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Stability Of Tearing Modes In Tokamak Plasmas
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Book Synopsis Tearing Mode Dynamics in Tokamak Plasmas by : Richard Fitzpatrick
Download or read book Tearing Mode Dynamics in Tokamak Plasmas written by Richard Fitzpatrick and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Stability of Tearing Modes in Tokamak Plasmas by : C.C. Hegna
Download or read book Stability of Tearing Modes in Tokamak Plasmas written by C.C. Hegna and published by . This book was released on 1994 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability of Tearing Modes in Tokamak Plasmas by :
Download or read book Stability of Tearing Modes in Tokamak Plasmas written by and published by . This book was released on 1994 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory of Tokamak Plasmas by : R.B. White
Download or read book Theory of Tokamak Plasmas written by R.B. White and published by Elsevier. This book was released on 2017-01-31 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Tearing Mode Stability of Tokamak Plasmas with Elliptical Cross Section by :
Download or read book Tearing Mode Stability of Tokamak Plasmas with Elliptical Cross Section written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The effect of the ellipticity of the plasma cross section on tearing mode stability is investigated. The induced coupling between modes is shown to be destabilizing; however, the modification of the equilibrium tends to stabilize the tearing modes. The net effect depends on the manner in which the equilibrium is modified as the plasma cross-section shape is changed.
Book Synopsis Magnetohydrodynamic Stability of Tokamaks by : Hartmut Zohm
Download or read book Magnetohydrodynamic Stability of Tokamaks written by Hartmut Zohm and published by John Wiley & Sons. This book was released on 2015-02-09 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges the gap between general plasma physics lectures and the real world problems in MHD stability. In order to support the understanding of concepts and their implication, it refers to real world problems such as toroidal mode coupling or nonlinear evolution in a conceptual and phenomenological approach. Detailed mathematical treatment will involve classical linear stability analysis and an outline of more recent concepts such as the ballooning formalism. The book is based on lectures that the author has given to Master and PhD students in Fusion Plasma Physics. Due its strong link to experimental results in MHD instabilities, the book is also of use to senior researchers in the field, i.e. experimental physicists and engineers in fusion reactor science. The volume is organized in three parts. It starts with an introduction to the MHD equations, a section on toroidal equilibrium (tokamak and stellarator), and on linear stability analysis. Starting from there, the ideal MHD stability of the tokamak configuration will be treated in the second part which is subdivided into current driven and pressure driven MHD. This includes many examples with reference to experimental results for important MHD instabilities such as kinks and their transformation to RWMs, infernal modes, peeling modes, ballooning modes and their relation to ELMs. Finally the coverage is completed by a chapter on resistive stability explaining reconnection and island formation. Again, examples from recent tokamak MHD such as sawteeth, CTMs, NTMs and their relation to disruptions are extensively discussed.
Book Synopsis Stabilization of Neoclassical Tearing Modes in Tokamak Fusion Plasmas Via Extremum Seeking by : William P. Wehner
Download or read book Stabilization of Neoclassical Tearing Modes in Tokamak Fusion Plasmas Via Extremum Seeking written by William P. Wehner and published by . This book was released on 2009 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis A Study of Tearing Modes Via Electron Cyclotron Emission from Tokamak Plasmas by :
Download or read book A Study of Tearing Modes Via Electron Cyclotron Emission from Tokamak Plasmas written by and published by . This book was released on 1998 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis studies several tearing mode problems from both theoretical and experimental points of view. A major part of this thesis is to demonstrate that Electron Cyclotron Emission (ECE) is an excellent diagnostic for studying an MHD mode structure and its properties in a tokamak plasma. It is shown that an MHD mode can be detected from the electron temperature fluctuations measured by ECE. The amplitude and phase profiles of the fluctuations contain detailed information about the mode structure. The ECE fluctuation phase profile indicates the magnetic island deformation due to the combination of sheared flow and viscosity. A model is presented to relate qualitatively the observed phase gradient to the local magnetic field, flow velocity shear and viscosity in a 2D slab geometry, using an ideal Ohm's law and the plasma momentum equation including flow and viscosity. Numerical solution of the resultant Grad-Shafranov-like equation describing the deformed island shows that the experimentally observed value of the phase gradient can be obtained under realistic parameters for the shear in the flow velocity and viscosity. A new approach to the tearing mode stability boundary and saturation level is also presented.
Book Synopsis Tearing Mode Stability in a Sheared Slab Model of the Tokamak Plasma by :
Download or read book Tearing Mode Stability in a Sheared Slab Model of the Tokamak Plasma written by and published by . This book was released on 2008 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Turbulent Stabilization of the Tearing Mode in Tokamak Plasmas by : E. Esarey
Download or read book Turbulent Stabilization of the Tearing Mode in Tokamak Plasmas written by E. Esarey and published by . This book was released on 1985 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Study of Tearing Modes Via Electron Cyclotron Emission from Tokamak Plasmas by : Chuang Ren
Download or read book A Study of Tearing Modes Via Electron Cyclotron Emission from Tokamak Plasmas written by Chuang Ren and published by . This book was released on 1998 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tearing Mode Stability in a Sheard Slab Model of the Tokamak Plasma by : Martin James
Download or read book Tearing Mode Stability in a Sheard Slab Model of the Tokamak Plasma written by Martin James and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tearing Mode Dynamics in Tokamak Plasmas by : Nikolaos Vergos
Download or read book Tearing Mode Dynamics in Tokamak Plasmas written by Nikolaos Vergos and published by . This book was released on 2016 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most problematic instabilities in tokamak plasmas is tearing modes; they are driven by current and pressure gradients, and involve a reconfiguration of the magnetic and velocity fields localized into a narrow region located at a resonant magnetic surface. While the equilibrium magnetic field lines are located on concentric nested toroidal flux surfaces, the instability creates magnetic islands in which field lines connect flux tubes together, allowing for a high radial heat transport, and, thus, resulting in a loss of confinement, and, potentially, disruptions. In order for the magnetic field lines to break and reconnect, we need to take into account the resistivity of the plasma and solve the resistive magnetohydrodynamics (MHD) equations. The analytical solution consists of a boundary layer analysis (asymptotic matching) and takes advantage of the small radial width of the region where the perturbations vary significantly. Indeed, ideal magnetohydrodynamics can be used everywhere except in that narrow region where the full resistive problem must be solved. This dissertation addresses two related problems in the study of resistive tearing modes, and their interactions with externally induced resonant magnetic perturbations (error-fields). First, an in-depth investigation of the bifurcated states of a rotating, quasi-cylindrical, tokamak plasma in the presence of a resonant error-field is performed, within the context of constant-[greek letter psi] resistive MHD theory. The response of the rotating plasma is studied in both the linear, and the nonlinear regime. In general, there is a "forbidden band" of tearing mode rotation frequencies that separates a branch of high-frequency solutions from a branch of low-frequency solutions. When a high-frequency solution crosses the upper boundary of the forbidden band there is a bifurcation to a low-frequency solution, and vice versa. Second, the analysis is extended to include the study of braking and locking of tearing mode rotation by the interaction of the mode with an error-field. It is found that this interaction can brake the plasma rotation, suppress magnetic island evolution and drive locked modes.
Book Synopsis Stabilization of the Tearing Mode in Low Density Tokamak Plasmas by Turbulent Electron Diffusion by : E. Esarey
Download or read book Stabilization of the Tearing Mode in Low Density Tokamak Plasmas by Turbulent Electron Diffusion written by E. Esarey and published by . This book was released on 1982 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tokamaks written by John Wesson and published by Oxford University Press. This book was released on 2011-10-13 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tokamak is the principal tool in controlled fusion research. This book acts as an introduction to the subject and a basic reference for theory, definitions, equations, and experimental results. The fourth edition has been completely revised, describing their development of tokamaks to the point of producing significant fusion power.
Book Synopsis Effects of Toroidicity on Resistive Tearing Modes by :
Download or read book Effects of Toroidicity on Resistive Tearing Modes written by and published by . This book was released on 1983 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A reduced set of resistive MHD equations is solved numerically in three dimensions to study the stability of tokamak plasmas. Toroidal effects are included self-consistently to leading and next order in inverse aspect ratio, epsilon. The equations satisfy an energy integral. In addition, the momentum equation yields the Grad-Shafranov equation correct to all orders in epsilon. Low beta plasma are studied using several different q-profiles. In all cases, the linear growth rates are reduced by finite toroidicity. Excellent agreement with resistive PEST is obtianed. In some cases, toroidal effects lead to complete stabilization of the mode. Nonlinear results show smaller saturated island widths for finite aspect ratio compared to the cylindrical limit. If the current channel is wide enough so as to produce steep gradients towards the outside of the plasma, both the finite aspect ratio cases and cylindrical cases disrupt.
Book Synopsis Tearing Mode Analysis in Tokamaks, Revisited by :
Download or read book Tearing Mode Analysis in Tokamaks, Revisited written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: A new[Delta][prime] shooting code has been developed to investigate tokamak plasma tearing mode stability in a cylinder and large aspect ratio ([epsilon][le] 0.25) toroidal geometries, neglecting toroidal mode coupling. A different computational algorithm is used (shooting out from the singular surface instead of into it) to resolve the strong singularities at the mode rational surface, particularly in the presence of finite pressure term. Numerical results compare favorably with Furth et al. results. The effects of finite pressure, which are shown to decrease[Delta][prime], are discussed. It is shown that the distortion of the flux surfaces by the Shafranov shift, which modifies the geometry metric element stabilizes the tearing mode significantly, even in a low[beta] regime before the toroidal magnetic curvature effects come into play. Double tearing modes in toroidal geometries are examined as well. Furthermore, m[ge] 2 tearing mode stability criteria are compared with three dimensional initial value MHD simulation by the FAR code.
