Computational Plasma Physics

With Applications To Fusion And Astrophysics

Toshi Tajima

• Publisher: CRC Press
• Year: 2018
• eBook ISBN: 9780429981104
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

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.

1

INTRODUCTION

1.1 Computer and Computer Simulation

Recently, the growth in computer technology has been explosive. Its speed, cost⁻¹, capacity, or their product can be described as increasing explosively as a function of time. The trend of speed can be seen in Fig. 1.1. A set of orbit calculations which would take a human brain and hand seven hours to finish was carried out in a matter of three seconds on the first computer ENIAC in 1945. This is a reduction of computing time by a factor of 10⁻⁴. A story of the first computer is described in Ref. 1. The latest model of high power scientific computers such as the CRAY-1 executes calculations in approximately 10⁻⁸ (of 7 hours) a human would take. We can look at this rapid development of scientific computing capabilities in a concrete example. The Magnetic Fusion Energy Computer Center (MFECC) CDC 7600 computer (1975), which revolutionized the way the plasma physicists compute, was installed only a decade ago, and the MFECC CRAY was introduced only several years ago. Correspondingly, many new disciplines of computational science burst into existence recently. Some examples are computational geophysics, computational astrophysics, computational solid state physics, and computational high energy physics. It all started only two or three decades ago.

Ever since Galileo Galilei dropped a metal ball from the Pisa tower and shattered Aristotle’s theory of gravity, experiment and theory became the two essential ingredients of physics and (natural) sciences in general. Thus the traditional means of investigating physical phenomena are through laboratory experiments and through the analytic application of well-established (or proposed) physical laws. In the case of large-scale natural phenomenon, one must often substitute observations of what is taking place for controlled experiments. In fact, this is almost always the case for astrophysical phenomena. The traditional methods have their limitations; often the complexity of the phenomenon and the simultaneous interaction of many effects make a complete analysis impossible. On the experimental side, one is limited to measurements of only a small fraction of the quantities of interest in a process and even these may be sampled only at a few times and positions and with a limited degree of accuracy. This is particularly true for observations of natural phenomena such as those that are encountered in fusion, space, and astrophysical plasmas. Thus, one is then faced with the task of interpreting limited observations with theories that are incomplete; and often, many different theories that can explain the observations exist. For the case of fusion research, the sustained and controlled thermonuclear plasma has yet to be realized. Even for plasmas with lesser parameters, it is very costly or time-consuming to perform experiments. For space and astrophysical plasmas, it is difficult or impossible to do experiments, and the observational data available are sparse and sporadic. It is very difficult to perform experiments only for instance, a gravitational system such as interacting galaxies. Yet another example is quark confinement. Here, because of the perfect confinement, no physicist has observed quarks, which interact strongly with each other.

FIGURE 1.1 Rapid progress in the speed of computer over the years. (Flop floating point operations per second)

Recently, a powerful tool has been added to these two traditional methods; it is that of computer simulation, a kind of Gedanken experiment of the physical system wi...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• 1 Introduction
• 2 Finite Size Particle Method
• 3 Time Integration
• 4 Grid Method
• 5 Electromagnetic Model
• 6 Magnetohydrodynamic Model of Plasmas
• 7 Guiding-Center Method
• 8 Hybrid Models of Plasmas
• 9 Implicit Particle Codes
• 10 Geometry
• 11 Information and Computation
• 12 Interaction Between Radiation and a Plasma
• 13 Drift Waves and Plasma Turbulence
• 14 Magnetic Reconnection
• 15 Transport
• Epilogue: Numerical Laboratory
• Subject Index
• Author Index
• Credits