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Register a new userFeedforward and feedback control of locked mode phase and rotation in DIII-D with application to modulated ECCD experiments
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The toroidal phase and rotation of otherwise locked magnetic islands of toroidal mode number n=1 are controlled in the DIII-D tokamak by means of applied magnetic perturbations of n=1. Pre-emptive perturbations were applied in feedforward to catch the mode as it slowed down and entrain it to the rotating field before complete locking, thus avoiding the associated major confinement degradation. Additionally, for the first time, the phase of the perturbation was optimized in real-time, in feedback with magnetic measurements, in order for the modes phase to closely match a prescribed phase, as a function of time. Experimental results confirm the capability to hold the mode in a given fixed-phase or to rotate it at up to 20 Hz with good uniformity. The control coil currents utilized in the experiments agree with the requirements estimated by an electromechanical model. Moreover, controlled rotation at 20 Hz was combined with Electron Cyclotron Current Drive (ECCD) modulated at the same frequency. This is simpler than regulating the ECCD modulation in feedback with spontaneous mode rotation, and enables repetitive, reproducible ECCD deposition at or near the island O-point, X-point and locations in between, for careful studies of how this affects the island stability. Current drive was found to be radially misaligned relative to the island, and resulting growth and shrinkage of islands matched expectations of the Modified Rutherford Equation for some discharges presented here. Finally, simulations predict the as designed ITER 3D coils can entrain a small island at sub-10 Hz frequencies.
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The calculation presented in A neoclassical calculation of rotation profiles and comparison with DIII-D measurements by Stacey, Johnson, and Mandrekas, [Physics of Plasmas, 13, (2006)], contains several errors, including the neglect of the toroidal electric field, an unphysical expression for the electrostatic potential, and an unevaluated relation among its parameters. An alternative formulation is discussed.
Extended-MHD modeling of DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] quiescent H-mode (QH-mode) discharges with nonlinear NIMROD [C. R. Sovinec et al., J. Comput. Phys. 195, 355 (2004)] simulations saturates into a turbulent state but does not saturate when the steady-state flow inferred from measurements is not included. This is consistent with the experimental observations of the quiescent regime on DIII-D. The simulation with flow develops into a saturated turbulent state where the n=1 and 2 toroidal modes become dominant through an inverse cascade. Each mode in the range of n=1-5 is dominant at a different time. Consistent with experimental observations during QH-mode, the simulated state leads to large particle transport relative to the thermal transport. Analysis shows that the amplitude and phase of the density and temperature perturbations differ resulting in greater fluctuation-induced convective particle transport relative to the convective thermal transport. Comparison to magnetic-coil measurements shows that rotation frequencies differ between the simulation and experiment, which indicates that more sophisticated extended-MHD two-fluid modeling is required.
The free-streaming plus recycling model (FSRM) has recently been developed to understand and predict tungsten gross erosion rates from the divertor during edge localized modes (ELMs). In this work, the FSRM was tested against experimental measurements of W sputtering during ELMs, conducted via fast WI spectroscopy. Good agreement is observed using a variety of controlling techniques, including gas puffing, neutral beam heating, and plasma shaping to modify the pedestal stability boundary and thus the ELM behavior. ELM mitigation by pellet pacing was observed to strongly reduce W sputtering by flushing C impurities from the pedestal and reducing the divertor target electron temperature. No reduction of W sputtering was observed during the application of resonant magnetic perturbations (RMPs), in contrast to the prediction of the FSRM. Potential sources of this discrepancy are discussed. Finally, the framework of the FSRM is utilized to predict intra-ELM W sputtering rates in ITER. It is concluded that W erosion during ELMs in ITER will be caused mainly by free-streaming fuel ions, but free-streaming seeded impurities (N or Ne) may increase the erosion rate significantly if present in the pedestal at even the 1% level. Impurity recycling is not expected to cause significant W erosion in ITER due to the very low target electron temperature.
The purpose of this paper is to present simple and general algebraic methods for describing series connections in quantum networks. These methods build on and generalize existing methods for series (or cascade) connections by allowing for more general interfaces, and by introducing an efficient algebraic tool, the series product. We also introduce another product, which we call the concatenation product, that is useful for assembling and representing systems without necessarily having connections. We show how the concatenation and series products can be used to describe feedforward and feedback networks. A selection of examples from the quantum control literature are analyzed to illustrate the utility of our network modeling methodology.
The physical processes taking place at the edge region are crucial for the operation of tokamaks as they govern the interaction of hot plasma with the vessel walls. Numerical modeling of the edge with state-of-the-art codes attempts to elucidate interactions between neoclassical drifts, turbulence, poloidal and parallel flows that control the physical set-up of the SOL region. Here, we present post-processing analysis of simulations from the gyrokinetic code XGC1, comparing edge turbulence characteristics from a simulation of DIII-D against one of C-Mod. We find that the equilibrium $E times B$ flux across the separatrix has a similar poloidal pattern in both discharges which can be explained by magnetic drifts and trapped ion excursions. However, collisionality is noted to play a major role in that it prevents local charge accumulations from having global effects in C-Mod. In both cases, turbulent electron heat flux is higher than the ion one. This seems to be a universal characteristic of the tokamak edge. We identify turbulent frequencies and growth rates of the dominant mode in both simulations. In C-Mod, these numbers point to the presence of a drift wave. In DIII-D, linear simulations with Gene reveal a trapped electron mode. Furthermore, we present the amplitude and size distributions of the blobs from both simulations. Amplitude distributions are in qualitative agreement with experimental observations while size distributions are consistent with the fact that most blobs are not connecting to the divertor plates and suggest that they are generated by the shearing of the turbulent modes.
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