part IV. Concluding remarks. 11. The beauty and simplicity in controlled fusion research
Appendix A. Table of integrals and vector formula
Appendix B. Supplementary derivation of drift kinetic equation
Appendix C. Acronym list.
part I. Introduction. 1. Introduction
1.1. Background for controlled thermonuclear fusion researches
1.2. From fluid to kinetic descriptions
1.3. Scope of the book
part II. General theoretical formalism. 2. Charged particle motion in an electromagnetic field
2.1. Introduction
2.2. Guiding center motion of charged particles
2.3. Energy conversion and adiabatic invariants
2.4. Conclusions and discussion
3. Lagrangian and Hamiltonian theories of guiding center motion
3.1. The Lagrangian and Hamiltonian theories
3.2. Guiding center Lagrangian in phase space
3.3. Noether's theorem, invariants, and adiabatic invariants
3.4. Lie transform perturbation theory
3.5. Lie transform theory for guiding center motion
3.6. Modification of the Lie transform for describing the guiding center motion
3.7. Conclusions and discussion
4. Drift kinetic theory
4.1. The drift kinetic equation and its recursive derivation
4.2. Kinetic equations in transport time scale
4.3. Conclusions and discussion
5. Gyrokinetic theory
5.1. Linear gyrokinetic theory
5.2. Nonlinear gyrokinetic theory
5.3. Lie transform perturbation theory for gyrokinetics
5.4. Conclusions and discussion
6. Variational theories in the guiding center description
6.1. Lagrangian and Euler descriptions of magnetic perturbations
6.2. Energy principle in the guiding center description
6.3. Generalized energy principle for energetic particles
6.4. Conclusions and discussion
part III. Applications : stability analyses. 7. Fundamentals of kinetic analysis of plasma oscillations
7.1. The kinetic theory by L Landau
7.2. The Case-Van Kampen theory
7.3. Nonlinear effects, BGK theory
7.4. Conclusions and discussion
8. Electrostatic modes
8.1. General theoretical framework
8.2. The low frequency regime
8.3. The intermediate frequency regime
8.4. The comparable frequency regime
8.5. Conclusions and discussion
9. Electromagnetic modes
9.1. General framework
9.2. Kinetic ballooning modes in the low frequency regime
9.3. Kinetic ballooning modes in the comparable frequency regime
9.4. Kinetic theory in the intermediate frequency regime
9.5. Collisional effects
9.6. Conclusions and discussion
10. Energetic particle theory
10.1. Background : from the rigid current model to kinetic description
10.2. Energetic particle effects on ballooning modes
10.3. Energetic particle modified Mercier criterion
10.4. Energetic particle modes (EPMs)
10.5. Fishbone instabilities
10.6. Nonlinear theory of kinetic instabilities near threshold
10.7. Conclusions and discussion