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The neoclassical tearing mode (NTM) instability produces magnetic islands in tokamak plasmas that can degrade confinement and lead to plasma disruptions. NTMs are driven by a lack of bootstrap current inside the magnetic island where the pressure profile is flattened. Suppression of these islands is necessary for sustained energy confinement and efficient operation in tokamak magnetic-fusion reactors. Compensating for the lack of bootstrap current by an Electron Cyclotron Current Drive (ECCD) has been proved experimentally as an effective method to stabilize NTMs. The effectiveness of this method is limited in practice by the uncertainties in the width of the island, the relative position between the island and the EC beam, and the EC power threshold for NTM stabilization. Heuristic Search and Suppress algorithms have been proposed and shown effective to improve the alignment of the EC beam with the island by just using an estimate of the island width. Making use of this estimate, a real-time, non-model-based, extremum-seeking optimization algorithm is proposed for EC beam steering and modulation in order to minimize the island-beam misalignment and the time (control energy) required for NTM stabilization. The efficiency of the proposed method is compared with traditional search and suppress algorithms. It is shown that the Extremum Seeking method has the potential of reducing NTM suppression times. In addition, it is shown that the Extremum Seeking method has the ability of modulating simultaneously other parameters beyond island-beam alignment that improve the effectiveness of the ECCD such as modulation duty-cycle and the phase mismatch between the ECCD and island O-point.
Improved models for neoclassical tearing modes and anomalous transport are developed and validated within integrated modeling codes to predict toroidal rotation, temperature and current density profiles in tokamak plasmas. Neoclassical tearing modes produce helical filaments of plasma, called magnetic islands, which have the effect of degrading tokamak plasma confinement or terminating the discharge. An improved code is developed in order to compute the widths of multiple simultaneous magnetic islands whose shapes are distorted by the radial variation in the magnetic perturbation [F. D. Halpern, et al., J. Plasma Physics 72 (2006) 1153]. It is found in simulations of DIII-D and JET tokamak discharges that multiple simultaneous magnetic islands produce a 10% to 20% reduction in plasma thermal confinement. If magnetic islands are allowed to grow to their full width in ITER fusion reactor simulations, fusion power production is reduced by a factor of four [F. D. Halpern, et al., Phys. Plasmas 13 (2006) 062510]. In addition to improving the prediction of neoclassical tearing modes, a new Multi-Mode transport model, MMM08, was developed to predict temperature and toroidal angular frequency profiles in simulations of tokamak discharges. The capability for predicting toroidal rotation is motivated by ITER simulation results that indicate that the effects of toroidal rotation can increase ITER fusion power production [F. D. Halpern et al., Phys. Plasmas 15 (2008), 062505]. The MMM08 model consists of an improved model for transport driven by ion drift modes [F. D. Halpern et al., Phys. Plasmas 15 (2008) 012304] together with a model for transport driven by short wavelength electron drift modes combined with models for transport driven by classical processes. The new MMM08 transport model was validated by comparing predictive simulation results with experimental data for 32 discharges in the DIII-D and JET tokamaks. It was found that the prediction of intrinsic plasma rotation is consistent with experimental measurements in discharges with zero net torque. A scaling relation was developed for the toroidal momentum confinement time (angular momentum divided by net torque) as a function of plasma current and torque per ion.
This is a graduate textbook on tokamak physics, designed to provide a basic introduction to plasma equilibrium, particle orbits, transport, and those ideal and resistive magnetohydrodynamic instabilities which dominate the behavior of a tokamak discharge, and to develop the mathematical methods necessary for their theoretical analysis.
The development of humankind's ultimate energy source, nuclear fusion, has proceeded slowly but surely over the course of the last 60 years. This comprehensive book aims to outline a realistic, comprehensive, self-consistent, analytic theory of tearing mode dynamics in tokamak plasmas. It discusses a fluid theory of a highly magnetized plasma that treats the electrons and ions as independent fluids, and then proceeds to develop the theory of tearing modes, first approximating the geometry of a tokamak plasma as a periodic cylinder, but eventually considering the toroidal structure of real tokamak plasmas. This book also describes the stability of tearing modes, the saturation of such modes, and the evolution of their phase velocity due to interaction with other tearing modes, as well as the resistive vacuum vessel, and imperfections in the tokamak's magnetic field. This text will appeal to scientists and graduate students engaged in nuclear fusion research, and would make a useful reference for graduate plasma physics courses. Part of IOP Series in Plasma Physics.