Fusion Plasma Physics E-Book

Weston M. Stacey

• Herausgeber: Wiley-VCH
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 873

Veröffentlichungsjahr: 2012

Beschreibung

This revised and enlarged second edition of the popular textbook and reference contains comprehensive treatments of both the established foundations of magnetic fusion plasma physics and of the newly developing areas of active research. It concludes with a look ahead to fusion power reactors of the future. The well-established topics of fusion plasma physics -- basic plasma phenomena, Coulomb scattering, drifts of charged particles in magnetic and electric fields, plasma confinement by magnetic fields, kinetic and fluid collective plasma theories, plasma equilibria and flux surface geometry, plasma waves and instabilities, classical and neoclassical transport, plasma-materials interactions, radiation, etc. -- are fully developed from first principles through to the computational models employed in modern plasma physics.
The new and emerging topics of fusion plasma physics research -- fluctuation-driven plasma transport and gyrokinetic/gyrofluid computational methodology, the physics of the divertor, neutral atom recycling and transport, impurity ion transport, the physics of the plasma edge (diffusive and non-diffusive transport, MARFEs, ELMs, the L-H transition, thermal-radiative instabilities, shear suppression of transport, velocity spin-up), etc. -- are comprehensively developed and related to the experimental evidence. Operational limits on the performance of future fusion reactors are developed from plasma physics and engineering constraints, and conceptual designs of future fusion power reactors are discussed.

Leseprobe

Contents

Preface for 2nd Edition

Preface

1 Basic Physics

1.1 Fusion

1.2 Plasma

1.3 Coulomb Collisions

1.4 Electromagnetic Theory

2 Motion of Charged Particles

2.1 Gyromotion and Drifts

2.2 Constants of the Motion

2.3 Diamagnetism*

3 Magnetic Confinement

3.1 Confinement in Mirror Fields

3.2 Closed Toroidal Confinement Systems

4 Kinetic Theory

4.1 Boltzmann and Vlasov Equations

4.2 Drift Kinetic Approximation

4.3 Fokker–Planck Theory of Collisions

4.4 Plasma Resistivity

4.5 Coulomb Collisional Energy Transfer

4.6 Krook Collision Operators*

5 Fluid Theory

5.1 Moments Equations

5.2 One-Fluid Model

5.3 Magnetohydrodynamic Model

5.4 Anisotropic Pressure Tensor Model*

5.5 Strong Field, Transport Time Scale Ordering

6 Plasma Equilibria

6.1 General Properties

6.2 Axisymmetric Toroidal Equilibria

6.3 Large Aspect Ratio Tokamak Equilibria

6.4 Safety Factor

6.5 Shafranov Shift*

6.6 Beta*

6.7 Magnetic Field Diffusion and Flux Surface Evolution*

6.8 Anisotropic Pressure Equilibria*

6.9 Elongated Equilibria*

7 Waves

7.1 Waves in an Unmagnetized Plasma

7.2 Waves in a Uniformly Magnetized Plasma

7.3 Langmuir Waves and Landau Damping

7.4 Vlasov Theory of Plasma Waves*

7.5 Electrostatic Waves*

8 Instabilities

8.1 Hydromagnetic Instabilities

8.2 Energy Principle

8.3 Pinch and Kink Instabilities

8.4 Interchange (Flute) Instabilities

8.5 Ballooning Instabilities

8.6 Drift Wave Instabilities

8.7 Resistive Tearing Instabilities*

8.8 Kinetic Instabilities*

8.9 Sawtooth Oscillations*

9 Neoclassical Transport

9.1 Collisional Transport Mechanisms

9.2 Classical Transport

9.3 Neoclassical Transport – Toroidal Effects in Fluid Theory

9.4 Multifluid Transport Formalism*

9.5 Closure of Fluid Transport Equations*

9.6 Neoclassical Transport – Trapped Particles

9.7 Extended Neoclassical Transport – Fluid Theory*

9.8 Electrical Currents

9.9 Orbit Distortion*

9.10 Neoclassical Ion Thermal Diffusivity

9.11 Paleoclassical Electron Thermal Diffusivity

9.12 Transport in a Partially Ionized Gas*

10 Plasma Rotation*

10.1 Neoclassical Viscosity

10.2 Rotation Calculations

10.3 Momentum Confinement Times

10.4 Rotation and Transport in Elongated Geometry

11 Turbulent Transport

11.1 Electrostatic Drift Waves

11.2 Magnetic Fluctuations

11.3 Wave–Wave Interactions*

11.4 Drift Wave Eigenmodes*

11.5 Microinstability thermal diffusivity models*

11.6 Gyrokinetic and Gyrofluid Theory*

11.7 Zonal Flows*

12 Heating and Current Drive

12.1 Inductive

12.2 Adiabatic Compression*

12.3 Fast Ions

12.4 Electromagnetic Waves

13 Plasma-Material Interaction

13.1 Sheath

13.2 Recycling

13.3 Atomic and Molecular Processes

13.4 Penetration of Recycling Neutrals

13.5 Sputtering

13.6 Impurity Radiation

14 Divertors

14.1 Configuration, Nomenclature and Physical Processes

14.2 Simple Divertor Model

14.3 Divertor Operating Regimes*

14.4 Impurity Retention

14.5 Thermal Instability*

14.6 2D Fluid Plasma Calculation*

14.7 Drifts

14.8 Thermoelectric Currents

14.9 Detachment

14.10 Effect of Drifts on Divertor and SOL Plasma Properties*

14.11 Blob Transport*

15 Plasma Edge

15.1 H-Mode Edge Plasma

15.2 Transport in the Plasma Edge

15.3 Differences Between L-Mode and H-Mode Plasma Edges

15.4 Effect of Recycling Neutrals

15.5 E × B Shear Stabilization of Turbulence

15.6 Thermal Instabilities

15.7 Poloidal Velocity Spin-Up*

15.8 ELM Stability Limits on Edge Pressure Gradients

15.9 MARFEs

15.10 Radiative Mantle

15.11 Edge Operation Boundaries

16 Neutral Particle Transport

16.1 Fundamentals*

16.2 PN Transport and Diffusion Theory*

16.3 Multidimensional Neutral Transport*

16.4 Integral Transport Theory*

16.5 Collision Probability Methods*

16.6 Interface Current Balance Methods

16.7 Extended Transmission-Escape Probabilities Method*

16.8 Discrete Ordinates Methods*

16.9 Monte Carlo Methods*

16.10 Navier–Stokes Fluid Model*

16.11 Tokamak Plasma Refueling by Neutral Atom Recycling

17 Power Balance

17.1 Energy Confinement Time

17.2 Radiation

17.3 Impurities

17.4 Burning Plasma Dynamics

18 Operational Limits

18.1 Disruptions

18.2 Disruption Density Limit

18.3 Nondisruptive Density Limits

18.4 Empirical Density Limit

18.5 MHD Instability Limits

19 Fusion Reactors and Neutron Sources

19.1 Plasma Physics and Engineering Constraints

19.2 International Tokamak Program

19.3 Fusion Beyond ITER

19.4 Fusion-Fission Hybrids?

Appendices

Appendix A: Frequently Used Physical Constants

Appendix B: Dimensions and Units

Appendix C: Vector Calculus

Appendix D: Curvilinear Coordinates

Appendix E: Plasma Formulas1

Appendix F: Further Reading

Appendix G: Attributions

Subject Index

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The Author

Prof. Weston M. Stacey

Georgia Institute of Technology

Fusion Research Center

Atlanta, GA 30332-0745

USA

Cover Picture

MAST Tokamak

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Print ISBN: 978-3-527-41134-4

ePDF ISBN: 978-3-527-66954-7

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Preface for 2nd Edition

There have been significant developments in magnetic fusion plasma physics (and supporting technology) since the first edition of this book was published almost seven years ago. The formation of the ITER project, in which Europe, Japan, Russia, the USA, China, India and South Korea are collaborating on the construction and subsequent operation in the 2020s of the first experimental fusion power reactor, has done much to focus the world’s fusion research efforts on resolving the resolvable physics issues that remain for this perhaps penultimate step on the path to fusion power. This focused attention has stimulated substantial progress in better understanding the physics of burning plasmas, the transport of particles and energy from the central plasma core to the edge, the physics of the edge plasma where the interaction with the surrounding material wall takes place, and other areas important to the success of ITER.

It is the intention of this second edition to incorporate these advances in understanding of tokamak plasma physics into a comprehensive textbook and reference on the state-of-the-art in fusion plasma physics. Major additions have been made to the sections on the physics of the plasma edge, on the divertor, on the recycling of neutral atoms to refuel the plasma, on the physics models for the transport of energy and particles from the plasma core into and across the plasma edge, on the evolving first-principles physics calculations of the turbulent processes thought to govern transport of energy from the core and on several other physics issues important to ITER. Other sections containing material that has been supplanted or found to be not as relevant as the newer material have been reduced or eliminated.

As with the 1st edition, this 2nd edition is intended as a textbook for advanced undergraduate and graduate students in physics, nuclear engineering and other disciplines offering courses in fusion plasma physics. It is also intended as a reference for practicing physicists and engineers in the field of fusion plasma physics, and as a combination textbook and reference for those who are entering that field. The book should be accessible to anyone with the background in math and physics of a university senior in physics or a physics-based branch of engineering. The material was developed for graduate courses in nuclear engineering at Georgia Tech (an asterisk denotes the material that we defer until the second graduate course), but the first graduate course is routinely taken by a few seniors.

As always, the production of a book like this involves a lot more people than the author. I am grateful to a few generations of students who have helped me hone the material into a form they found more understandable, to my administrative assistants at Georgia Tech who have helped with the assembling of figures, permissions, etc., and of course to the very good team under Anja Tschoertner at Wiley-VCH who pulled it all together. I am also grateful to my wife, Penelope, for tolerating with reasonably good grace the numerous holiday and weekend hours that I put into this effort, which she no doubt correctly predicts “will never make you a household name”.

Atlanta, Georgia

January 2012

Weston M. Stacey

Preface

The development of mankind’s ultimate energy source, thermonuclear fusion, is a compelling intellectual challenge for those involved and a matter of enormous importance for all. Progress to date has been hard won, but substantial. We have come a long way from the beginning of this quest in the middle of the past century and now stand on the threshold of significant power production. The temperatures of laboratory plasmas (the working gas of fusion) have been increased from the tens of thousands of degrees of the early fusion experiments to above solar temperatures and then to the hundreds of millions of degrees required for terrestrial fusion. The proximity to the conditions at which this temperature could be maintained indefinitely by the self-heating of the fusion event has been reduced from the factor of hundreds of thousands that characterized the early experiments to within less than a factor of ten. Tens of kilowatts of fusion power have been produced. The engineering design and R & D for the International Thermonuclear Experimental Reactor (ITER), which will produce hundreds of millions of watts, has been completed. The construction of ITER in France willl begin in the near future.

This progress in fusion energy development has been based on an ever-expanding understanding of the physics of magnetically confined plasmas and on improvements in the technology used for their heating and confinement. Most of the advances cited above have been realized in a toroidal confinement concept known as the “tokamak,” and there are “advanced” variants of the tokamak which promise certain advantages relative to the “conventional” tokamak. Moreover, there are a number of other, less developed magnetic confinement concepts that may also lead to improved performance. The next quarter century will surely witness steps on the path to fusion power equally as exciting as those of the past.

I have worked on the development of fusion power for about 30 years and have taught graduate and advanced undergraduate courses in fusion plasma physics at Georgia Tech for almost that long. Over this period, both the details and the scope of the material that I felt was appropriate to include in a course on fusion plasma physics has changed significantly, so that the available textbooks (including one of my own) gradually became if not out of date at least somewhat dated, as more complete developments of the “conventional” topics of plasma physics (e.g. individual particle motion in electromagnetic fields, kinetic and fluid theory, MHD equilibrium, plasma instabilities, classical transport, neutral beam and wave heating) became available and as the portfolio of plasma physics was broadened to include new topics (e.g. non–inductive current-drive, fluctuation-driven transport, rotation, plasma–materials interactions, H-mode edge transport barriers, thermal instabilities, neutral atom transport, divertors, operational density and pressure limits, future fusion reactor and neutron source concepts). As my lecture notes evolved over the years, the new material came to dominate the conventional material found in the available textbooks on plasma physics; hence my decision to publish a new book based on these lecture notes.

This book is intended as a textbook for students with little or no knowledge of plasma physics but with the background in math and physics that would be expected of the graduate of a good undergraduate physics or nuclear engineering department. Essentially all of the material can be covered in a two-semester course. The sections that are not marked with an asterisk contain material that can be covered in a one-semester course for students at the senior or first year graduate level. The sections marked with an asterisk contain material that I would omit from a one-semester course either because it is of lower priority or at a more advanced level. The book should also serve as a self-study guide for advanced students and professionals on the newer material not found in other textbooks. Since the book provides many practical computational formulas, it should further serve as a useful reference for practicing professionals, and it has a detailed index for that purpose.

It is always necessary to be selective in choosing what to include and what to omit in a textbook. Most importantly, I have chosen to describe fusion plasma physics from a theoretical viewpoint, although the field is predominantly experimental, because this seems the best way to convey an understanding of the basic principles. I have attempted to be comprehensive in the treatment of plasma physics topics that are important to the development of fusion power, but have omitted other plasma physics topics. I have usually chosen a tokamak application to illustrate these topics because the tokamak applications are the most highly developed. I have tried both to develop the basic principles and to provide formulas that can be used in analyzing experimental results or designing future reactors, but I have stopped short of describing the calculational procedures used in the big codes of the field. I have included some discussion of experimental results, in particular for areas of current research, but have omitted any discussion of plasma diagnostics.

The person who masters the material in this book should be able to understand the work that is going on in fusion research laboratories and should be able to understand the research reported in the major fusion plasma physics research journals. He or she should have the background necessary to acquire the detailed expertise required for original research in any area of current interest in fusion plasma physics.

The author of a textbook such as this is always indebted to the many people who developed the subject matter and to the many other people who produced the lecture notes and finally the book. The subject matter of this book is based on material from many sources – the archival literature of the field, specialized monographs and reference books, earlier textbooks, laboratory reports, etc., only a fraction of which are cited in the section on further reading. John Mandrekas and Edward Thomas were involved in the assembling of material on plasma edge physics and plasma-materials interactions for an early version of the lecture notes. Several versions of the lecture notes and the final manuscript were prepared by Shauna Bennett-Boyd and Candace Salim. A generation of students called my attention to typos and worse in the lecture notes, and Zach Friis, Dingkang Zhang and Rob Johnson helped with the proofreading final. Finally, the team at Wiley-VCH – Cornelia Wanka, Claudia Grössl, Plamen Tanovski and others – expertly handled the conversion of the lecture notes into a book. To all of these people I am grateful.

Atlanta, Georgia

August 2005

Weston M. Stacey

1

Basic Physics

We will begin our study of fusion plasmas by considering the basic physics that ultimately determines the properties of a thermonuclear plasma. The fusion process will be considered in the first section, and the conditions necessary for the achievement of fusion reactions will be established. In the second section, we will examine some fundamental properties of a plasma and will establish the criterion that determines when a collection of charged particles may be treated as a plasma. The consequences of charged-particle (Coulomb) collisions upon the particles that make up a plasma will be examined in the third section. Finally, the basic equations of electromagnetic theory will be reviewed in the fourth section.

1.1 Fusion

The actual mass of an atomic nucleus is not the sum of the masses (mp) of the Z-protons and the masses (mn) of the A–Z neutrons of which it is composed. The stable nuclides have a mass defect

(1.1)

Any process which results in nuclides being converted to other nuclides with more binding energy per nucleon will result in the conversion of mass into energy. The combination of low A-nuclides to form higher A-nuclides with a larger BE/A is the basis for the fusion process for the release of nuclear energy. The splitting of very high A-nuclides to form intermediate A-nuclides with a larger BE/A is the basis of the fission process for the release of nuclear energy.

The fusion of two light nuclei to form a compound nucleus in an excited state that then decays into reaction products, with an attendant conversion of mass into kinetic energy, is represented schematically by

(1.2)

The mass difference

(1.3)

is converted into kinetic energy according to Einstein’s celebrated formula

(1.4)

Figure 1.1. Binding energy per nucleon

In order for the fusion reaction to take place, the two nuclei must overcome the longrange Coulomb repulsion force and approach sufficiently close that the short-range nuclear attraction forces can lead to the formation of a compound nucleus. From the observation that hydrogen, deuterium, helium, and so on, do not fuse spontaneously under normal conditions, we conclude that the electrostatic repulsion between positively charged nuclei prevents nuclei approaching each other sufficiently close for the short-range attractive nuclear forces to become dominant. For fusion to occur as a result of random encounters between atomic nuclei, the nuclei must be made sufficiently energetic to overcome the Coulomb repulsive force. We will see that energies of the order of 10 keV to 100 keV are required, which corresponds to temperatures of 108 K to 109 K. At these thermonuclear temperatures, which are comparable to those of the sun’s interior, light atoms are completely stripped of their orbital electrons. This macroscopically neutral gas of positively charged light atomic nuclei and electrons is a thermonuclear plasma.

The rate at which fusion reactions take place between atomic nuclei of species 1 and 2 in a thermonuclear plasma is

(1.5)

where n1 is the density, υ1 is the velocity, and f1 is the velocity distribution function, respectively, of species 1, and σf is the fusion cross section. The velocity distributions of ions in a plasma can be represented in many cases by a Maxwellian distribution

Figure 1.2. Fusion reaction rates

(1.6)

Fusion reaction rates for the three reactions of primary interest for thermonuclear plasmas are shown in Fig. 1.2. At temperatures below the threshold value shown in Fig. 1.2 the reaction rates are negligible. As is apparent from this figure, and from Table 1.1, the reaction rate which becomes significant at the lowest temperature is for deuterium (D)–tritium (T) fusion. Table 1.1 also gives the amount of thermonuclear energy produced by a fusion event and indicates the part of that energy that is the kinetic energy of a neutron. The two branches shown for the D–D reaction occur with about equal probability. There are many other possible fusion reactions, but they generally have even higher threshold energies.

We can identify the principal challenges of fusion research from these data. The plasma must be heated to thermonuclear temperature (108 K to 109 K) and confined sufficiently long that the thermonuclear energy produced significantly exceeds the energy required to heat the plasma. A simple energy balance (which ignores many important effects),

Table 1.1. Fusion reactions of primary interest

(1.7)

which states that the product of the fusion energy production rate and the energy confinement time, τE, must exceed the amount of energy required to heat ions per unit volume and electrons to temperature , may be used to derive a break-even criterion for the scientific feasibility of fusion power. Using physical constants typical of a D–T plasma, can be rearranged to write the criterion