J.P.Freidberg "PLASMA PHYSICS AND FUSION ENERGY"

CAMBRIDGE UNIVERSITY PRESS 2007

Preface
Acknowledgements
Units

Part I Fusion power

1 Fusion and world energy
1.1 Introduction
1.2 The existing energy options
1.3 The role of fusion energy
1.4 Overall summary and conclusions
Bibliography

2 The fusion reaction
2.1 Introduction
2.2 Nuclear vs. chemical reactions
2.3 Nuclear energy by fission
2.4 Nuclear energy by fusion
2.5 The binding energy curve and why it has the shape it does
2.6 Summary
Bibliography
Problems

3 Fusion power generation
3.1 Introduction
3.2 The concepts of cross section, mean free path, and collision frequency
3.3 The reaction rate
3.4 The distribution functions, the fusion cross sections, and the fusion power density
3.5 Radiation losses
3.6 Summary
Bibliography
Problems

4 Power balance in a fusion reactor
4.1 Introduction
4.2 The 0-D conservation of energy relation
4.3 General power balance in magnetic fusion
4.4 Steady state 0-D power balance
4.5 Power balance in the plasma
4.6 Power balance in a reactor
4.7 Time dependent power balance in a fusion reactor
4.8 Summary of magnetic fusion power balance
Bibliography
Problems

5 Design of a simple magnetic fusion reactor
5.1 Introduction
5.2 A generic magnetic fusion reactor
5.3 The critical reactor design parameters to be calculated
5.4 Design goals, and basic engineering and nuclear physics constraints
5.5 Design of the reactor
5.6 Summary
Bibliography
Problems

Part II The plasma physics of fusion energy

6 Overview of magnetic fusion
6.1 Introduction
6.2 Basic description of a plasma
6.3 Single-particle behavior
6.4 Self-consistent models
6.5 MHD equilibrium and stability
6.6 Magnetic fusion concepts
6.7 Transport
6.8 Heating and current drive
6.9 The future of fusion research
Bibliography

7 Definition of a fusion plasma
7.1 Introduction
7.2 Shielding DC electric fields in a plasma - the Debye length
7.3 Shielding AC electric fields in a plasma - the plasma frequency
7.4 Low collisionality and collective effects
7.5 Additional constraints for a magnetic fusion plasma
7.6 Macroscopic behavior vs. collisions
7.7 Summary
Bibliography
Problems

8 Single-particle motion in a plasma - guiding center theory
8.1 Introduction
8.2 General properties of single-particle motion
8.3 Motion in a constant В field
8.4 Motion in constant В and E fields: the E x В drift
8.5 Motion in fields with perpendicular gradients: the VB drift
8.6 Motion in a curved magnetic field: the curvature drift
8.7 Combined Vv# and V* drifts in a vacuum magnetic field
8.8 Motion in time varying E and В fields: the polarization drift
8.9 Motion in fields with parallel gradients: the magnetic moment and mirroring
8.10 Summary - putting all the pieces together
Bibliography
Problems

9 Single-particle motion - Coulomb collisions
9.1 Introduction
9.2 Coulomb collisions - mathematical derivation
9.3 The test particle collision frequencies
9.4 The mirror machine revisited
9.5 The slowing down of high-energy ions
9.6 Runaway electrons
9.7 Net exchange collisions
9.8 Summary
Bibliography
Problems

10 A self-consistent two-fluid model
10.1 Introduction
10.2 Properties of a fluid model
10.3 Conservation of mass
10.4 Conservation of momentum
10.5 Conservation of energy
10.6 Summary of the two-fluid model
Bibliography
Problems

11 MHD - macroscopic equilibrium
11.1 The basic issues of macroscopic equilibrium and stability
11.2 Derivation of MHD from the two-fluid model
11.3 Derivation of MHD from guiding center theory
11.4 MHD equilibrium - a qualitative description
11.5 Basic properties of the MHD equilibrium model
11.6 Radial pressure balance
11.7 Toroidal force balance 11.8 Summary of MHD equilibrium
Bibliography
Problems

12 MHD - macroscopic stability
12.1 Introduction
12.2 General concepts of stability
12.3 A physical picture of MHD instabilities
12.4 The general formulation of the ideal MHD stability problem
12.5 The infinite homogeneous plasma - MHD waves
12.6 The linear в -pinch
12.7 The m = 0 mode in a linear Z-pinch
12.8 The m = 1 mode in a linear Z-pinch
12.9 Summary of stability
Bibliography
Problems

13 Magnetic fusion concepts
13.1 Introduction
13.2 The levitated dipole (LDX)
13.3 The field reversed configuration (FRC)
13.4 The surface current model
13.5 The reversed field pinch (RFP)
13.6 The spheromak
13.7 The tokamak
13.8 The stellarator
13.9 Revisiting the simple fusion reactor
13.10 Overall summary
Bibliography
Problems

14 Transport
14.1 Introduction
14.2 Transport in a 1 -D cylindrical plasma
14.3 Solving the transport equations
14.4 Neoclassical transport
14.5 Empirical scaling relations
14.6 Applications of transport theory to a fusion ignition experiment
14.7 Overall summary
Bibliography
Problems

15 Heating and current drive
15.1 Introduction
15.2 Ohmic heating
15.3 Neutral beam heating
15.4 Basic principles of RF heating and current drive 15.5 The cold plasma dispersion relation 15.6 Collisionless damping 15.7 Electron cyclotron heating (ECH) 15.8 Ion cyclotron heating (ICH) 15.9 Lower hybrid current drive (LHCD) 15.10 Overall summary Basic principles of RF heating and current drive
The cold plasma dispersion relation
Collisionless damping
Electron cyclotron heating (ECH)
Ion cyclotron heating (ICH)
Lower hybrid current drive (LHCD)
Overall summary
Bibliography
Problems

16 The future of fusion research
16.1 Introduction
16.2 Current status of plasma physics research
16.3 ITER
16.4 A Demonstration Power Plant (DEMO)

Appendix A
Appendix В
Appendix С
Appendix D
Index
Introduction
Current status of plasma physics research
ITER
A Demonstration Power Plant (DEMO)
Bibliography
Analytical derivation of (or и >
Radiation from an accelerating charge
Derivation of Boozer coordinates
Poynting's theorem

Plasma Physics and Fusion Energy is a textbook about plasma physics, although it is plasma physics with a mission - magnetic fusion energy. The goal is to provide a broad, yet rigorous, overview of the plasma physics necessary to achieve the half century dream of fusion energy.

The pedagogical approach taken here fits comfortably within an Applied Physics or Nuclear Science and Engineering Department. The choice of material, the order in which it is presented, and the fact that there is a coherent storyline that always keeps the energy end goal in sight is characteristic of such applied departments. Specifically, the book starts with the design of a simple fusion reactor based on nuclear physics principles, power balance, and some basic engineering constraints. A major point, not appreciated even by many in the field, is that virtually no plasma physics is required for the basic design. However, one of the crucial outputs of the design is a set of demands that must be satisfied by the plasma in order for magnetic fusion energy to be viable. Specifically, the design mandates certain values of the pressure, temperature, magnetic field, and the geometry of the plasma. This defines the plasma parameter regime at the outset. It is then the job of plasma physicists to discover ways to meet these objectives, which separate naturally into the problems of macroscopic equilibrium and stability, transport, and heating. The focus on fusion energy thereby motivates the structure of the entire book - how can we, the plasma physics community, discover ways to make the plasma perform to achieve the energy mission.

Why write such a book now? Fusion research has increased worldwide over the last several years because of the internationally recognized pressure to develop new reliable energy sources. With the recently signed agreement to build the next generation International Thermonuclear Experimental Reactor (ITER), I anticipate a substantial increase in interest on the part of new students and young scientists to join the fusion program. While fusion still has a long way to go before becoming a commercially viable source of energy, the advent of ITER enhances the already existing worldwide interest and excitement in plasma physics and fusion research. The incredibly challenging science and engineering problems coupled with the dream of an energy system characterized by unlimited fuel, near environmental perfection, and economical competitiveness are still big draws to new students and researchers.

Who is the intended audience? This textbook is aimed at seniors, first year graduate students, and new scientists joining the field. In general, the style of presentation includes in depth physical explanations aimed at developing physical intuition. It also includes many detailed derivations to clarify some of the mathematical mysteries of plasma physics. The book should thus be reasonably straightforward for newcomers to fusion to read in a stand alone fashion. There is also an extensive set of homework problems developed over two decades of teaching the subject at MIT.

With more explanations and detailed derivations something must give or else the book would become excessively long. The answer is to carefully select the material covered. In deciding how to choose which material to include and not to include, there are clearly tough decisions to be made. I have made these choices based on the idea of providing newcomers with a good first pass at understanding all the essential issues of magnetic fusion energy. Consequently, the material included is largely focused on the plasma physics mandated by fusion energy, which for a first pass is most easily described by macroscopic fluid models. As to what is not included, there is very little discussion of fusion engineering. There is also very little discussion of plasma kinetic theory (e.g. the Vlasov equation and the Fokker- Planck equation). Somewhat surprisingly to me, it was not until the next-to-last chapter in the book that I first actually needed any of the detailed results of kinetic theory (i.e., the collisionless damping rates of RF heating and current drive), which I then derived using a simple, intuitive single-particle analysis. The point is that the first time through, the best way to develop an overall understanding of all the issues involved, with particular emphasis on self-consistent integration of the plasma physics, is to focus on macroscopic fluid models which are more easily tied to physical intuition and experimental reality. Ideally, a followon study based on kinetic theory would be the next logical step to master fusion plasma physics. In such a study, many of the topics described here would be analyzed at the more advanced level marking the present state of the art in fusion research.

As is clear from the length of the book, it would take a two semester course to cover the entire material in detail. However, a cohesive one semester course can also be easily constructed by picking and choosing from among the many topics covered. In terms of prerequisites, my assumption is that readers will have a solid foundation in undergraduate physics and mathematics. The specific requirements include: A) mathematics up to partial differential equations, B) mechanics, C) basic fluid dynamics, and D) electromagnetic theory (i.e., electrostatics, magnetostatics, and wave propagation). Experience has shown that an undergraduate degree in physics or most engineering disciplines provides satisfactory preparation.

In the end it is my hope that the book will help educate the next generation of fusion researchers, an important goal in view of the international decision to build ITER, the world's first reactor-scale, burning plasma experiment.