This is the third volume in a set of books describing state-of-the-art theories and applications of magnetically confined fusion plasmas. This volume presents advanced kinetic theory, aiming to fill the gap between plasma physics textbooks and up-to-date research developments in this field. Due to the complexity of magnetic confinement geometry, kinetic theory for fusion plasmas is also inherently complex. This requires in-depth physical considerations and skilled mathematical treatments. Guiding center theory, drift kinetic theory, gyrokinetic theory, as well as kinetic variational principles are thoroughly reviewed. Applications of these theories to fusion plasma research are also described. This book will appeal to graduate students and researchers in plasma physics.
Author(s): Linjin Zheng
Publisher: IOP Publishing
Year: 2022
Language: English
Pages: 259
City: Bristol
PRELIMS.pdf
Preface
Acknowledgements
Author biography
Linjin Zheng
CH001.pdf
Chapter 1 Introduction
1.1 Background for controlled thermonuclear fusion researches
1.2 From fluid to kinetic descriptions
1.3 Scope of the book
References
CH002.pdf
Chapter 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
2.3.1 Energy conservation and conversion
2.3.2 Magnetic moment
2.3.3 Longitudinal invariant
2.3.4 The third or flux adiabatic invariant
2.4 Conclusions and discussion
References
CH003.pdf
Chapter 3 Lagrangian and Hamiltonian theories of guiding center motion
3.1 The Lagrangian and Hamiltonian theories
3.1.1 Canonical Lagrangian and Hamiltonian theories
3.1.2 Lagrangian and Hamiltonian theories in phase space
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
References
CH004.pdf
Chapter 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
References
CH005.pdf
Chapter 5 Gyrokinetic theory
5.1 Linear gyrokinetic theory
5.1.1 Mode representation
5.1.2 Derivation of linear gyrokinetic equation
5.1.3 Equilibrium solution
5.1.4 Solution of linear gyrokinetic equation
5.2 Nonlinear gyrokinetic theory
5.3 Lie transform perturbation theory for gyrokinetics
5.4 Conclusions and discussion
References
CH006.pdf
Chapter 6 Variational theories in the guiding center description
6.1 Lagrangian and Euler descriptions of magnetic perturbations
6.1.1 Lagrangian description
6.1.2 Eulerian description
6.2 Energy principle in the guiding center description
6.3 Generalized energy principle for energetic particles
6.4 Conclusions and discussion
References
CH007.pdf
Chapter 7 Fundamentals of kinetic analysis of plasma oscillations
7.1 The kinetic theory by L Landau
7.2 The Case–Van Kampen theory
7.2.1 Continuum spectrum
7.2.2 The Case–Van Kampen theory
7.3 Nonlinear effects, BGK theory
7.4 Conclusions and discussion
References
CH008.pdf
Chapter 8 Electrostatic modes
8.1 General theoretical framework
8.2 The low frequency regime
8.3 The intermediate frequency regime
8.3.1 Fluid correspondence
8.3.2 Slab-like branch
8.3.3 Toroidal branch
8.4 The comparable frequency regime
8.4.1 Slab-like branch
8.4.2 Toroidal branch
8.5 Conclusions and discussion
References
CH009.pdf
Chapter 9 Electromagnetic modes
9.1 General framework
9.1.1 Basic set of equations
9.1.2 Recovery of ideal MHD from gyrokinetcs
9.1.3 Global mode formulation
9.1.4 High n ballooning mode formulation
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
9.4.1 Toroidal Alfvén eigenmodes
9.4.2 Kinetic toroidal Alfvén eigenmodes
9.5 Collisional effects
9.6 Conclusions and discussion
References
CH010.pdf
Chapter 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
References
CH011.pdf
Chapter 11 The beauty and simplicity in controlled fusion research
References
APPA.pdf
Chapter
APPB.pdf
Chapter
APPC.pdf
Chapter
