Chaos and structures in nonlinear plasmas
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| Sprache: | English |
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World Scientific
1996
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| 020 | |a 9810226365 |9 981-02-2636-5 | ||
| 035 | |a (OCoLC)247284906 | ||
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| 049 | |a DE-11 | ||
| 084 | |a UR 8500 |0 (DE-625)146645: |2 rvk | ||
| 100 | 1 | |a Horton, Claude W. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Chaos and structures in nonlinear plasmas |c W. Horton ; Y.-H. Ichikawa |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific |c 1996 | |
| 300 | |a XIII, 340 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 700 | 1 | |a Ichikawa, Yoshi H. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019649820&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-019649820 | |
Datensatz im Suchindex
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| adam_text | CHAOS AND STRUCTURES IN NONLINEAR PLASMAS W. HORTON UNIV. OF TEXAS AT
AUSTIN USA Y-H ICHIKAWA CHUBU UNIV. JAPAN WORLD SCIENTIFIC SINGAPORE *
NEW JERSEY * LONDON * HONG KONG CONTENTS PREFACE V 1 NONLINEAR
OSCILLATIONS 1 1.1 HARMONIC GENERATION IN SMALL AMPLITUDE OSCILLATIONS 2
1.2 AMPLITUDE DISPERSION FROM SECULAR TERMS 6 1.3 PARAMETRIC
INSTABILITIES 7 1.3.1 PARAMETRIC INSTABILITY THRESHOLD AND THE GROWTH
RATE 9 1.3.2 MATHIEU EQUATION AND FLOQUET THEORY 10 1.4 EXAMPLE 1.1
PARAMETRIC EXCITATION OF THE PENDULUM 13 1.5 EXAMPLE 1.2 STABILITY OF
THE PONDEROMOTIVE POTENTIAL 15 1.6 EXAMPLE 1.3 OSCILLATIONS OF A CHARGED
PARTICLE IN TWO LONGITUDINAL WAVES 18 2 HAMILTONIAN DYNAMICS 23 2.1
MEASURE-PRESERVING FLOWS AND THE HAMILTONIAN 23 2.2 POINCARE SURFACE OF
SECTION 25 2.3 FIXED POINTS AND INVARIANT CURVES 26 2.4 KAM THEORY 27
2.5 KAM TORII, THE GOLDEN MEAN AND LEAKY BARRIERS 28 2.6 KAM THEORY IN
LABORATORY PLASMAS 31 2.7 VISUALIZATION OF THE MAGNETIC FLUX SURFACES BY
ELECTRON BEAM MAPPING 31 2.8 MAGNETIC ISLANDS AND THE UNSTABLE-CHAOTIC
TRAJECTORIES OF FIELD LINES IN TOKAMAKS 36 2.9 MEASURE OF THE RESONANT
RATIONAL SURFACES 44 2.9.1 THE NUMBER OF IRREDUCIBLE FRACTIONS 44 2.9.2
MEASURE OF THE RESONANT SURFACES 45 2.10 EXAMPLE 2.1 HOW A SWING BEHAVES
47 2.11 INVARIANT TORI AND THE KAM THEOREM 48 3 STOCHASTICITY THEORY AND
APPLICATIONS IN PLASMAS 51 3.1 TRAJECTORIES IN STRAIGHT, NONUNIFORM
MAGNETIC FIELDS 53 3.1.1 INTEGRABLE ORBITS AND INVARIANTS OF CHARGED
PARTICLE MOTION 54 3.1.2 NONLINEAR OSCILLATOR FOR WEAKLY INHOMOGENEOUS
MAGNETIC FIELD 59 3.1.3 NONLINEAR ORBITS IN THE FIELD REVERSED
CONFIGURATION OR SHEET PINCH 60 3.2 ADIABATIC INVARIANTS 62 3.2.1 SMALL
GYRORADIUS LIMIT (2M E P 2Y ) 63 3.2.2 SMALL GYRORADIUS AND A WEAK
ELECTROSTATIC POTENTIAL 64 3.2.3 CURRENT SHEET INVARIANT 65 3.3 ONSET OF
CHAOS FROM A TRANSVERSE ELECTRIC FIELD 69 3.3.1 LF-D HAMILTONIAN 70
3.3.2 MELNIKOV-ARNOLD INTEGRAL 71 3.3.3 THE WHISKER MAP AND THE STANDARD
MAP 72 3.3.4 THE STANDARD MAP 73 3.4 ONSET OF CHAOS FROM A NORMAL
MAGNETIC FIELD COMPONENT 74 3.4.1 2D NONLINEAR COUPLED OSCILLATIONS 75
3.4.2 TWO DEGREES-OF-FREEDOM AND DEGENERACY 77 3.4.3 RESONANCE
CONDITIONS AND THE SURFACE OF SECTION 78 3.5 E X B MOTION IN TWO
LOW-FREQUENCY WAVES AND THE DIFFUSION APPROXIMATION 84 3.5.1 TEST
PARTICLE MOTION IN DRIFT WAVES 85 3.5.2 ACTION-ANGLE VARIABLES FOR E X B
MOTION 87 3.5.3 THE ONSET OF STOCHASTICITY IN TWO DRIFT WAVES 91 3.5.4
EXAMPLE 3.1: E X B DRIFT ISLANDS IN THE CYLINDRICAL PLASMA WITH SHEARED
FLOW 96 3.5.5 THE DIFFUSION APPROXIMATION 99 3.5.6 EXAMPLE 3.2: ONSET
O/EXB DIFFUSION FROM TWO EQUAL AMPLITUDE WAVES 100 3.6 RENORMALIZED E X
B DIFFUSION COEFFICIENTS 102 3.7 E X B MOTION IN A SHEARED MAGNETIC
SHEAR 107 3.8 HAMILTON S EQUATIONS OF MOTION IN NON-CANONICAL
COORDINATES 109 PHASE SPACE STRUCTURES IN HAMILTONIAN SYSTEMS 117 4.1
THE STANDARD MAP 117 4.2 MAPS FOR THE MOTION OF A CHARGED PARTICLE IN AN
INFINITE SPECTRUM OF LONGITUDINAL WAVES 120 4.3 FIXED POINTS,
ACCELERATOR ORBITS AND THE TANGENT MAP 122 4.4 STOCHASTIC MOTION AND THE
DIFFUSION COEFFICIENT 125 4.4.1 PROBABILITY DISTRIBUTION FUNCTIONS FOR
THE ORBITS 126 4.4.2 EVOLUTION OF THE MOMENTUM DISTRIBUTION FUNCTION 131
4.4.3 STANDARD MAP AT LARGE VALUES OF A 131 4.4.4 STANDARD MAP AT SMALL
VALUES OF A 134 4.4.5 DISCUSSION OF PHYSICS FOR THE DIFFUSION IN THE
STANDARD MAP . . 134 4.5 REGULAR MOTION IN THE RELATIVISTIC STANDARD MAP
136 4.6 SYMMETRIES OF THE RELATIVISTIC STANDARD MAP 140 4.7 STABILITY OF
THE PERIODIC ORBITS 145 4.8 POINCARE-BIRKHOFF MULTIFURCATION FOR THE
PERIOD-4 ORBIT 155 4.9 CONCLUDING REMARKS ON THE STANDARD AND
RELATIVISTIC MAPS 160 4.10 EXAMPLE 4-1 FERMI ACCELERATION 161 5 SOLITONS
IN PLASMAS 165 5.1 NONLINEAR COHERENT MODES IN VLASOV PLASMAS 166 5.2
AMPLITUDE MODULATION OF NEARLY MONOCHROMATIC WAVES AND THE MODULATIONAL
INSTABILITY 169 5.3 MODULATIONAL INSTABILITY AND NONLINEAR LANDAU
DAMPING 178 5.3.1 NLS SOLITONS WITH NONLINEAR LANDAU DAMPING 180 5.4
REDUCTIVE PERTURBATION ANALYSIS OF NONLINEAR WAVE PROPAGATION . . . 183
5.4.1 NONLINEAR ION ACOUSTIC WAVE 183 5.4.2 PARALLEL PROPAGATING RIGHT
AND LEFT POLARIZED ALFVEN WAVES . . . 187 5.4.3 GENERAL NONLINEAR
EQUATION FOR OBLIQUE WAVES 188 5.5 BIRTH OF THE SOLITON 190 5.6 THE
INVERSE SCATTERING TRANSFORMATION METHOD 191 5.7 GELFAND-LEVITAN
EQUATION FOR THE SCATTERING POTENTIAL 194 5.8 INVERSE SCATTERING
TRANSFORM (1ST) FOR THE NLS EQUATION 196 5.9 GENERALIZATION OF THE
INTEGRABILITY CONDITIONS 198 5.10 ALFVEN SOLITON 201 5.11
ONE-DIMENSIONAL SOLITON GAS MODELS 206 5.12 EXAMPLE 5.1 * ELASTIC
COLLISIONS OF TWO SOLITONS 206 5.12.1 PETVIASHVILI DRIFT WAVE SOLITONS
AND THE SOLITON GAS 209 5.13 EXAMPLE 5.2 * 3X3 MATRIX FORMALISM OF THE
INVERSE SCATTERING TRANSFORMATION 219 6 VORTEX STRUCTURES IN
HYDRODYNAMIC AND VLASOV SYSTEMS 223 6.1 THE DRIFT WAVE-ROSSBY WAVE
ANALOGY 223 6.2 THE DRIFT WAVE MECHANISM AND VORTEX 228 6.2.1 NONLINEAR
DRIFT WAVE EQUATION AND PASSIVE SCALAR EQUATION . . . 230 6.2.2
CONSERVATION LAWS 231 6.2.3 SOLITARY MONOPOLAR STRUCTURES AND THE
TRAPPING CONDITION . . . 234 6.3 SOLITARY DIPOLAR VORTEX SOLUTIONS 235
6.4 DRIFT WAVE-ION ACOUSTIC WAVE EQUATIONS 236 6.4.1 CONDITIONS FOR THE
CONSERVATION OF ENERGY AND ENSTROPHY . . . 239 6.4.2 ERTEL S
CONSERVATION THEOREM 240 6.4.3 SOLITARY DRIFT WAVE VORTICES: SHEARLESS
CASE 240 6.4.4 LARICHEV-REZNIK DIPOLE VORTICES 242 6.4.5 MAXIMUM
AMPLITUDE AND SIZE RELATIONS 243 6.4.6 ENERGY AND ENSTROPHY OF THE
DIPOLE VORTEX 244 6.5 EXPERIMENTAL FEATURES AND COMPUTER SIMULATIONS OF
THE DIPOLE VORTICES 246 6.5.1 PLASMA DRIFT WAVE EXPERIMENTS 246 6.5.2
DRIFT WAVE VORTEX COLLISIONS AND COALESCENCE 248 6.5.3 ANOMALOUS
TRANSPORT DURING INELASTIC VORTEX COLLISIONS 257 6.6 INTERMITTENT
TRANSPORT FROM VORTEX COLLISIONS 260 6.7 INTERACTION ENERGIES AND
KURTOSIS IN DISTRIBUTIONS OF VORTICES AND WAVES 263 6.8 FLUCTUATION
SPECTRUM FROM A GAS OF DIPOLE VORTICES 266 6.9 MONOPOLAR VORTICES
PRODUCED BY SHEARED FLOWS 268 6.9.1 MONOPOLE SOLUTIONS DUE TO THE
COMBINED ACTION OF THE POISSON BRACKET AND KDV NONLINEARITIES 268 6.9.2
DIPOLE VORTEX SPLITTING INTO MONOPOLES 272 6.10 DISCUSSION AND
CONCLUSIONS » 275 STATISTICAL PROPERTIES AND CORRELATION FUNCTIONS FOR
DRIFT WAVES 277 7.1 INTRODUCTORY REMARKS 277 7.2 NONLINEAR DRIFT WAVE
EQUATION 280 7.2.1 NONLINEAR DRIFT WAVE EQUATION IN CONFIGURATION SPACE
281 7.2.2 NONLINEAR DRIFT WAVE EQUATION IN K SPACE 284 7.2.3 VOLUME
CONTRACTION IN THE PHASE SPACE 285 7.2.4 STATISTICAL TURBULENCE THEORY
288 7.2.5 TWO-TIME CORRELATION FUNCTIONS 293 7.2.6 PROPERTIES OF
CORRELATION FUNCTIONS FOR KX + K2 = 0 294 7.2.7 SPACE CORRELATION
FUNCTION AND THE WAVENUMBER SPECTRUM . . . 295 7.2.8 EFFECT OF
DISSIPATION ON SPACE-TIME EVOLUTION 296 7.3 RENORMALIZED, MARKOVIANIZED
SPECTRAL EQUATIONS 297 7.3.1 INCOHERENT FLUCTUATION SOURCE 299 7.3.2
DYNAMICS OF THE CORRELATION FUNCTION IN RENORMALIZED TURBULENCE THEORY
299 7.3.3 PROPERTIES OF TK({E}) * THE NONLINEAR TRANSFER OPERATOR . . .
300 7.4 LOCAL, ISOTROPIC APPROXIMATION 301 7.4.1 HIGH-WAVENUMBER
SPECTRAL BALANCE 303 7.4.2 QUASILINEAR TRANSPORT FROM THE RENORMALIZED
TURBULENCE THEORY SPECTRUM 305 7.4.3 RELATION TO THE HASEGAWA-WAKATANI
DRIFT-WAVE EQUATION .... 306 7.5 LOW-ORDER WAVE COUPLING 308 7.5.1
THREE-WAVE COUPLING AND STRANGE ATTRACTORS 308 7.5.2 INTEGRABLE LIMIT OF
THE THREE-WAVE EQUATIONS 311 7.5.3 DISSIPATIVE DYNAMICS AND THE STRANGE
ATTRACTOR 312 7.5.4 RANDOM PHASE APPROXIMATION 314 BIBLIOGRAPHY 321
INDEX 335
|
| any_adam_object | 1 |
| author | Horton, Claude W. Ichikawa, Yoshi H. |
| author_facet | Horton, Claude W. Ichikawa, Yoshi H. |
| author_role | aut aut |
| author_sort | Horton, Claude W. |
| author_variant | c w h cw cwh y h i yh yhi |
| building | Verbundindex |
| bvnumber | BV024983156 |
| classification_rvk | UR 8500 |
| ctrlnum | (OCoLC)247284906 (DE-599)BVBBV024983156 |
| discipline | Physik |
| format | Book |
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| illustrated | Not Illustrated |
| indexdate | 2024-12-23T23:40:24Z |
| institution | BVB |
| isbn | 9810226365 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019649820 |
| oclc_num | 247284906 |
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| owner_facet | DE-11 |
| physical | XIII, 340 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Horton, Claude W. Ichikawa, Yoshi H. Chaos and structures in nonlinear plasmas |
| title | Chaos and structures in nonlinear plasmas |
| title_auth | Chaos and structures in nonlinear plasmas |
| title_exact_search | Chaos and structures in nonlinear plasmas |
| title_full | Chaos and structures in nonlinear plasmas W. Horton ; Y.-H. Ichikawa |
| title_fullStr | Chaos and structures in nonlinear plasmas W. Horton ; Y.-H. Ichikawa |
| title_full_unstemmed | Chaos and structures in nonlinear plasmas W. Horton ; Y.-H. Ichikawa |
| title_short | Chaos and structures in nonlinear plasmas |
| title_sort | chaos and structures in nonlinear plasmas |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019649820&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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