Tearing mode dynamics in tokamak plasmas [E-Book] /

Tearing mode dynamics in tokamak plasmas [E-Book] / Richard Fitzpatrick.

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 discu...

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Fitzpatrick, Richard, author
Bristol: IOP Publishing, 2023
1 online resource (various pagings)
englisch
9780750353670
9780750353663
10.1088/978-0-7503-5367-0
IOP series in plasma physics
Tokamaks.
Plasma (Ionized gases)



  • 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 plasmas
  • 2. 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. Discussion
  • 3. 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 equations
  • 4. 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 model
  • 5. 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 reconnection
  • 6. 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 equations
  • 7. 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 equations
  • 8. 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 integrals
  • 9. 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 frequency
  • 10. 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 model
  • 11. 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 integrals
  • 12. 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 current
  • 13. 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 evolution
  • 14. 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.