Topics in Magnetohydrodynamics

220 Pages·2012·12.111 MB·English

by  L. Zheng

TOPICS IN
MAGNETOHYDRODYNAMICS

Edited by Linjin Zheng
Topics in Magnetohydrodynamics
Edited by Linjin Zheng

Published by InTech
Janeza Trdine 9, 51000 Rijeka, Croatia

Copyright © 2012 InTech
All chapters are Open Access distributed under the Creative Commons Attribution 3.0
license, which allows users to download, copy and build upon published articles even for
commercial purposes, as long as the author and publisher are properly credited, which
ensures maximum dissemination and a wider impact of our publications. After this work
has been published by InTech, authors have the right to republish it, in whole or part, in
any publication of which they are the author, and to make other personal use of the
work. Any republication, referencing or personal use of the work must explicitly identify
the original source.

As for readers, this license allows users to download, copy and build upon published
chapters even for commercial purposes, as long as the author and publisher are properly
credited, which ensures maximum dissemination and a wider impact of our publications.

Notice
Statements and opinions expressed in the chapters are these of the individual contributors
and not necessarily those of the editors or publisher. No responsibility is accepted for the
accuracy of information contained in the published chapters. The publisher assumes no
responsibility for any damage or injury to persons or property arising out of the use of any
materials, instructions, methods or ideas contained in the book.

Publishing Process Manager Silvia Vlase
Technical Editor Teodora Smiljanic
Cover Designer InTech Design Team

First published March, 2012
Printed in Croatia

A free online edition of this book is available at www.intechopen.com
Additional hard copies can be obtained from [email protected]

Topics in Magnetohydrodynamics, Edited by Linjin Zheng
p. cm.
978-953-51-0211-3

Contents

Preface VII
Chapter 1 Overview of Magnetohydrodynamics
Theory in Toroidal Plasma Confinement 1
Linjin Zheng
Chapter 2 Sub-Fluid Models in
Dissipative Magneto-Hydrodynamics 35
Massimo Materassi, Giuseppe Consolini and Emanuele Tassi
Chapter 3 Implicit Numerical Methods for Magnetohydrodynamics 59
Ravi Samtaney
Chapter 4 Dynamics of Magnetic Relaxation in Spheromaks 85
Pablo L. Garcia-Martinez
Chapter 5 MHD Activity in an Extremely
High-Beta Compact Toroid 117
Tomohiko Asai and Tsutomu Takahashi
Chapter 6 Review of the Magnetohydrodynamic Waves and
Their Stability in Solar Spicules and X-Ray Jets 135
Ivan Zhelyazkov
Chapter 7 Hamiltonian Representation of
Magnetohydrodynamics for Boundary Energy Controls 167
Gou Nishida and Noboru Sakamoto
Chapter 8 Magnetohydrodynamic Rotating Flow of a
Fourth Grade Fluid Between Two Parallel Infinite Plates 189
M.A. Rana, Akhlaq Ahmed and Rashid Qamar

Preface

Magnetohydrodynamics (MHD) is concerned with the dynamic motion of electrically
conducting medium (i.e., so-called plasma) in the presence of magnetic field, which is
either applied externally or self-generated. MHD is traditionally interpreted as
follows: “Magneto” has to do with electro-magnetic fields; “hydro” indicates to deal
with fluid medium; while “dynamics” designates to study its time evolution of
physical processes. Another kind of interpretation can, however, be as follows:
“Magnetohydro” refers to the “magneto” type of fluids, in which particles are stuck
together primarily by magnetic field, instead of by collisions. Due to the presentation
of strong magnetic field, charged particles gyrate around magnetic field lines, so that
the guiding center of charged particle’s gyro-motion is primarily frozen in the
magnetic field line. Therefore, even in the weak collision case charged particles can
move collectively as if fluid in the perpendicular direction. The later interpretation
covers a broad scope in which MHD theory applies.
MHD theory has been used to study controlled nuclear fusion, space/astronomic
plasma physics, such as solar physics, and low temperature plasma physics, such as
plasma processing, MHD generator, etc. The collective motion of charged particles is
an intrinsically complicated issue, due to the long-range correlation feature of
Coulomb and Lorentz forces. Nevertheless, MHD theory is able to catch the leading
behaviors in a clear and tractable manner. This has led to the success of MHD theory.
There are several excellent MHD books in the market. Also, MHD theory is described
about in every plasma physics books. Nevertheless, as plasma physics science
advances, the gap between cutting-edge researches and textbooks always develops. To
fill in this gap, several MHD-related topics are reviewed by eight authors in this book,
according to authors’ expertise.
In Chapter 1 an overview of MHD theory for toroidal plasma confinement in
controlled nuclear fusion is given. Especially, the toroidal theories for four major types
of MHD modes: interchange, ballooning, toroidal Alfven egenmodes, and kinetically
driven modes (such as energetic particle modes) are reviewed. In Chapter 2 the recent
development of sub-fluid models in dissipative MHD is reviewed. Especially, three
models to approach “stochastic coherent structures theory” are described. In Chapter 3
the implicit numerical methods for resistive MHD is reviewed. Especially two broad
VIII Preface

classes of nonlinear methods: Newton-Krylov and nonlinear multigrid are detailed. In
Chapter 4 magnetic relaxation in spheromaks is investigated and reviewed. Simulation
results show that full relaxation to Taylor state is only achieved when the magnetic
fluctuations produce stochastic field line regions of size comparable of that of the
whole system. In Chapter 5 MHD activity in an extremely high-beta compact device:
field-reversed configuration (FRC) is reviewed. Both the formation methods for FRC
plasmas and the MHD behaviors are described. In Chapter 6 MHD theory for solar
spicules and X-ray jets is presented, to explain the enduring mystery in solar physics
for why Sun’s outer atmosphere or corona is much hotter than its surface. In Chapter 7
Hamiltonian representation of MHD for boundary energy controls is described. A
passive boundary control formalism for ideal MHD systems is then derived from the
distributed port-Hamiltonian (DPH) representations. In Chapter 8 the MHD rotating
flow of a fourth grade fluid between two parallel infinite plates is investigated through
solving nonlinear momentum and mass equations. The results for Newtonian and
non-Newtonian fluids are compared.
These results are published in this book to take the advantage of open-access feature
for distribution through InTech.

Dr. Linjin Zheng
The University of Texas at Austin,
Institute for Fusion Studies, Austin, Texas,
USA