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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
