Plasma Physics

Classical Methods of Statistics is a guidebook combining theory and practical methods. It is especially conceived for graduate students and scientists who are interested in the applications of statistical methods to plasma physics. Thus it provides also concise information on experimental aspects of fusion-oriented plasma physics. In view of the first three basic chapters it can be fruitfully used by students majoring in probability theory and statistics. The first part deals with the mathematical foundation and framework of the subject. Some attention is given to the historical background. Exercises are added to help readers understand the underlying concepts. In the second part, two major case studies are presented which exemplify the areas of discriminant analysis and multivariate profile analysis, respectively. To introduce these case studies, an outline is provided of the context of magnetic plasma fusion research. In the third part an overview is given of statistical software; separate attention is devoted to SAS and S-PLUS.

In the interest of speed and economy the notation of the original text has been retained so that the cross product of two vectors A and B is denoted by [AB], the dot product by (AB) , the Laplacian operator by . 6" etc. It might also be worth pointing out that the temperature is frequently expressed in energy units in the Soviet literature so that the Boltzmann constant will be missing in various familiar expressions. In matters of terminology, whenever possible several forms are used when a term is first introduced, e. g. , magnetoacoustic and magnetosonic waves, "probkotron" and mirror machine, etc. It is hoped in this way to help the reader to relate the terms used here with those in exist­ ing translations and with the conventional nomenclature. In general, in the bibliographies, when a translated version of a given citation is available, only the English translation is cited, unless reference is made to a specific portion of the Russian version. Except for the correction of some obvious misprints the text is that of the original. We wish to express our gratitude to Academician Leontovich for kindly providing the latest corrections and additions to the Russian text, and especially for some new material, which appears for the first time in the American edition. v CONTENTS Chapter 1 PLASMA CONFINEMENT IN CLOSED MAGNETIC SYSTEMS L. S. Solov'ev and V. D. Shafranov . . . . . . . . . . . . . . . . . . 1 § 1. Introduction. . . • . . . . . . . . . . . . . . . . . . . . . . • . . . . . . . 1 § 2. General Properties of Toroidal Configurations. . . . . . . . . . . .

This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries.

The enlarged new edition of this textbook provides a comprehensive introduction to the basic processes in plasmas and demonstrates that the same fundamental concepts describe cold gas-discharge plasmas, space plasmas,

The enlarged new edition of this textbook provides a comprehensive introduction to the basic processes in plasmas and demonstrates that the same fundamental concepts describe cold gas-discharge plasmas, space plasmas, and hot fusion plasmas. Starting from particle drifts in magnetic fields, the principles of magnetic confinement fusion are explained and compared with laser fusion. Collective processes are discussed in terms of plasma waves and instabilities.