Bøger af Roscoe B (Princeton Univ White

A useful graduate level text on the asymptotic analysis of ordinary differential equations, this book covers various important methods including dominant balance, the use of divergent asymptotic series, phase integral methods, asymptotic evaluation of integrals, and boundary layer analysis.

This graduate level textbook develops the theory of magnetically confined plasma, with the aim of bringing the reader to the level of current research in the field of thermonuclear fusion. It begins with the basic concepts of magnetic field description, plasma equilibria and stability, and goes on to derive the equations for guiding center particle motion in an equilibrium field. Topics include linear and nonlinear ideal and resistive modes and particle transport. It is of use to workers in the field of fusion both for its wide-ranging account of tokamak physics and as a kind of handbook or formulary. This edition has been extended in a number of ways. The material on mode-particle interactions has been reformulated and much new information added, including methodology for Monte Carlo implementation of mode destabilization. These results give explicit means of carrying out mode destabilization analysis, in particular for the dangerous fishbone mode. A new chapter on cyclotron motion in toroidal geometry has been added, with comparisons of the analysis of resonances using guiding center results. A new chapter on the use of lithium lined walls has been added, a promising means of lowering the complexity and cost of full scale fusion reactors. A section on nonlocal transport has been added, including an analysis of Levy flight simulations of ion transport in the reversed field pinch in Padova, RFX.

Offers the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory. This book focuses on the techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.