appearance of a secondary heat flux peak, whose intensity depends on amplitude of the applied 3D field and toroidal location.

3D heat flux↗

NASA NTRS1985

Retrieval of sea-surface temperatures from HIRS2/MSU

The methods used at the Goddard Laboratory for Atmospheres to retrieve sea surface temperatures from HIRS2/MSU data for the four months of the NASA sea surface temperature intercomparison workshop are described. Results are shown comparing anomaly fields produced using data from ships, AVHRR, HIRS2/MSU, SMMR AND VAS for the last three of these months. Fields from AVHRR and HIRS2 show the highest accuracy compared to ship fields. Errors in the HIRS2 fields appear more random while AVHRR data shows large area, spatially coherent errors. The random errors in the HIRS2 fields can be further reduced by performing the retrievals at a higher spatial resolution.

Susskind, J.↗