Nonlinear magnetohydrodynamics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge u.a.
Cambridge Univ. Press
1993
|
| Edition: | 1. publ. |
| Series: | Cambridge monographs on plasma physics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 378 S. graph. Darst. |
| ISBN: | 0521402069 |
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Record in the Search Index
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| adam_text | NONLINEAR MAGNETOHYDRODYNAMICS DIETER BISKAMP MAX PLANCK INSTITUTE FOR
PLASMA PHYSICS, GARCHING I CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE
XIII 1 INTRODUCTION 1 2 BASIC PROPERTIES OF MAGNETOHYDRODYNAMICS 8 2.1
THE MHD EQUATIONS 8 2.2 CONSERVATION LAWS IN IDEAL MHD 11 2.3 MAGNETIC
HELICITY 14 2.4 REDUCED MHD EQUATIONS 17 2.5 VALIDITY LIMITS OF IDEAL
MHD AND DISSIPATION EFFECTS 21 3 MAGNETOSTATIC EQUILIBRIA 24 3.1
ONE-DIMENSIONAL CONFIGURATIONS 24 3.2 THE TWO-DIMENSIONAL EQUILIBRIUM
EQUATION 27 3.3 SOME EXACT TWO-DIMENSIONAL EQUILIBRIUM SOLUTIONS 32
3.3.1 SOLOV EV S SOLUTION 32 3.3.2 ELLIPTICAL PLASMA CYLINDER 35 3.3.3
CONSTANT-^I, FORCE-FREE EQUILIBRIA 38 3.3.4 NONLINEAR EQUILIBRIA WITH J
Z = E~ Y 40 3.4 NUMERICAL SOLUTION OF THE GRAD-SHAFRANOV EQUATION 42
3.5 THREE-DIMENSIONAL EQUILIBRIA 44 3.5.1 THE GENERAL EQUILIBRIUM
PROBLEM 44 3.5.2 NUMERICAL EQUILIBRIUM COMPUTATIONS 47 4 NORMAL MODES
AND INSTABILITY 49 4.1 THE NORMAL MODE PROBLEM IN MHD 50 4.2 WAVES IN A
HOMOGENEOUS PLASMA 51 4.3 THE ENERGY PRINCIPLE 53 4.3.1 PROOF OF THE
ENERGY PRINCIPLE 54 4.3.2 DIFFERENT FORMS OF THE ENERGY INTEGRAL 56 4.4
THE CYLINDRICAL PINCH 60 4.4.1 NORMAL MODES IN A CYLINDRICAL PINCH 60 IX
X CONTENTS 4.4.2 THE ENERGY PRINCIPLE FOR A CYLINDRICAL EQUILIBRIUM 62
4.5 THE CIRCULAR CYLINDRICAL TOKAMAK 64 4.6 TOROIDAL EFFECTS ON IDEAL
TOKAMAK STABILITY 67 4.6.1 INTERCHANGE AND BALLOONING MODES 67 4.6.2 THE
TOROIDAL INTERNAL KINK MODE 69 4.7 RESISTIVE INSTABILITIES 71 4.7.1 THE
TEARING MODE 73 4.7.2 THE RESISTIVE INTERNAL KINK MODE 77 4.7.3
RESISTIVE ENERGY PRINCIPLE 81 4.7.4 THE TOROIDAL TEARING MODE 83 5
NONLINEAR EVOLUTION OF MHD INSTABILITIES 85 5.1 THE QUASI-LINEAR
APPROXIMATION 87 5.2 NONLINEAR EXTERNAL KINK MODES 90 5.2.1 NONLINEAR
ENERGY INTEGRAL FOR FREE BOUNDARY MODES 91 5.2.2 VACUUM BUBBLES 95 5.2.3
EFFECT OF MAGNETIC SHEAR 101 5.3 NONLINEAR THEORY OF THE IDEAL INTERNAL
KINK MODE 103 5.4 THE SMALL-AMPLITUDE NONLINEAR BEHAVIOR OF THE TEARING
MODE 107 5.4.1 STANDARD LOW-SS CASE 107 5.4.2 INFLUENCE OF FINITE SS AND
FIELD LINE CURVATURE 114 5.5 SATURATION OF THE TEARING MODE 117 5.5.1
QUASI-LINEAR THEORY OF TEARING-MODE SATURATION 118 5.5.2 INFLUENCE OF
THE EQUILIBRIUM CURRENT PROFILE 120 5.5.3 EFFECT OF DYNAMIC RESISTIVITY
122 6 MAGNETIC RECONNECTION 127 6.1 CURRENT SHEETS: BASIC PROPERTIES 128
6.1.1 SWEET-PARKER CURRENT SHEET MODEL 128 6.1.2 EFFECTS OF
HYPERRESISTIVITY AND VISCOSITY 131 6.2 QUASI-IDEAL MODEIS OF STATIONARY
RECONNECTION 132 6.2.1 DRIVEN RECONNECTION 132 6.2.2 PETSCHEK S SLOW
SHOCK MODEL 133 6.2.3 SYROVATSKII S CURRENT SHEET SOLUTION 138 6.3
SCALING LAWS IN STATIONARY CURRENT SHEET RECONNECTION 142 6.4 CURRENT
SHEETS: REFINED THEORY 147 6.4.1 STATIONARY SOLUTION IN THE VICINITY OF
THE NEUTRAL POINT 147 6.4.2 CURRENT SHEET EDGE REGION 150 6.5 TEARING
INSTABILITY OF A SWEET-PARKER CURRENT SHEET 152 6.6 EXAMPLES OF 2-D
RECONNECTING SYSTEMS 156 6.6.1 COALESCENCE OF MAGNETIC ISLANDS 156 6.6.2
NONLINEAR EVOLUTION OF THE RESISTIVE KINK MODE 159 6.6.3 PLASMOIDS 164
6.7 MAGNETIC RECONNECTION IN GENERAL THREE-DIMENSIONAL SYSTEMS 166 6.8
TURBULENT RECONNECTION 172 CONTENTS XI 7 MHD TURBULENCE 175 7.1
HOMOGENEOUS ISOTROPIC TURBULENCE 177 7.2 PROPERTIES OF NONDISSIPATIVE
MHD TURBULENCE 179 7.2.1 IDEAL INVARIANTS 179 7.2.2 ABSOLUTE EQUILIBRIUM
DISTRIBUTIONS 181 7.2.3 CASCADE DIRECTIONS 183 7.3 SELF-ORGANIZATION AND
TURBULENCE DECAY LAWS 184 7.3.1 SELECTIVE DECAY 185 7.3.2 THE A-TERM AND
TURBULENT DYNAMO THEORY 188 7.3.3 DYNAMIC ALIGNMENT OF VELOCITY AND
MAGNETIC FIELD 193 7.3.4 ENERGY DECAY LAWS 195 7.4 ENERGY SPECTRA 196
7.4.1 INERTIAL RAENGE SPECTRA IN MHD TURBULENCE 196 7.4.2 DISSIPATION
SCALES 200 7.4.3 ENERGY SPECTRA IN HIGHLY ALIGNED SYSTEMS 205 7.5
CLOSURE THEORY FOR MHD TURBULENCE 208 7.5.1 THE PROBLEM OF CLOSURE 209
7.5.2 EDDY-DAMPED QUASI-NORMAL MARKOVIAN APPROXIMATION 212 7.6 ENERGY
DISSIPATION IN 2-D MHD TURBULENCE 214 7.6.1 SPONTANEOUS EXCITATION OF
SMALL-SCALE TURBULENCE 214 7.6.2 ENERGY DISSIPATION RATES 216 7.7
INTERMITTENCY 217 7.7.1 THE LOG-NORMAL THEORY 218 7.7.2 THE JSS-MODEL AND
ITS GENERALIZATIONS 222 7.7.3 PROBABILITY DISTRIBUTION FUNCTIONS 225
7.7.4 INTERMITTENCY IN MHD TURBULENCE 228 7.8 TURBULENT CONVECTION OF
MAGNETIC FIELDS 232 7.8.1 MAGNETOCONVECTION IN 3-D SYSTEMS 232 7.8.2
CONVECTION OF MAGNETIC FLUX IN 2-D 235 8 DISRUPTIVE PROCESSES IN TOKAMAK
PLASMAS 239 8.1 SAWTOOTH OSCILLATIONS 240 8.1.1 EARLY EXPERIMENTAL
OBSERVATIONS 240 8.1.2 KADOMTSEV S THEORY OF THE SAWTOOTH COLLAPSE 242
8.1.3 SAWTOOTH BEHAVIOR IN LARGE-DIAMETER, HIGH-TEMPERATURE TOKA- MAK
PLASMAS 247 8.1.4 NUMERICAL SIMULATIONS OF SAWTOOTH OSCILLATIONS 249
8.1.5 ALTERNATIVE CONCEPTS OF FAST SAWTOOTH RECONNECTION 253 8.1.6
KINK-MODE STABILIZATION AND THE PROBLEM OF SUDDEN COLLAPSE ONSET 255
8.1.7 EXPERIMENTAL OBSERVATION OF PARTIAL RECONNECTION IN THE SAW- TOOTH
COLLAPSE 257 8.1.8 COLLAPSE DYNAMICS AT HIGH S-VALUES 260 8.2 MAJOR
DISRUPTIONS 262 8.2.1 DISRUPTION-IMPOSED OPERATIONAL LIMITS 262 8.2.2
DISRUPTION DYNAMICS 265 XII CONTENTS 8.2.3 SINGLE-HELICITY MODEIS 271
8.2.4 HOLLOW CURRENT PROFILE DISRUPTIONS 273 8.2.5 MULTI-HELICITY
DYNAMICS 275 8.3 EDGE-LOCALIZED MODES 281 8.3.1 THE L -* H TRANSITION
281 8.3.2 THE ELM PHENOMENON 284 9 DYNAMICS OF THE REVERSED-FIELD PINCH
289 9.1 MINIMUM-ENERGY STATES 290 9.1.1 TAYLOR S THEORY 290 9.1.2
EXPERIMENTAL RESULTS 294 9.2 STABILITY PROPERTIES OF RFP EQUILIBRIA 297
9.2.1 IDEAL INSTABILITIES 297 9.2.2 RESISTIVE KINK MODES IN THE RFP 300
9.3 SINGLE-HELICITY BEHAVIOR 301 9.3.1 NONLINEAR EVOLUTION OF THE M = 1
INSTABILITY 301 9.3.2 HELICAL OHMIC STATES 304 9.3.3 NUMERICAL
SIMULATION OF HELICAL STATES 307 9.4 THREE-DIMENSIONAL RFP DYNAMICS 309
9.4.1 TURBULENT RFP DYNAMO 309 9.4.2 QUASI-LINEAR THEORY OF RFP DYNAMICS
312 10 SOLAR FLARES 316 10.1 THE SOLAR CONVECTION ZONE 317 10.1.1
PHENOMENOLOGICAL DESCRIPTION OF THERMAL CONVECTION 319 10.1.2
COMPRESSIBLE CONVECTION IN A STRONGLY STRATIFIED FLUID 322 10.1.3 SOLAR
MAGNETOCONVECTION 324 10.2 MAGNETIC FIELDS IN THE SOLAR ATMOSPHERE 326
10.2.1 STRUCTURE OF THE SOLAR ATMOSPHERE 326 10.2.2 ACTIVE REGIONS 328
10.2.3 MAGNETIC BUOYANCY 329 10.2.4 MAGNETIC STRUCTURES IN ACTIVE
REGIONS 330 10.3 SOLAR FLARES 331 10.3.1 PHENOMENOLOGY OF FLARES 332
10.3.2 ENERGY STORAGE 335 10.3.3 STABILITY OF TWISTED FLUX TUBES 338
10.3.4 CURRENT SHEET FORMATION AND CATASTROPHE THEORY IN A SHEARED
ARCADE 341 10.3.5 DYNAMICAL MODEIS OF PLASMOID GENERATION AND ERUPTION
345 OUTLOOK 349 REFERENCES 351 INDEX 372
|
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| language | English |
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| physical | XIV, 378 S. graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
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| series | Cambridge monographs on plasma physics |
| series2 | Cambridge monographs on plasma physics |
| spelling | Biskamp, Dieter Verfasser aut Nonlinear magnetohydrodynamics Dieter Biskamp 1. publ. Cambridge u.a. Cambridge Univ. Press 1993 XIV, 378 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge monographs on plasma physics 1 Magnetohydrodynamics Nonlinear theories Plasma astrophysics Solar flares Nichtlineares Phänomen (DE-588)4136065-5 gnd rswk-swf Magnetohydrodynamik (DE-588)4130803-7 gnd rswk-swf Magnetohydrodynamik (DE-588)4130803-7 s Nichtlineares Phänomen (DE-588)4136065-5 s DE-604 Cambridge monographs on plasma physics 1 (DE-604)BV008279908 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005504930&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Biskamp, Dieter Nonlinear magnetohydrodynamics Cambridge monographs on plasma physics Magnetohydrodynamics Nonlinear theories Plasma astrophysics Solar flares Nichtlineares Phänomen (DE-588)4136065-5 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd |
| subject_GND | (DE-588)4136065-5 (DE-588)4130803-7 |
| title | Nonlinear magnetohydrodynamics |
| title_auth | Nonlinear magnetohydrodynamics |
| title_exact_search | Nonlinear magnetohydrodynamics |
| title_full | Nonlinear magnetohydrodynamics Dieter Biskamp |
| title_fullStr | Nonlinear magnetohydrodynamics Dieter Biskamp |
| title_full_unstemmed | Nonlinear magnetohydrodynamics Dieter Biskamp |
| title_short | Nonlinear magnetohydrodynamics |
| title_sort | nonlinear magnetohydrodynamics |
| topic | Magnetohydrodynamics Nonlinear theories Plasma astrophysics Solar flares Nichtlineares Phänomen (DE-588)4136065-5 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd |
| topic_facet | Magnetohydrodynamics Nonlinear theories Plasma astrophysics Solar flares Nichtlineares Phänomen Magnetohydrodynamik |
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