Fundamentals of Plasma Physics and Controlled Fusion

Primary objective of this lecture note is to provide a basic text for the students to study
plasma physics and controlled fusion researches. Secondary objective is to offer a reference book
describing analytical methods of plasma physics for the researchers. This was written based
on lecture notes for a graduate course and an advanced undergraduate course those have been
offered at Department of Physics, Faculty of Science, University of Tokyo.
In ch.1 and 2, basic concept of plasma and its characteristics are explained. In ch.3, orbits
of ion and electron are described in several magnetic field configurations. Chapter 4 formulates
Boltzmann equation of velocity space distribution function, which is the basic relation of plasma
physics.
From ch.5 to ch.9, plasmas are described as magnetohydrodynamic (MHD) fluid. MHD equation of motion (ch.5), equilibrium (ch.6) and diffusion and confinement time of plasma (ch.7) are
described by the fluid model. Chapters 8 and 9 discuss problems of MHD instabilities whether
a small perturbation will grow to disrupt the plasma or will damp to a stable state. The basic
MHD equation of motion can be derived by taking an appropriate average of Boltzmann equation. This mathematical process is described in appendix A. The derivation of useful energy
integral formula of axisymmetric toroidal system and the analysis of high n ballooning mode are
described in appendix B.
From ch.10 to ch.14, plasmas are treated by kinetic theory. This medium, in which waves and
perturbations propagate, is generally inhomogeneous and anisotropic. It may absorb or even
amplify the wave. Cold plasma model described in ch.10 is applicable when the thermal velocity
of plasma particles is much smaller than the phase velocity of wave. Because of its simplicity,
the dielectric tensor of cold plasma can be easily derived and the properties of various wave
can be discussed in the case of cold plasma. If the refractive index becomes large and the
phase velocity of the wave becomes comparable to the thermal velocity of the plasma particles,
then the particles and the wave interact with each other. In ch.11, Landau damping, which
is the most characteristic collective phenomenon of plasma, as well as cyclotron damping are
described. Chapter 12 discusses wave heating (wave absorption) in hot plasma, in which the
thermal velocity of particles is comparable to the wave phase velocity, by use of the dielectric
tensor of hot plasma. In ch.13 the amplification of wave, that is, the growth of perturbation
and instabilities, is described. Since long mathematical process is necessary for the derivation of
dielectric tensor of hot plasma, its processes are described in appendix C. In ch.14 instabilities
driven by energetic particles, that is, fishbone instability and toroidal Alfv´en eigenmodes are
described.
In ch.15, confinement researches toward fusion grade plasmas are reviewed. During the last
decade, tokamak experiments have made remarkable progresses. Now realistic designs of tokamak reactors have been actively pursued. In ch.16, research works of critical subjects on tokamak
plasmas and reactors are explained. As non-tokamak confinement systems, reversed field pinch,
stellarator, tandem mirror are described in ch.17. Elementary introduction of inertial confinement is added in ch.18.
Readers may have impression that there is too much mathematics in this lecture note. However
there is a reason for it. If a graduate student tries to read and understand, for examples,
frequently cited short papers on the analysis of high n ballooning mode by Connor, Hastie,
Taylor, fishbone instability by L.Chen, White, Rosenbluth without preparative knowledge, he
must read and understand a few tens of cited references and references of references. I would
guess from my experience that he would be obliged to work hard for a few months. It is one
of motivation to write this lecture note to save his time to struggle with the mathematical
derivation so that he could spend more time to think physics and experimental results.
This lecture note has been attempted to present the basic physics and analytical methods
which are necessary for understanding and predicting plasma behavior and to provide the recent
status of fusion researches for graduate and senior undergraduate students. I also hope that it
will be a useful reference for scientists and engineers working in the relevant fields.