Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts neces

In this book, we report on research in methods of computational magneto hydrodynamics supported by the United States Department of Energy under Contract EY-76-C-02-3077 with New York University. The work has re sulted in a computer code for mathematical analysis of the equilibrium and stability of a plasma in three dimensions with toroidal geometry but no sym metry. The code is listed in the final chapter. Versions of it have been used for the design of experiments at the Los Alamos Scientific Laboratory and the Max Planck Institute for Plasma Physics in Garching. We are grateful to Daniel Barnes, Jeremiah Brackbill, Harold Grad, William Grossmann, Abraham Kadish, Peter Lax, Guthrie Miller, Arnulf Schliiter, and Harold Weitzner for many useful discussions of the theory. We are especially indebted to Franz Herrnegger for theoretical and pedagogical comments. Constance Engle has provided outstanding assistance with the typescript. We take pleasure in acknowledging the help of the staff of the Courant Mathematics and Com puting Laboratory at New York University. In particular we should like to express our thanks to Max Goldstein, Kevin McAuliffe, Terry Moore, Toshi Nagano and Tsun Tam. Frances Bauer New York Octavio Betancourt September 1978 Paul Garabedian v Contents Chapter 1. Introduction 1 1. 1 Formulation of the Problem 1 1. 2 Discussion of Results 2 Chapter 2. The Variational Principle 4 4 2. 1 The Magnetostatic Equations 6 2. 2 Flux Constraints in the Plasma . 7 2. 3 The Ergodic Constraint.

The physics of plasmas is an extremely rich and complex subject as the variety of topics addressed in this book demonstrates. This richness and complexity demands new and powerful techniques for investigating plasma physics. An outgrowth from his graduate course teaching, now with corrections, Tajima's text provides not only a lucid introduction to computational plasma physics, but also offers the reader many examples of the way numerical modeling, properly handled, can provide valuable physical understanding of the nonlinear aspects so often encountered in both laboratory and astrophysical plasmas. Included here are computational methods for modern nonlinear physics as applied to hydrodynamic turbulence, solitons, fast reconnection of magnetic fields, anomalous transports, dynamics of the sun, and more. The text contains examples of problems now solved using computational techniques including those concerning finite-size particles, spectral techniques, implicit differencing, gyrokinetic approaches, and particle simulation.

Because magnetically confined plasmas are generally not found in a state of thermodynamic equilibrium, they have been studied extensively with methods of applied kinetic theory. In closed magnetic field line confinement devices such as the tokamak, non-Maxwellian distortions usually occur as a result of auxiliary heating and transport. In magnetic mirror configurations even the intended steady state plasma is far from local thermodynamic equilibrium because of losses along open magnetic field lines. In both of these major fusion devices, kinetic models based on the Boltzmann equation with Fokker-Planck collision terms have been successful in representing plasma behavior. The heating of plasmas by energetic neutral beams or microwaves, the production and thermalization of a-particles in thermonuclear reactor plasmas, the study of runaway electrons in tokamaks, and the performance of two-energy compo nent fusion reactors are some examples of processes in which the solution of kinetic equations is appropriate and, moreover, generally necessary for an understanding of the plasma dynamics. Ultimately, the problem is to solve a nonlinear partial differential equation for the distribution function of each charged plasma species in terms of six phase space variables and time. The dimensionality of the problem may be reduced through imposing certain symmetry conditions. For example, fewer spatial dimensions are needed if either the magnetic field is taken to be uniform or the magnetic field inhomogeneity enters principally through its variation along the direction of the field.

Looking for the real state of play in computational many-particle physics? Look no further. This book presents an overview of state-of-the-art numerical methods for studying interacting classical and quantum many-particle systems. A broad range of techniques and algorithms are covered, and emphasis is placed on their implementation on modern high-performance computers. This excellent book comes complete with online files and updates allowing readers to stay right up to date.

The physics of plasmas is an extremely rich and complex subject as the variety of topics addressed in this book demonstrates. This richness and complexity demands new and powerful techniques for investigating plasma physics. An outgrowth from his graduate course teaching, now with corrections, Tajima's text provides not only a lucid introduction to computational plasma physics, but also offers the reader many examples of the way numerical modeling, properly handled, can provide valuable physical understanding of the nonlinear aspects so often encountered in both laboratory and astrophysical plasmas. Included here are computational methods for modern nonlinear physics as applied to hydrodynamic turbulence, solitons, fast reconnection of magnetic fields, anomalous transports, dynamics of the sun, and more. The text contains examples of problems now solved using computational techniques including those concerning finite-size particles, spectral techniques, implicit differencing, gyrokinetic approaches, and particle simulation.

Computational Approaches in Physics reviews computational schemes which are used in the simulations of physical systems. These range from very accurate ab initio techniques up to coarse-grained and mesoscopic schemes. The choice of the method is based on the desired accuracy and computational efficiency. A bottom-up approach is used to present the various simulation methods used in Physics, starting from the lower level and the most accurate methods, up to particle-based ones. The book outlines the basic theory underlying each technique and its complexity, addresses the computational implications and issues in the implementation, as well as present representative examples. A link to the most common computational codes, commercial or open source is listed in each chapter. The strengths and deficiencies of the variety of techniques discussed in this book are presented in detail and visualization tools commonly used to make the simulation data more comprehensive are also discussed. In the end, specific techniques are used as bridges across different disciplines. To this end, examples of different systems tackled with the same methods are presented. The appendices include elements of physical theory which are prerequisites in understanding the simulation methods.

This advanced textbook provides an introduction to the basic methods of computational physics.