Tearing mode dynamics in tokamak plasmas /

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"Version: 202306"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Introduction -- 1.2. Thermonuclear fusion -- 1.3. Nuclear fusion reactions -- 1.4. The Lawson criterion -- 1.5. Fusion plasma parameters -- 1.6. Particle balance -- 1.7. Energy balance -- 1.8. Linear pinches -- 1.9. Toroidal pinches -- 1.10. Tokamaks -- 1.11. Tearing modes -- 1.12. Tearing mode rotation -- 1.13. Error field penetration -- 1.14. Neoclassical tearing modes -- 1.15. Tearing modes in toroidal plasmas2. Plasma fluid theory -- 2.1. Introduction -- 2.2. Kinetic theory -- 2.3. Fluid theory -- 2.4. Fundamental quantities -- 2.5. Fluid closure schemes -- 2.6. The classical closure scheme -- 2.7. Trapped and passing particles -- 2.8. The neoclassical closure scheme -- 2.9. Drift and transport orderings -- 2.10. Toroidal plasma equilibrium -- 2.11. Lowest-order flows -- 2.12. The flux-surface average operator -- 2.13. Chew-Goldberger-Low forms -- 2.14. Parallel flows -- 2.15. Useful results -- 2.16. Friction force densities -- 2.17. Parallel viscous force densities -- 2.18. The determination of ion flows -- 2.19. The determination of electron flows -- 2.20. Parallel current density -- 2.21. Neoclassical transport -- 2.22. The perpendicular closure scheme -- 2.23. The parallel closure scheme -- 2.24. The derivation of the neoclassical fluid equations -- 2.25. The normalization of the neoclassical fluid equations -- 2.26. Discussion3. Cylindrical tearing-mode theory -- 3.1. Introduction -- 3.2. Cylindrical tokamak equilibrium -- 3.3. Magnetic field and current density perturbations -- 3.4. Density and temperature perturbations -- 3.5. Fluid continuity -- 3.6. Velocity perturbation -- 3.7. The cylindrical tearing-mode equation -- 3.8. The solution in the presence of a perfectly conducting wall -- 3.9. The solution in the presence of a resistive wall -- 3.10. Resistive-wall physics -- 3.11. Resistive-layer physics -- 3.12. The solution in the presence of an external magnetic field coil -- 3.13. Electromagnetic torques -- 3.14. The plasma angular equations of motion -- 3.15. The solution of the plasma angular equations of motion -- 3.16. Modification of the rotational frequency -- 3.17. The tearing-mode evolution equations4. Reduced resonant response model -- 4.1. Introduction -- 4.2. The drift-MHD fluid equations -- 4.3. The normalization scheme -- 4.4. The reduction process -- 4.5. The reduced drift-MHD model5. Linear resonant response model -- 5.1. Introduction -- 5.2. The reduced drift-MHD model -- 5.3. Plasma equilibrium -- 5.4. Linearized reduced drift-MHD equations -- 5.5. Resonant-layer equations -- 5.6. Asymptotic matching -- 5.7. Fourier transformation -- 5.8. The constant-[Psi] limit -- 5.9. Constant-[Psi] linear resonant response regimes -- 5.10. The nonconstant-[Psi] limit -- 5.11. Nonconstant-[Psi] linear resonant response regimes -- 5.12. Linear resonant response regimes -- 5.13. Response regimes in tokamak fusion reactors -- 5.14. The numerical solution of the resonant-layer equations -- 5.15. Plasma rotation -- 5.16. Magnetic reconnection6. Linear tearing-mode stability -- 6.1. Introduction -- 6.2. The linear dispersion relation -- 6.3. The determination of linear growth rates -- 6.4. Linear growth-rate regimes -- 6.5. Resonant-layer thickness -- 6.6. The numerical solution of the resonant-layer equations7. Error-field penetration in tokamak plasmas -- 7.1. Introduction -- 7.2. Asymptotic matching -- 7.3. The resonant-layer response -- 7.4. Torque balance -- 7.5. Error-field penetration -- 7.6. The numerical solution of the layer equations8. The nonlinear resonant response model -- 8.1. Introduction -- 8.2. The reduced drift-MHD model -- 8.3. The rescaled reduced drift-MHD model -- 8.4. The ordering scheme -- 8.5. The lowest-order solution -- 8.6. The flux-surface average operator -- 8.7. Fluid velocities -- 8.8. The need for a higher-order solution -- 8.9. The higher-order solution -- 8.10. Asymptotic matching -- 8.11. The evaluation of the integrals9. Nonlinear tearing-mode stability -- 9.1. Introduction -- 9.2. The Rutherford island-width evolution equation -- 9.3. The composite linear/nonlinear model -- 9.4. Saturated island width -- 9.5. The island rotation frequency10. Rotation braking in tokamak plasmas -- 10.1. Introduction -- 10.2. Rotation braking by a thin conducting wall -- 10.3. Rotation braking by a thick conducting wall -- 10.4. An improved torque balance model11. The nonlinear neoclassical resonant response model -- 11.1. Introduction -- 11.2. The neoclassical drift-magnetohydrodynamic equations -- 11.3. The reduced neoclasssical drift-MHD model -- 11.4. Magnetic field-line curvature -- 11.5. The rescaled reduced neoclassical drift-MHD model -- 11.6. The ordering scheme -- 11.7. The zeroth-order solution -- 11.8. The higher-order solution -- 11.9. Asymptotic matching -- 11.10. The evaluation of the integrals12. Neoclassical tearing modes -- 12.1. Introduction -- 12.2. The isolated magnetic island chain -- 12.3. The island rotation frequency -- 12.4. The generalized Rutherford equation -- 12.5. Stabilization via rf-driven current13. Mode locking in tokamak plasmas -- 13.1. Introduction -- 13.2. Asymptotic matching -- 13.3. The Rutherford island width evolution equation -- 13.4. Island phase evolution equations -- 13.5. The analytic solution of the phase evolution equations -- 13.6. A numerical solution of the phase evolution equations -- 13.7. Locked magnetic island chains -- 13.8. Island width evolution14. Toroidal tearing modes -- 14.1. Introduction -- 14.2. Coordinate systems -- 14.3. Useful identities -- 14.4. The equilibrium magnetic field -- 14.5. The equilibrium plasma current density -- 14.6. The Grad-Shafranov equation -- 14.7. The perturbed magnetic field -- 14.8. The perturbed current density -- 14.9. Electromagnetic torques -- 14.10. Magnetic island chains -- 14.11. The inductance matrix -- 14.12. The calculation of the inductance matrix -- 14.13. The toroidal tearing-mode dispersion relation -- 14.14. An example tokamak discharge -- 14.15. Linear calculation -- 14.16. Nonlinear calculation -- 14.17. The effect of electromagnetic torques -- 14.18. Neoclassical tearing modes -- Appendix A. Neoclassical theory.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.Scientists engaged in nuclear fusion research.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Richard Fitzpatrick is a professor of physics at the University of Texas at Austin, where he has been a faculty member since 1994. He is a member of the Royal Astronomical Society, a fellow of the American Physical Society, and the author of Maxwell's Equations and the Principles of Electromagnetism (2008), An Introduction to Celestial Mechanics (2012), Oscillations and Waves: An Introduction (2013), Plasma Physics: An Introduction (2014), Quantum Mechanics (2015), Theoretical Fluid Mechanics (2018), and Newtonian Dynamics: An Introduction (2022).Title from PDF title page (viewed on July 6, 2023).

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1 online resource (various pagings) :illustrations (some color).

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English

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9780750353670

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621.484

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SCIENCE / Physics / Atomic & Molecular.
Plasma (Ionized gases)
Plasma physics.
Tokamaks.

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Richard Fitzpatrick.

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