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3. Operational Space and Performance Limiting Events in the First Physics Campaign of MAST-U

Author(s):
Berkery, John
Abstract:
The MAST-U fusion plasma research device, the upgrade to the Mega Amp Spherical Tokamak, has recently completed its first campaign of physics operation. MAST-U operated with Ohmic, or one or two neutral beams for heating, at 400-800 kA plasma current, in conventional or “SuperX” divertor configurations. Equilibrium reconstructions provide key plasma physics parameters vs. time for each discharge, and diagrams are produced which show where the prevalence of operation occurred as well as the limits in various operational spaces. When compared to stability limits, the operation of MAST-U so far has generally stayed out of the low q, low density instability region, and below the high density Greenwald limit, high beta global stability limits, and high elongation vertical stability limit. MAST-U still has the potential to reach higher elongation, which could benefit the plasma performance. Despite the majority of operation happening below established stability limits, disruptions did occur in the flat-top phase of MAST-U plasmas. The reasons for these disruptions are highlighted, and possible strategies to avoid them and to extend the operational space of MAST-U in future campaigns are discussed.
Type:
Dataset
Issue Date:
18 January 2023

4. Reduced Physics Model of the Tokamak Scrape-off-Layer for Pulse Design

Author(s):
Zhang, Xin
Abstract:
The dynamic interplay between the core and the edge plasma has important consequences in the confinement and heating of fusion plasma. The transport of the Scrape-Off-Layer (SOL) plasma imposes boundary conditions on the core plasma, and neutral transport through the SOL influences the core plasma sourcing. In order to better study these effects in a self-consistent, time-dependent fashion with reasonable turn-around time, a reduced model is needed. In this paper we introduce the SOL Box Model, a reduced SOL model that calculates the plasma temperature and density in the SOL given the core-to-edge particle and power fluxes and recycling coefficients. The analytic nature of the Box Model allows one to readily incorporate SOL physics in time-dependent transport solvers for pulse design applications in the control room. Here we demonstrate such a coupling with the core transport solver TRANSP and compare the results with density and temperature measurements, obtained through Thomson scattering and Langmuir probes, of an NSTX discharge. Implications for future interpretive and predictive simulations are discussed.
Type:
Dataset
Issue Date:
January 2023

6. Thermal ion kinetic effects and Landau damping in fishbone modes

Author(s):
Liu, Chang; Jardin, Stephen; Bao, Jian; Gorelenkov, Nikolai; Brennan, Dylan; Yang, James
Abstract:
The data set consists of the figures in a manuscript titled Thermal ion kinetic effects and Landau damping in fishbone modes, and plotting script used for figure generation. There are 16 figures with captions.
Type:
Dataset
Issue Date:
22 November 2022

8. Electron Temperature Gradient Driven Transport Model for Tokamak Plasmas

Author(s):
Rafiq, Tariq; Wilson, Christopher; Luo, Lixiang; Weiland, Jan; Schuster, Eugenio; Pankin, Alexei; Guttenfelder, Walter; Kaye, Stan
Abstract:
A new model for electron temperature gradient (ETG) modes is developed as a component of the Multi-Mode anomalous transport module [T. Rafiq \textit{et al.,} Phys Plasmas \textbf{20}, 032506 (2013)] to predict a time dependent electron temperature profile in conventional and low aspect ratio tokamaks. This model is based on two-fluid equations that govern the dynamics of low-frequency short- and long-wavelength electromagnetic toroidal ETG driven drift modes. A low collisionality NSTX discharge is used to scan the plasma parameter dependence on the ETG real frequency, growth rate, and electron thermal diffusivity. Electron thermal transport is discovered in the deep core region where modes are more electromagnetic in nature. Several previously reported gyrokinetic trends are reproduced, including the dependencies of density gradients, magnetic shear, $\beta$ and gradient of $\beta$ $(\betap)$, collisionality, safety factor, and toroidicity, where $\beta$ is the ratio of plasma pressure to the magnetic pressure. The electron heat diffusivity associated with the ETG mode is discovered to be on a scale consistent with the experimental diffusivity determined by power balance analysis.
Type:
Dataset
Issue Date:
30 August 2022

9. Global gyrokinetic study of shaping effects on electromagnetic modes at NSTX aspect ratio with ad hoc parallel magnetic perturbation effects

Author(s):
Sharma, A. Y.; Cole, M. D. J.; Görler, T.; Chen, Y.; Hatch, D. R.; Guttenfelder, W.; Hager, R.; Sturdevant, B. J.; Ku, S.; Chang, C. S.
Abstract:
Plasma shaping may have a stronger effect on global turbulence in tight-aspect-ratio tokamaks than in conventional-aspect-ratio tokamaks due to the higher toroidicity and more acute poloidal asymmetry in the magnetic field. In addition, previous local gyrokinetic studies have shown that it is necessary to include parallel magnetic field perturbations in order to accurately compute growth rates of electromagnetic modes in tight-aspect-ratio tokamaks. In this work, the effects of elongation and triangularity on global, ion-scale, linear electromagnetic modes are studied at NSTX aspect ratio and high plasma beta using the global gyrokinetic particle-in-cell code XGC. The effects of compressional magnetic perturbations are approximated via a well-known modification to the particle drifts that was developed for flux-tube simulations [N. Joiner et al., Phys. Plasmas 17, 072104 (2010)], without proof of its validity in a global simulation. Magnetic equilibria are re-constructed for each distinct plasma profile that is used. Coulomb collision effects are not considered. Within the limitations imposed by the present study, it is found that linear growth rates of electromagnetic modes (collisionless microtearing modes and kinetic ballooning modes) are significantly reduced by NSTX-like shaping. For example, growth rates of kinetic ballooning modes at high beta are reduced to the level of that of collisionless trapped electron modes.
Type:
Dataset
Issue Date:
2022

10. Internal Rotation of ELM Filaments on NSTX

Author(s):
Lampert, Mate; Diallo, Ahmed; Zweben, Stewart; Myra, Jim
Abstract:
The data is formatted to text files. A corresponding file is provided for each figure.
Type:
Dataset
Issue Date:
September 2022

12. Nonlinear growth of magnetic islands by passing fast ions in NSTX

Author(s):
Yang, James; Fredrickson, Eric; Podestà, Mario; Poli, Francesca
Abstract:
The growth of magnetic islands in NSTX is modeled successfully, with the consideration of passing fast ions. It is shown that a good quantitative agreement between simulation and experimental measurement can be achieved when the uncompensated cross-field current induced by passing fast ions is included in the island growth model. The fast ion parameters, along with other equilibrium parameters, are obtained self-consistently using the TRANSP code with the assumptions of the ‘kick’ model (Podestà et al 2017 Plasma Phys. Control. Fusion 59 095008). The results show that fast ions can contribute to overcoming the stabilizing effect of polarization current for magnetic island growth.
Type:
Dataset
Issue Date:
2022

14. Parametric dependencies of resonant layer responses across linear, two-fluid, drift-MHD regimes

Author(s):
Park, Jong-Kyu
Abstract:
Non-axisymmetric magnetic fields arising in a tokamak either by external or internal perturbations can induce complex non-ideal MHD responses in their resonant surfaces while remaining ideally evolved elsewhere. This layer response can be characterized in a linear regime by a single parameter called the inner-layer Delta, which enables outer-layer matching and the prediction of torque balance to non-linear island regimes. Here, we follow strictly one of the most comprehensive analytic treatments including two-fluid and drift MHD effects and keep the fidelity of the formulation by incorporating the numerical method based on the Riccati transformation when quantifying the inner-layer Delta. The proposed scheme reproduces not only the predicted responses in essentially all asymptotic regimes but also with continuous transitions as well as improved accuracies. In particular, the Delta variations across the inertial regimes with viscous or semi-collisional effects have been further resolved, in comparison with additional analytic solutions. The results imply greater shielding of the electromagnetic torque at the layer than what would be expected by earlier work when the viscous or semi-collisional effects can compete against the inertial effects, and also due to the intermediate regulation by kinetic Alfven wave resonances as rotation slows down. These are important features that can alter the nonaxisymmetric plasma responses including the field penetration by external fields or island seeding process in rotating tokamak plasmas.
Type:
Dataset
Issue Date:
26 July 2022

16. A software package for plasma facing component analysis and design: the Heat flux Engineering Analysis Toolkit (HEAT)

Author(s):
Looby, Tom; Reinke, Matthew; Wingen, Andreas; Menard, Jonathan; Gerhardt, Stefan; Gray, Travis; Donovan, David; Unterberg, Ezekial; Klabacha, Jonathan; Messineo, Mike
Abstract:
The engineering limits of plasma facing components (PFCs) constrain the allowable operational space of tokamaks. Poorly managed heat fluxes that push the PFCs beyond their limits not only degrade core plasma performance via elevated impurities, but can also result in PFC failure due to thermal stresses or melting. Simple axisymmetric assumptions fail to capture the complex interaction between 3D PFC geometry and 2D or 3D plasmas. This results in fusion systems that must either operate with increased risk or reduce PFC loads, potentially through lower core plasma performance, to maintain a nominal safety factor. High precision 3D heat flux predictions are necessary to accurately ascertain the state of a PFC given the evolution of the magnetic equilibrium. A new code, the Heat flux Engineering Analysis Toolkit (HEAT), has been developed to provide high precision 3D predictions and analysis for PFCs. HEAT couples many otherwise disparate computational tools together into a single open source python package. Magnetic equilibrium, engineering CAD, finite volume solvers, scrape off layer plasma physics, visualization, high performace computing, and more, are connected in a single web-based user interface. Linux users may use HEAT without any software prerequisites via an appImage. This manuscript introduces HEAT, discusses the software architecture, presents first HEAT results, and outlines physics modules in development.
Type:
Dataset
Issue Date:
March 2021

18. Dynamics of filaments during the edge-localized mode crash on NSTX

Author(s):
Lampert,Mate; Diallo,Ahmed; Myra,James R.; Zweben, Stewart J.
Abstract:
Edge localized modes (ELMs) are routinely observed in H-mode plasma regimes of the National Spherical Torus Experiment (NSTX). Due to the explosive nature of the instability, only diagnostics with high temporal and spatial resolution could provide a detailed insight into the dynamics associated with the ELMs. Gas-puff imaging (GPI) at NSTX provides 2D measurements of the magnetic field aligned fluctuations (e.g. ELM filaments) in the scrape-off layer and the at the plasma edge with 2.5 us temporal and 10 mm optical resolution.A novel analysis technique was developed to estimate the frame-by-frame velocities and the spatial parameters of the dominant structures associated with the ELMs. The analysis was applied to single ELM events to characterize the ELM crash dynamics, and then extended to a database of 169 ELM events.Statistical analysis was performed in order to find the characterizing dynamics of the ELM crash. The results show that on average an ELM crash consists of a filament with a circular cross-section which is propelled outwards with a characterizing peak radial velocity of ~3.3 km/s. The radial velocity was found to be linearly dependent on the distance of the filament from the separatrix, which has never been seen before. The ELM filament is characterized by propagation in the ion-diamagnetic direction poloidally with a peak velocity of 11.4 km/s. The ELM crash lasts for approximately 100us until the radial propulsion settles back to the pre-ELM level. The experimental findings were compared with analytical theory. Two possible mechanisms were identified for explaining the observations: the curvature interchange model and the current-filament interaction model.
Type:
Dataset
Issue Date:
January 2021

19. Impact of edge harmonic oscillations on the divertor heat flux in NSTX

Author(s):
Gan, Kaifu; Gray, Travis; Zweben, Stewart; Eric, Fredrickson; Maingi, Rajesh; Battaglia, Devon; McLean, Adam; Wirth, Brian
Abstract:
All the data was uploaded with .cvs file, we have not uploaded the figure 1 data since it is just photo show field of view of IR and GPI diagnostic.
Type:
Dataset
Issue Date:
6 December 2021

20. Inversion technique to obtain local ion temperature profiles for an axisymmetric plasma with toroidal and radial velocities

Author(s):
Bell, Ronald E.
Abstract:
A matrix inversion technique is derived to calculate local ion temperature from line-integrated measurements of an extended emission source in an axisymmetric plasma which exactly corrects for both toroidal velocity and radial velocity components. Local emissivity and toroidal velocity can be directly recovered from line-integrated spectroscopic measurements, but an independent measurement of the radial velocity is necessary to complete the temperature inversion. The extension of this technique to handle the radial velocity is relevant for magnetic reconnection and merging compression devices where temperature inversion from spectroscopic measurements is desired. A simulation demonstrates the effects of radial velocity on the determination of ion temperature.
Type:
Dataset
Issue Date:
February 2021

21. Microtearing Instabilities and Electron Thermal Transport in Low and High Collisionality NSTX Discharges

Author(s):
Rafiq T; Kaye S; Guttenfelder W; Weiland J; Schuster E; Anderson J; Luo L;
Abstract:
Microtearing mode (MTM) real frequency, growth rate, magnetic fluctuation amplitude and resulting electron thermal transport are studied in systematic NSTX scans of relevant plasma parameters. The dependency of the MTM real frequency and growth rate on plasma parameters, suitable for low and high collision NSTX discharges, is obtained by using the reduced MTM transport model [T. Rafiq, et al., Phys. Plasmas 23, 062507 (2016)]. The plasma parameter dependencies are compared and found to be consistent with the results obtained from MTM using the Gyrokinetic GYRO code. The scaling trend of collision frequency and plasma beta is found to be consistent with the global energy confinement trend observed in the NSTX experiment. The strength of the magnetic fluctuation is found to be consistent with the gyrokinetic estimate.In earlier studies, it was found that the version of the Multi-Mode (MM) anomalous transport model, which did not contain the effect of MTMs, provided an appropriate description of the electron temperature profiles in standard tokamak discharges and not in spherical tokamaks. When the MM model, which involves transport associated with MTMs, is incorporated in the TRANSP code and is used in the study of electron thermal transport in NSTX discharges, it is observed that the agreement with the experimental electron temperature profile is substantially improved.
Type:
Dataset
Issue Date:
February 2021

24. Prediction of electron density and pressure profile shapes on NSTX-U using neural networks

Author(s):
Boyer, Mark; Chadwick, Jason
Abstract:
A new model for prediction of electron density and pressure profile shapes on NSTX and NSTX-U has been developed using neural networks. The model has been trained and tested on measured profiles from experimental discharges during the first operational campaign of NSTX-U. By projecting profiles onto empirically derived basis functions, the model is able to efficiently and accurately reproduce profile shapes. In order to project the performance of the model to upcoming NSTX-U operations, a large database of profiles from the operation of NSTX is used to test performance as a function of available data. The rapid execution time of the model is well suited to the planned applications, including optimization during scenario development activities, and real-time plasma control. A potential application of the model to real-time profile estimation is demonstrated.
Type:
Dataset
Issue Date:
February 2021

26. Synergy of Coupled Kink and Tearing Modes in Fast Ion Transport

Author(s):
Yang, J.; Podesta, M.; Fredrickson, E.
Abstract:
One aspect of the interaction between fast ions and magnetohydrodynamic (MHD) instabilities is the fast ion transport. Coupled kink and tearing MHD instabilities have also been reported to cause fast ion transport. Recently, the ''kick" model has been developed to compute the evolution of the fast ion distribution from the neutral beam injection using instabilities as phase space resonance sources. The goal of this paper is to utilize the kick model to understand the physics of fast ion transport caused by the coupled kink and tearing modes. Soft X-ray diagnostics are used to identify the mode parameters in NSTX. The comparison of neutron rates measured and computed from time-dependent TRANSP simulation with the kick model shows the coupling of kink and tearing mode is important in determination of the fast ion transport. The numerical scan of the mode parameters shows that the relative phase of the kink and tearing modes and the overlapping of kink and tearing mode resonances in the phase space can affect the fast ion transport, suggesting that the synergy of the coupled modes may be causing the fast ion transpor
Type:
Dataset
Issue Date:
February 2021

27. The updated ITPA global H-mode confinement database: description and analysis

Author(s):
Verdoolaege, G.; Kaye, S.M.; Angioni, C.; Kardaunn, O.W.J.F.; Maslov, M.; Romanelli, M.; Ryter, F.; Thomsen, K.
Abstract:
The multi-machine ITPA Global H-mode Confinement Database has been upgraded with new data from JET with the ITER-like wall and ASDEX Upgrade with the full tungsten wall. This paper describes the new database and presents results of regression analysis to estimate the global energy confinement scaling in H-mode plasmas using a standard power law. Various subsets of the database are considered, focusing on type of wall and divertor materials, confinement regime (all H-modes, ELMy H or ELM-free) and ITER-like constraints. Apart from ordinary least squares, two other, robust regression techniques are applied, which take into account uncertainty on all variables. Regression on data from individual devices shows that, generally, the confinement dependence on density and the power degradation are weakest in the fully metallic devices. Using the multi-machine scalings, predictions are made of the confinement time in a standard ELMy H-mode scenario in ITER. The uncertainty on the scaling parameters is discussed with a view to practically useful error bars on the parameters and predictions. One of the derived scalings for ELMy H-modes on an ITER-like subset is studied in particular and compared to the IPB98(y,2) confinement scaling in engineering and dimensionless form. Transformation of this new scaling from engineering variables to dimensionless quantities is shown to result in large error bars on the dimensionless scaling. Regression analysis in the space of dimensionless variables is therefore proposed as an alternative, yielding acceptable estimates for the dimensionless scaling. The new scaling, which is dimensionally correct within the uncertainties, suggests that some dependencies of confinement in the multi- machine database can be reconciled with parameter scans in individual devices. This includes vanishingly small dependence of confinement on line-averaged density and normalized plasma pressure (β), as well as a noticeable, positive dependence on effective atomic mass and plasma triangularity. Extrapolation of this scaling to ITER yields a somewhat lower confinement time compared to the IPB98(y, 2) prediction, possibly related to the considerably weaker dependence on major radius in the new scaling (slightly above linear). Further studies are needed to compare more flexible regression models with the power law used here. In addition, data from more devices concerning possible ‘hidden variables’ could help to determine their influence on confinement, while adding data in sparsely populated areas of the parameter space may contribute to further disentangling some of the global confinement dependencies in tokamak plasmas.
Type:
Dataset
Issue Date:
March 2021

28. Analytic stability boundaries for compressional and global Alfven eigenmodes driven by fast ions. I. Interaction via ordinary and anomalous cyclotron resonances.

Author(s):
Lestz J.B., Gorelenkov N.N., Belova E.V., Tang S.X., Crocker N.A.
Abstract:
Conditions for net fast ion drive are derived for beam-driven, sub-cyclotron compressional (CAE) and global (GAE) Alfven eigenmodes, such as those routinely observed in spherical tokamaks such as NSTX(-U) and MAST. Both co- and counter-propagating CAEs and GAEs are investigated, driven by the ordinary and anomalous Doppler-shifted cyclotron resonance with fast ions. Whereas prior results were restricted to vanishingly narrow distributions in velocity space, broad parameter regimes are identified in this work which enable an analytic treatment for realistic fast ion distributions generated by neutral beam injection. The simple, approximate conditions derived in these regimes for beam distributions of realistic width compare well to the numerical evaluation of the full analytic expressions for fast ion drive. Moreover, previous results in the very narrow beam case are corrected and generalized to retain all terms in omega/omega_{ci} and k_{||}/kperp, which are often assumed to be small parameters but can significantly modify the conditions of drive and damping when they are non-negligible. Favorable agreement is demonstrated between the approximate stability criterion, simulation results, and a large database of NSTX observations of cntr-GAEs.
Type:
Dataset
Issue Date:
September 2019

29. Analytic stability boundaries for compressional and global Alfven eigenmodes driven by fast ions. II. Interaction via Landau resonance.

Author(s):
Lestz, J.B.; Gorelenkov, N.N.; Belova, E.V.; Tang, S.X.; Crocker, N.A.
Abstract:
Conditions for net fast ion drive are derived for beam-driven, co-propagating, sub-cyclotron compressional (CAE) and global (GAE) Alfven eigenmodes driven by the Landau resonance with super-Alfvenic fast ions. Approximations applicable to realistic neutral beam distributions and mode characteristics observed in spherical tokamaks enable the derivation of marginal stability conditions for these modes. Such conditions successfully reproduce the stability boundaries found from numerical integration of the exact expression for local fast ion drive/damping. Coupling between the CAE and GAE branches of the dispersion due to finite \omega/\omega_{ci} and k_\parallel/k_\perp is retained and found to be responsible for the existence of the GAE instability via this resonance. Encouraging agreement is demonstrated between the approximate stability criterion, simulation results, and a database of NSTX observations of co-CAEs.
Type:
Dataset
Issue Date:
January 2020

30. Enhanced Pedestal H-mode at low edge ion collisionality on NSTX

Author(s):
Battaglia, D.J.; Guttenfelder, W.; Bell, R.E.; Diallo, A.; Ferraro, N.;, Fredrickson, E.; Gerhardt, S.P.; Kaye, S.M.; Maingi, R.; Smith, D.R.
Abstract:
The Enhanced Pedestal (EP) H-mode regime is an attractive wide-pedestal ELM-free high-betap scenario for NSTX-U and next-step devices as it achieves enhanced energy confinement (H98y,2 > 1.5), large normalized pressure (betaN > 5) and significant bootstrap fraction (f_BS > 0.6) at I_p/B_T = 2 MA/T. This regime is realized when the edge ion collisionality becomes sufficiently small that a positive feedback interaction occurs between a reduction in the ion neoclassical energy transport and an increase in the particle transport from pressure-driven edge instabilities. EP H-mode was most often observed as a transition following a large ELM in conditions with low edge neutral recycling. It is hypothesized that the onset of pressure-driven instabilities prior to the full recovery of the neutral density leads to a temporary period with elevated ion temperature gradient that triggers the transition to EP H-mode. Linear CGYRO and M3D-C1 calculations are compared to beam emission spectroscopy (BES) and magnetic spectroscopy in order to describe the evolution of the edge particle transport mechanisms during the ELM recovery and the saturated EP H-mode state. The observations are consistent with the hypothesis that the onset of pressure-driven edge instabilities, such as the KBM and kink-peeling, can be responsible for the increased particle transport in EP H-mode.
Type:
Dataset
Issue Date:
June 2020

31. MHD-blob correlations in NSTX

Author(s):
Zweben SJ; Fredrickson ED; Myra JR; Podesta M; Scotti F
Abstract:
This paper describes a study of the cross-correlations between edge fluctuations as seen in the gas puff imaging (GPI) diagnostic and low frequency coherent magnetic fluctuations (MHD) in H-mode plasmas in NSTX. The main new result was that large blobs in the SOL were significantly correlated with MHD activity the 3-6 kHz range in 21 of the 223 shots examined. There were also many other shots in which fluctuations in the GPI signal level and its peak radius Rpeak were correlated with MHD activity, but without any significant correlation of the MHD with large blobs. The structure and motion of the MHD is compared with that of the correlated blobs, and some possible theoretical mechanisms for the MHD-blob correlation are discussed.
Type:
Dataset
Issue Date:
May 2020

32. Machine Learning Characterization of Alfvénic and Sub-Alfvénic Chirping and Correlation With Fast-Ion Loss at NSTX

Author(s):
Woods, B. J. Q.; Duarte, V. N.; Fredrickson, E. D.; Gorelenkov, N. N.; Podestà, M.; Vann, R. G. L.
Abstract:
Abrupt large events in the Alfvenic and sub-Alfvenic frequency bands in tokamaks are typically correlated with increased fast-ion loss. Here, machine learning is used to speed up the laborious process of characterizing the behavior of magnetic perturbations from corresponding frequency spectrograms that are typically identified by humans. The analysis allows for comparison between different mode character (such as quiescent, fixed frequency, and chirping, avalanching) and plasma parameters obtained from the TRANSP code, such as the ratio of the neutral beam injection (NBI) velocity and the Alfven velocity (v_inj./v_A), the q-profile, and the ratio of the neutral beam beta and the total plasma beta (beta_beam,i / beta). In agreement with the previous work by Fredrickson et al., we find a correlation between beta_beam,i and mode character. In addition, previously unknown correlations are found between moments of the spectrograms and mode character. Character transition from quiescent to nonquiescent behavior for magnetic fluctuations in the 50200-kHz frequency band is observed along the boundary v_phi ~ (1/4)(v_inj. - 3v_A), where v_phi is the rotation velocity.
Type:
Dataset
Issue Date:
December 2019

33. Modeling of resistive plasma response in toroidal geometry using an asymptotic matching approach

Author(s):
Z. R. Wang; A. H. Glasser; D. Brennan; Y. Q. Liu; J-K. Park
Abstract:
The method of solving linear resistive plasma response, based on the asymptotic matching approach, is developed for full toroidal tokamaks by upgrading the Resistive DCON code [A.H. Glasser, Z.R. Wang and J.-K. Park, Physics of Plasmas, \textbf{23}, 112506 (2016)]. The derived matching matrix, asymptotically matching the outer and inner regions, indicates that the applied three dimension (3-D) magnetic perturbations contribute additional small solutions at each resonant surface due to the toroidal coupling of poloidal modes. In contrast, the resonant harmonic only affects the corresponding resonant surface in the cylindrical plasma. Since the solution of ideal outer region is critical to the asymptotic matching and is challenging to be solved in the toroidal geometry due to the singular power series solution at the resonant surfaces, systematic verification of the outer region $\Delta^\prime$ matrix is made by reproducing the well known analytical $\Delta^{\prime}$ result in [H.P. Furth, P.H. Rutherford and H. Selberg, The Physics of Fluids, \textbf{16}, 1054-1063 (1073)] as well as by making a quantitative benchmark with the PEST3 code [A. Pletzer and R.L. Dewar, J. Plasma Physics, \textbf{45}, 427-451 (1991)]. Finally, the reconstructed numerical solution of resistive plasma response from the toroidal matching matrix is presented. Comparing with the ideal plasma response, the global structure of the response can be affected by the small finite island at the resonant surfaces.
Type:
Dataset
Issue Date:
October 2020

34. Simulating pitch angle scattering using an explicitly solvable energy-conserving algorithm

Author(s):
Zhang, Xin; Fu, Yichen; Qin, Hong
Abstract:
Particle distribution functions evolving under the Lorentz operator can be simulated with the Langevin equation for pitch angle scattering. This approach is frequently used in particle based Monte-Carlo simulations of plasma collisions, among others. However, most numerical treatments do not guarantee energy conservation, which may lead to unphysical artifacts such as numerical heating and spectra distortions. We present a novel structure-preserving numerical algorithm for the Langevin equation for pitch angle scattering. Similar to the well-known Boris algorithm, the proposed numerical scheme takes advantage of the structure-preserving properties of the Cayley transform when calculating the velocity-space rotations. The resulting algorithm is explicitly solvable, while preserving the norm of velocities down to machine precision. We demonstrate that the method has the same order of numerical convergence as the traditional stochastic Euler-Maruyama method.
Type:
Dataset
Issue Date:
September 2020

35. Toward fusion plasma scenario planning for NSTX-U using machine-learning-accelerated models

Author(s):
Mark D. Boyer
Abstract:
One of the most promising devices for realizing power production through nuclear fusion is the tokamak. To maximize performance, it is preferable that tokamak reactors achieve advanced operating scenarios characterized by good plasma confinement, improved magnetohydrodynamic (MHD) stability, and a largely non-inductively driven plasma current. Such scenarios could enable steady-state reactor operation with high \emph{fusion gain} --- the ratio of produced fusion power to the external power provided through the plasma boundary. Precise and robust control of the evolution of the plasma boundary shape as well as the spatial distribution of the plasma current, density, temperature, and rotation will be essential to achieving and maintaining such scenarios. The complexity of the evolution of tokamak plasmas, arising due to nonlinearities and coupling between various parameters, motivates the use of model-based control algorithms that can account for the system dynamics. In this work, a learning-based accelerated model trained on data from the National Spherical Torus Experiment Upgrade (NSTX-U) is employed to develop planning and control strategies for regulating the density and temperature profile evolution around desired trajectories. The proposed model combines empirical scaling laws developed across multiple devices with neural networks trained on empirical data from NSTX-U and a database of first-principles-based computationally intensive simulations. The reduced execution time of the accelerated model will enable practical application of optimization algorithms and reinforcement learning approaches for scenario planning and control development. An initial demonstration of applying optimization approaches to the learning-based model is presented, including a strategy for mitigating the effect of leaving the finite validity range of the accelerated model. The approach shows promise for actuator planning between experiments and in real-time.
Type:
Dataset
Issue Date:
May 2020

36. A scalable real-time framework for Thomson scattering analysis: Application to NSTX-U

Author(s):
F. M. Laggner, A. Diallo, B. P. LeBlanc, R. Rozenblat, G. Tchilinguirian, E.Kolemen, the NSTX-U team
Abstract:
A detailed description of a prototype setup for real-time (rt) Thomson scattering (TS) analysis is presented and implemented in the multi-point Thomson scattering (MPTS) diagnostic system at the National Spherical Torus Experiment Upgrade(NSTX-U). The data acquisition hardware was upgraded with rt capable electronics (rt-analog digital converters (ADCs) and a rt server) that allow for fast digitization of the laser pulse signal of eight radial MPTS channels. In addition, a new TS spectrum analysis software for a rapid calculation of electron temperature (Te) and electron density (ne) was developed. Testing of the rt hardware and data analysis soft-ware was successfully completed and benchmarked against the standard, post-shot evaluation. Timing tests were performed showing that the end-to-end processing time was reproducibly below 17 ms for the duration of at least 5 s, meeting a 60 Hz deadline by the laser pulse repetition rate over the length of a NSTX-U discharge. The presented rt framework is designed to be scalable in system size, i.e. incorporation of additional radial channels by solely adding additional rt capable hardware. Furthermore, it is scalable in its operation duration and was continuously run for up to 30 min, making it an attractive solution for machines with long discharge duration such as advanced, non-inductive tokamaks or stellarators.
Type:
Dataset
Issue Date:
March 2019

37. Application of transient CHI plasma startup to future ST and AT devices

Author(s):
Hammond, K.C.; Raman, R.; Jardin, S.C.
Abstract:
Employment of non-inductive plasma start-up techniques would considerably simplify the design of a spherical tokamak fusion reactor. Transient coaxial helicity injection (CHI) is a promising method, expected to scale favorably to next-step reactors. However, the implications of reactor-relevant parameters on the initial breakdown phase for CHI have not yet been considered. Here, we evaluate CHI breakdown in reactor-like configurations using an extension of the Townsend avalanche theory. We find that a CHI electrode concept in which the outer vessel wall is biased to achieve breakdown, while previously successful on NSTX and HIT-II, may exhibit a severe weakness when scaled up to a reactor. On the other hand, concepts which employ localized biasing electrodes such as those used in QUEST would avoid this issue. Assuming that breakdown can be successfully attained, we then apply scaling relationships to predict plasma parameters attainable in the transient CHI discharge. Assuming the use of 1 Wb of injector flux, we find that plasma currents of 1 MA should be achievable. Furthermore, these plasmas are expected to Ohmically self-heat with more than 1 MW of power as they decay, facilitating efficient hand-off to steady-state heating sources. These optimistic scalings are supported by TSC simulations.
Type:
Dataset
Issue Date:
February 2019

38. Blob wakes in NSTX

Author(s):
Zweben SJ, Myra JR, Diallo A, Russell DA, Scotti F, Stotler DP
Abstract:
Transient small-scale structures were identified in the wake of blobs movingpoloidally through the SOL of high-powered H-mode plasmas in NSTX, using the gaspuff imaging (GPI) diagnostic. These blob wakes had a poloidal wavelength in therange 3.5 cm, which is significantly smaller than the average blob scale of~12 cm, and the wakes had a poloidal velocity of 1.5 km/sec in theelectron diamagnetic direction, which is opposite to the blob poloidal velocity inthese shots. These wakes were radially localized 0-4 cm outside the separatrix andoccurred within ~50 microsec after the passage of a blob through the GPI field of view.The clearest wakes were seen when the GPI viewing angle was well aligned with thelocal B field line, as expected for such small-scale structures given the diagnosticgeometry. A plausible theoretical interpretation of the wakes is discussed: theobserved wakes share some features of drift waves and/or drift-Alfven waves whichcould be excited
Type:
Dataset
Issue Date:
July 2019

39. Design and simulation of the snowflake divertor control for NSTX-U

Author(s):
Vail, P. J.; Boyer, M. D.; Welander, A. S.; Kolemen, E.; U.S. Department of Energy contract number DE-AC02-09CH11466
Abstract:
This paper presents the development of a physics-based multiple-input-multiple-output algorithm for real-time feedback control of snowflake divertor (SFD) configurations on the National Spherical Torus eXperiment Upgrade (NSTX-U). A model of the SFD configuration response to applied voltages on the divertor control coils is first derived and then used, in conjunction with multivariable control synthesis techniques, to design an optimal state feedback controller for the configuration. To demonstrate the capabilities of the controller, a nonlinear simulator for axisymmetric shape control was developed for NSTX-U which simultaneously evolves the currents in poloidal field coils based upon a set of feedback-computed voltage commands, calculates the induced currents in passive conducting structures, and updates the plasma equilibrium by solving the free-boundary Grad-Shafranov problem. Closed-loop simulations demonstrate that the algorithm enables controlled operations in a variety of SFD configurations and provides capabilities for accurate tracking of time-dependent target trajectories for the divertor geometry. In particular, simulation results suggest that a time-varying controller which can properly account for the evolving SFD dynamical response is not only desirable but necessary for achieving acceptable control performance. The algorithm presented in this paper has been implemented in the NSTX-U Plasma Control System in preparation for future control and divertor physics experiments.
Type:
Dataset
Issue Date:
April 2019

40. Elemental and topographical imaging of microscopic variations in deposition on NSTX-U and DIII-D samples2

Author(s):
C.H. Skinner, C.P. Chrobak, R. Kaita, B.E.Koel
Abstract:
Abstract: Tokamak plasma facing components have surface roughness that can cause microscopic spatial variations in erosion and deposition and hence influence material migration, erosion lifetime, dust and tritium accumulation, and plasma contamination. However high spatial resolution measurements of deposition on the scale of the surface roughness have been lacking to date. We will present elemental images of graphite samples from NSTX-U and DIII-D DiMES experiments performed with a Scanning Auger Microprobe at sub-micron resolution that show strong microscopic variations in deposition and correlate this with 3D topographical maps of surface irregularities. The NSTX-U samples were boronized and exposed to deuterium plasmas and the DiMES samples had localized Al and W films and were exposed to dedicated helium plasmas. Topographical maps of the samples were performed with a 3D confocal optical microscope and compared to the elemental deposition pattern. The results revealed localized deposition concentrated in areas shadowed from the ion flux, incident in a direction calculated (for the DiMES case) by taking account of the magnetic pre-sheath.
Type:
Dataset
Issue Date:
April 2019

41. Global modeling of wall material migration following boronization in NSTX-U

Author(s):
Nichols, J.H.; Jaworski, M.A.; Skinner, C.H.; Bedoya, F.; Scotti, F.; Soukhanovskii, V.A.; Schmid, K.
Abstract:
Boronization is commonly utilized in tokamaks to suppress intrinsic impurities, most notably oxygen from residual water vapor. However, this is a temporary solution, as oxygen levels typically return to pre-boronization levels following repeated plasma exposure. The global impurity migration model WallDYN has been applied to the post-boronization surface impurity evolution in NSTX-U. A “Thin Film Model” has been incorporated into WallDYN to handle spatially inhomogeneous conditioning films of varying thicknesses, together with an empirical boron conditioning model for the NSTX-U glow discharge boronization process. The model qualitatively reproduces the spatial distribution of boron in the NSTX-U vessel, the spatially-resolved divertor emission pattern, and the increase in oxygen levels following boronization. The simulations suggest that oxygen is primarily sourced from wall locations without heavy plasma flux or significant boron deposition, namely the lower and upper passive plates and the lower private flux zone.
Type:
Dataset
Issue Date:
March 2019

42. Initial transport and turbulence analysis and gyrokinetic simulation validation in NSTX-U L-mode plasmas

Author(s):
Guttenfelder, W.; Kaye, S.M.; Kreite, D.M.; Bell, R.E.; Diallo, A.; LeBlanc, B.P.; McKee, G.R.; Podesta, M.; Sabbagh, S.A.; Smith, D.R.
Abstract:
Transport analysis, ion-scale turbulence measurements, and initial linear and nonlinear gyrokinetic simulations are reported for a transport validation study based on low aspect ratio NSTX-U L-mode discharges. The relatively long, stationary L-modes enabled by the upgraded centerstack provide a more ideal target for transport validation studies that were not available during NSTX operation. Transport analysis shows that anomalous electron transport dominates energy loss while ion thermal transport is well described by neoclassical theory. Linear gyrokinetic GYRO analysis predicts that ion temperature gradient (ITG) modes are unstable around normalized radii $\rho$=0.6-0.8, although $E\timesB$ shearing rates are larger than the linear growth rates over much of that region. Deeper in the core ($\rho$=0.4-0.6), electromagnetic microtearing modes (MTM) are unstable as a consequence of the relatively high beta and collisionality in these particular discharges. Consistent with the linear analysis, local, nonlinear ion-scale GYRO simulations predict strong ITG transport at $\rho$=0.76, whereas electromagnetic MTM transport is important at $\rho$=0.47. The prediction of ion-scale turbulence is consistent with 2D beam emission spectroscopy (BES) that measures the presence of broadband ion-scale fluctuations. Interestingly, the BES measurements also indicate the presence of bi-modal poloidal phase velocity propagation that could be indicative of two different turbulence types. However, in the region between ($\rho$=0.56, 0.66), ion-scale simulations are strongly suppressed by the locally large $E\timesB$ shear. Instead, electron temperature gradient (ETG) turbulence simulations predict substantial transport, illustrating electron-scale contributions can be important in low aspect ratio L-modes, similar to recent analysis at conventional aspect ratio. However, agreement within experimental uncertainties has not been demonstrated, which requires additional simulations to test parametric sensitivities. The potential need to include profile-variation effects (due to the relatively large value of $\rho_*$=$\rho_i$/a at low aspect ratio), including electromagnetic and possibly multi-scale effects, is also discussed.
Type:
Dataset
Issue Date:
March 2019

43. Machine Learning Characterization of Alfvénic and Sub-Alfvénic Chirping and Correlation With Fast-Ion Loss at NSTX

Author(s):
Woods, B. J. Q.; Duarte, V. N.; Fredrickson, E. D.; Gorelenkov, N. N.; Podestà, M.; Vann, R. G. L.
Abstract:
Abrupt large events in the Alfvenic and sub-Alfvenic frequency bands in tokamaks are typically correlated with increased fast-ion loss. Here, machine learning is used to speed up the laborious process of characterizing the behavior of magnetic perturbations from corresponding frequency spectrograms that are typically identified by humans. The analysis allows for comparison between different mode character (such as quiescent, fixed frequency, and chirping, avalanching) and plasma parameters obtained from the TRANSP code, such as the ratio of the neutral beam injection (NBI) velocity and the Alfven velocity (v_inj./v_A), the q-profile, and the ratio of the neutral beam beta and the total plasma beta (beta_beam,i / beta). In agreement with the previous work by Fredrickson et al., we find a correlation between beta_beam,i and mode character. In addition, previously unknown correlations are found between moments of the spectrograms and mode character. Character transition from quiescent to nonquiescent behavior for magnetic fluctuations in the 50200-kHz frequency band is observed along the boundary v_phi ~ (1/4)(v_inj. - 3v_A), where v_phi is the rotation velocity.
Type:
Dataset
Issue Date:
December 2019

44. Modelling of Ablatant Deposition from Electromagnetically Driven Radiative Pellets for Disruption Mitigation Studies

Author(s):
Lunsford, Robert; Raman, Roger; Brooks, Arthur; Ellis, Robert A.; Lay, W-S;
Abstract:
The Electromagnetic Particle Injector (EPI) concept is advanced through the simulation of ablatant deposition into ITER H-mode discharges with calculations showing penetration past the H-mode pedestal for a range of injection velocities and granule sizes concurrent with the requirements of disruption mitigation. As discharge stored energy increases in future fusion devices such as ITER, control and handling of disruption events becomes a critical issue. An unmitigated disruption could lead to failure of the plasma facing components resulting in financially and politically costly repairs. Methods to facilitate the quench of an unstable high current discharge are required. With the onset warning time for some ITER disruption events estimated to be less than 10 ms, a disruption mitigation system needs to be considered which operates at injection speeds greater than gaseous sound speeds. Such an actuator could then serve as a means to augment presently planned pneumatic injection systems. The EPI uses a rail gun concept whereby a radiative payload is delivered into the discharge by means of the JxB forces generated by an external current pulse, allowing for injection velocities in excess of 1 km/s. The present status of the EPI project is outlined, including the addition of boost magnetic coils. These coils augment the self-generated rail gun magnetic field and thus provide a more efficient acceleration of the payload. The coils and the holder designed to constrain them have been modelled with the ANSYS code to ensure structural integrity through the range of operational coil cu
Type:
Dataset
Issue Date:
June 2019

45. Real-time capable modeling of neutral beam injection on NSTX-U using neural networks

Author(s):
Boyer, M.D.; Kaye, S.; Erickson, K.
Abstract:
A new model of heating, current drive, torque and other effects of neutral beam injection on NSTX-U that uses neural networks has been developed. The model has been trained and tested on the results of the Monte Carlo code NUBEAM for the database of experimental discharges taken during the first operational campaign of NSTX-U. By projecting flux surface quantities onto empirically derived basis functions, the model is able to efficiently and accurately reproduce the behavior of both scalars, like the total neutron rate and shine through, and profiles, like beam current drive and heating. The model has been tested on the NSTX-U real-time computer, demonstrating a rapid execution time orders of magnitude faster than the Monte Carlo code that is well suited for the iterative calculations needed to interpret experimental results, optimization during scenario development activities, and real-time plasma control applications. Simulation results of a proposed design for a nonlinear observer that embeds the neural network calculations to estimate the poloidal flux profile evolution, as well as effective charge and fast ion diffusivity, are presented.
Type:
Dataset
Issue Date:
February 2019

46. Reduced Model for Direct Induction Startup Scenario Development on MAST-U and NSTX-U

Author(s):
Battaglia, D.J.; Thornton, A.J.; Gerhardt, S.P.; Kirk, A.; Kogan, L; Menard, J.E.
Abstract:
A reduced semi-empirical model using time-dependent axisymmetric vacuum field calculations is used to develop the prefill and feed-forward coil current targets required for reliable direct induction (DI) startup on the new MA-class spherical tokamaks, MAST-U and NSTX-U. The calculations are constrained by operational limits unique to each device, such as the geometry of the conductive elements and active coils, power supply specifications and coil heating and stress limits. The calculations are also constrained by semi-empirical models for sufficient breakdown, current drive, equilibrium and stability of the plasma developed from a shared database. A large database of DI startup on NSTX and NSTX-U is leveraged to quantify the requirements for achieving a reliable breakdown (Ip ~ 20 kA). It is observed that without pre-ionization, STs access the large E/P regime at modest loop voltage (Vloop) where the electrons in the weakly ionized plasma are continually accelerating along the open field lines. This ensures a rapid (order millisecond) breakdown of the neutral gas, even without pre-ionization or high-quality field nulls. The timescale of the initial increase in Ip on NSTX is reproduced in the reduced model provided a mechanism for impeding the applied electric field is included. Most discharges that fail in the startup phase are due to an inconsistency in the evolution of the plasma current (Ip) and equilibrium field or loss of vertical stability during the burn-through phase. The requirements for the self-consistent evolution of the fields in the weakly and full-ionized plasma states are derived from demonstrated DI startup on NSTX, NSTX-U and MAST. The predictive calculations completed for MAST-U and NSTX-U illustrate that the maximum Ip ramp rate (dIp/dt) in the early startup phase is limited by the voltage limits on the poloidal field coils on MAST-U and passive vertical stability on NSTX-U.
Type:
Dataset
Issue Date:
August 2019

47. Study of liquid metal surface wave damping in the presence of magnetic fields and electrical currents

Author(s):
Fisher, A.E.; Hvasta, M.G.; Kolemen, E.
Abstract:
Experiments and predictions of surface wave damping in liquid metal due to a surface aligned magnetic field and externally regulated j × B force are presented. Fast-flowing, liquid-metal plasma facing components (LM-PFCs) are a proposed alternative to solid PFCs that are unable to handle the high heat flux, thermal stresses, and radiation damage in a tokamak. The significant technical challenges associated with LM-PFCs compared to solid PFCs are justified by greater heat flux management, self-healing properties, and reduced particle recycling. However, undesirable engineering challenges such as evaporation and splashing of the liquid metal introduce excessive impurities into the plasma and degrade plasma performance. Evaporation may be avoided through high-speed flow that limits temperature rise of the liquid metal by reducing heat flux exposure time, but as flow speed increases the surface may become more turbulent and prone to splashing and uneven surfaces. Wave damping is one mechanism that reduces surface disturbance and thus the chances of liquid metal impurity introduction into the plasma. Experiments on the Liquid Metal eXperiment Upgrade (LMX-U) examined damping under the influence of transverse magnetic fields and vertically directed Lorentz force.
Type:
Dataset
Issue Date:
March 2019

48. Study of the impact of pre- and real-time deposition of lithium on plasma performance on NSTX

Author(s):
Canal, G.P.; Maingi, R.; Evans, T.E.; Kaye, S.M.; Mansfield, D.K.
Abstract:
The efficiency of two lithium (Li) injection methods used on the National Spherical Torus Experiment (NSTX) are compared in terms of the amount of Li used to produce equivalent plasma performance improvements, namely Li evaporation over the divertor plates, prior to the initiation of the discharge, and real-time Li injection directly into the plasma scrape-off layer during the discharge. The measurements show that the real-time method can affect the energy confinement and edge stability of NSTX plasmas in a more efficient way than the Li evaporation method as it requires only a fraction of the amount of Li used by the evaporation method to produce similar improvements.
Type:
Dataset
Issue Date:
January 2019

49. TRANSP-based Optimization Towards Tokamak Scenario Development

Author(s):
W.P. Wehner, E. Schuster, M.D. Boyer, F. Poli
Abstract:
An optimization approach that incorporates the predictive transport code TRANSP is proposed for tokamak scenario development. Optimization methods are often employed to develop open-loop control strategies to aid access to high performance tokamak scenarios. In general, the optimization approaches use control-oriented models, i.e. models that are reduced in complexity and prediction accuracy as compared to physics-oriented transport codes such as TRANSP. In the presented approach, an optimization procedure using the TRANSP code to simulate the tokamak plasma is considered for improved predictive capabilities. As a test case, the neutral beam injection (NBI) power is optimized to develop a control strategy that maximizes the non-inductive current fraction during the ramp-up phase for NSTX-U. Simulation studies towards the achievement of non-inductive ramp up in NSTX-U have already been carried out with the TRANSP code. The optimization-based approach proposed in this work is used to maximize the non-inductive current fraction during ramp-up in NSTX-U, demonstrating that the scenario development task can be automated. An additional test case considers optimization of the current ramp rate in DIII-D for obtaining a stationary plasma characterized by a flat loop voltage profile in the flattop phase.
Type:
Dataset
Issue Date:
April 2019

50. TRANSP-based closed-loop simulations of current profile optimal regulation in NSTX-Upgrade

Author(s):
Ilhan, Z.O.; Boyer. M.D.; Schuster, E.
Abstract:
Active control of the toroidal current density profile is critical for the upgraded National Spherical Torus eXperiment device (NSTX-U) to maintain operation at the desired high-performance, MHD-stable, plasma regime. Initial efforts towards current density profile control have led to the development of a control-oriented, physics-based, plasma-response model, which combines the magnetic diffusion equation with empirical correlations for the kinetic profiles and the non-inductive current sources. The developed control-oriented model has been successfully tailored to the NSTX-U geometry and actuators. Moreover, a series of efforts have been made towards the design of model-based controllers, including a linear-quadratic-integral optimal control strategy that can regulate the current density profile around a prescribed target profile while rejecting disturbances. In this work, the tracking performance of the proposed current-profile optimal controller is tested in numerical simulations based on the physics-oriented code TRANSP. These high-fidelity closed-loop simulations, which are a critical step before experimental implementation and testing, are enabled by a flexible framework recently developed to perform feedback control design and simulation in TRANSP.
Type:
Dataset
Issue Date:
March 2019

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