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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↗

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↗

DOE OSTI2019

Mapping of the HIDRA stellarator magnetic flux surfaces

The Hybrid Illinois Device for Research and Applications (HIDRA) is a classical stellarator designed for conducting plasma material interaction experiments and developing novel Plasma Facing Components (PFCs). Notably, the testing of two open-channel liquid lithium PFCs is imminent. Determining the shape of the plasma and its magnetic structure inside HIDRA is essential to carry out these tests. For this, electron traces were captured to build up the images of the HIDRA magnetic flux surfaces for several magnetic configurations, following the same procedure previously employed on the WEGA stellarator coupling an electron gun with a fluorescent detector. The FIELDLINES code has then been used to generate computational surfaces matching the experimental results. The obtained surfaces were found to be subject to a similar n = 1 error field as the one observed on WEGA, suggesting that the origin of this error field is inherent to the HIDRA vacuum vessel. Also, the effect of adding a vertical field was investigated, demonstrating the ability to radially shift the magnetic axis and move to a regime free of low-order rational resonances. Finally, this additional control over the HIDRA plasma and magnetic structure allows more freedom in setting up the PFC tests in the limiter and divertor regions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Simultaneous stabilization and control of the n = 1 and n = 2 resistive wall mode

Abstract DIII-D experiments demonstrate simultaneous stability measurements and control of resistive wall modes (RWMs) with toroidal mode numbers n = 1 and n = 2. RWMs with n > 1 are sometimes observed on DIII-D following the successful feedback stabilization of the n = 1 mode, motivating the development of multi- n control. A new model-based multi-mode feedback algorithm based on the VALEN physics code has been implemented on the DIII-D tokamak using a real-time GPU installed directly into the DIII-D plasma control system. In addition to stabilizing RWMs, the feedback seeks to control the stable plasma error field response, enabling compensation of the typically unaddressed DIII-D n = 2 error field component. Experiments recently demonstrated this algorithm’s ability to simultaneously control n = 1 and n = 2 perturbed fields for the first time in a tokamak, using reactor relevant external coils. Control was maintained for hundreds of wall-times above the n = 1 no-wall pressure limit and approaching the n = 1 and n = 2 ideal-wall limits. Furthermore, a rotating non-zero target was set for the feedback, allowing stability to be assessed by monitoring the rotating plasma response (PR) while maintaining control. This novel technique can be viewed as a closed-loop extension of active MHD spectroscopy, which has been used to validate stability models through comparisons of the PR to applied, open-loop perturbations. The closed-loop response measurements are consistent with open-loop MHD spectroscopy data over a wide range of β N approaching the n = 1 ideal-wall limit. These PR measurements were then fit to produce both VALEN and single-mode stability models. These models allowed for important plasma stability information to be determined and have been shown to agree with experimentally observed RWM growth rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

PM4Stell: A prototype permanent magnet stellarator structure

Permanent magnets provide a possible solution to simplify complicated stellarator coils. Here, a prototype permanent magnet stellarator structure, PM4Stell, has been funded to demonstrate the technical feasibility of using permanent magnets to create the shaping field of a stellarator. Permanent magnets in uniform cubes with three polarization directions will be carefully placed to generate the required magnetic field for a National Compact Stellarator eXperiment-like equilibrium together with planar toroidal field coils. Discrete magnets will be glued together and inserted into a “post-office-box-like” supporting structure. Electromagnetic and structural analyses have been done to validate the design. Error field correction magnets will be used to shim possible error fields. The design efforts of the prototype permanent magnet stellarator structure are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

Field Tolerances for the Triplet Quadrupoles of the LHC High Luminosity Lattice

It has been proposed to implement the so-called Achromatic Telescopic Squeezing (ATS) scheme in the LHC high luminosity (HL) lattice to reduce beta functions at the Interaction Points (IP) up to a factor of 8. As a result, the nominal 4.5 km peak beta functions reached in the Inner Triplets (IT) at collision will be increased by the same factor. This, therefore, justifies the installation of new, larger aperture, superconducting IT quadrupoles. The higher beta functions will enhance the effects of the triplet quadrupole field errors leading to smaller beam dynamic aperture (DA). To maintain the acceptable DA, the effects of the triplet field errors must be re-evaluated, thus specifying new tolerances. Such a study has been performed for the so-called '4444' collision option of the HL-LHC layout version SLHCV3.01, where the IP beta functions are reduced by a factor of 4 in both planes with respect to a pre-squeezed value of 60 cm at two collision points. The dynamic aperture calculations were performed using SixTrack. The impact on the triplet field quality is presented.

43 PARTICLE ACCELERATORS↗

DOE OSTI2012

A Description of the Full Particle Orbit Following SPIRAL Code for Simulating Fast-ion Experiments in Tokamaks

The numerical methods used in the full particle-orbit following SPIRAL code are described and a number of physics studies performed with the code are presented to illustrate its capabilities. The SPIRAL code is a test-particle code and is a powerful numerical tool to interpret and plan fast-ion experiments in Tokamaks. Gyro-orbit effects are important for fast ions in low-field machines such as NSTX and to a lesser extent in DIII-D. A number of physics studies are interlaced between the description of the code to illustrate its capabilities. Results on heat loads generated by a localized error-field on the DIII-D wall are compared to measurements. The enhanced Triton losses caused by the same localized error-field are calculated and compared to measured neutron signals. MHD activity such as tearing modes and Toroidicity-induced Alfven Eigenmodes (TAEs) have a profound effect on the fast-ion content of Tokamak plasmas and SPIRAL can calculate the effects of MHD activity on the confined and lost fast-ion population as illustrated for a burst of TAE activity in NSTX. The interaction between Ion Cyclotron Range of Frequency (ICRF) heating and fast ions depends solely on the gyro-motion of the fast ions and is captured exactly in the SPIRAL code. A calculation of ICRF absorption on beam ions in ITER is presented. The effects of high harmonic fast wave heating on the beam-ion slowing-down distribution in NSTX is also studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

First attempt to quantify W7-X island divertor plasma by local experiment-model comparison

As a complement to our recent work, which focused on understanding the basic detachment physics and general experimental and numerical trends observed in the W7-X island divertor, this paper compares EMC3-Eirene simulation results with different local diagnostics, including IR cameras, Langmuir probes, H α -cameras, and Thomson scattering. The main purposes are to (1) justify the simulation setup in the previous work, (2) identify the application limitations of the current EMC3-Eirene model, (3) verify the consistency of different diagnostics, and (4) isolate the main geometric and physical effects that need to be prioritized in further developing the EMC3-Eirene code and improving diagnostic capabilities. It turns out that the current version of the EMC3-Eirene code (without drifts) is not yet able to quantitatively reproduce all selected local measurements simultaneously under the current experimental conditions (in particular, the existence of error fields). Nevertheless, it can be shown that within a reasonable range of variation in magnetic configuration, cross-field transport, and SOL plasma state in the modeling, a region of overlap between the numerical results and the local measurements can be established. More accurate model-experiment comparisons will require clarification of error fields, implementation of drifts in EMC3, and improvement of diagnostic capabilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

Enhanced superbanana transport caused by chaotic scattering across an asymmetric separatrix

This paper discusses a novel 'chaotic' form of superbanana transport and compares the theory to experiments on non-neutral plasmas. Superbanana transport is caused by particles that cross local trapping separatrices (magnetic or electric ripples) in the presence of field 'errors' such as toroidal magnetic curvature. Traditionally, collisions (at rate {nu}) cause separatrix crossings, with resulting transport that scales as {nu}{sup 1/2}B{sup -1/2}. The 'chaotic' transport of interest here occurs when the separatrix is 'ruffled' in the direction of plasma drift; then, collisionless particle orbits give random trapping and detrapping. Prior theory assumed a 'stellarator symmetry' and suggested that these orbits give reduced transport scaling as {nu}{sup p} with p{approx}1. Here, we fully characterize chaotic transport and show that the transport is enhanced rather than reduced, scaling as {nu}{sup 0}B{sup -1}. Experiments on pure electron plasmas provide quantitative transport measurements, with precise control of the overall field error, and of the trapping separatrix with and without ruffles. The experiments show close agreement with theory over a decade in B, for both collisional neoclassical transport, and for the distinctive chaotic transport. At low magnetic fields, transport scaling as B{sup -p} with p>rsim2 becomes dominant, showing preliminary agreement with bounce-resonant theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Constrained stellarator coil curvature optimization with FOCUS

Finding less complicated coils that have adequately low field errors is a crucial step in stellarator development. One coil metric that is of high importance is the maximum curvature of the coil centreline, or coil single filament. Conductors cannot be bent below some threshold minimum radius of curvature. High coil curvatures can cause strains to exceed acceptable levels, especially in superconducting coils. We investigate three ways to optimize coil curvature and find that applying penalty functions to the coil curvature solves for coils that have a constrained maximum curvature and low field error. Penalty functions are implemented in FOCUS and coil solutions optimized for an HSX-like ‘plasma boundary’ are presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Conceptual design of extended magnetic probe set to improve 3D field detection in NSTX-U

Adding toroidal arrays of magnetic probes at the top and bottom of NSTX-U would improve both the detection of the multimodal plasma response to applied magnetic perturbations and the identification of the poloidal structure of unstable plasma modes, as well as contribute to the validation of MHD models, improve the understanding of the plasma response to external fields, and improve the error field correction. In this paper, the linear MHD code MARS-F/K has been used to identify poloidal locations that would improve the capability to measure stationary or near-stationary 3D fields that may result from the plasma response to external sources of non-axisymmetric fields. The study highlighted 6 poloidal positions where new arrays of both poloidal and radial magnetic field sensors would improve the poloidal resolution. Here, the proposed set of new arrays combined with the present ones is shown to be capable of measuring the poloidal structure of perturbations with n ≤ 6 and of detecting the multimodal plasma response. Assessment of the trade-off in the poloidal length of the probes leads to an ideal length between 10 cm and 30 cm. A method to configure the probes of a toroidal array based on the singular value decomposition condition number is proposed, and an ideal solution and a low-cost one are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗