K. Miyamoto


Fundamentals of Plasma Physics and Controlled Fusion -The Third Edition-

Date of publication:

June 24, 2011

Key words:


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 app. 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 app.C. In ch.14 instabilities driven by energetic particles, that is, fishbone instability and toroidal AlfvÅLen 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 construction stage of ”Iternational Tokamak Experimental Reactor”, called ITER, has already started. 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. New topics, zonal flow, is described in app. E Readers may have impression that there is too much mathematics in this lecture note. However there is a reason for that. If a graduate student tries to read and understand, for examples, two of 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 several 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 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.


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