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Tzenov S.I. — Contemporary Accelerator Physics
Tzenov S.I. — Contemporary Accelerator Physics

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Название: Contemporary Accelerator Physics

Автор: Tzenov S.I.

Аннотация:

This book adopts a non-traditional approach to accelerator theory. The exposition starts with the synchro-betatron formalism and continues with the linear and nonlinear theories of transverse betatron motion. Various methods of studying nonlinear dynamical systems (the canonical theory of perturbations and the methods of multiple scales and formal series) are explained through examples. The renormalization group approach to studying nonlinear (continuous and discrete) dynamical systems as applied to accelerators and storage rings is used throughout the book. The statistical description of charged particle beams (the Balescu–Lenard and Landau kinetic equations as well as the Vlasov equation) is dealt with in the second part of the book. The processes of pattern formation and formation of coherent structures (solitons) are also described.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 323

Добавлена в каталог: 15.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel’s theorem      183
Accelerator mode      225
Action integral      6
Action-angle variables      29
Adiabatic crossing      48
Adiabatic damping      12 33
Adiabatic invariant      78
Anticommutator      144
Antisymmetric matrix      143
Asymptotic series      79
Average beam emittance      248
Balescu — Lenard collision integral      185 197
BBGKY hierarchy      179
Beam envelope      247
Beam plasma frequency      191
Beam size      31
Beam-plasma parameter      228
Beta-function      278
Betatron motion      1
Betatron oscillations      18
Betatron tune      27 110 238 264
Boltzmann constant      186
Bose — Einstein condensation      278
Boundary curve      242
Bra-ket notation      210 221
Caldirola — Kanay Hamiltonian      32
Campbell — Baker — Hausdorff theorem      139
Canonical perturbation theory      50 64
Canonical transformation      5 16
Canonical variables      3
Catastrophe theory      45
Cauchy principal value      258
Cauchy problem      173
Caviton      277
Cavity      10
Chandrasekhar function      203
Characteristic polynomial      132
Chirikov — Taylor map      168 220
Chromatic tune shift      71
Chromaticity      55 71
Classical radius      234
Coarse-grained description      186
Coherent structure      291
Collisionless beam      227
Commutator      105 138
Consistency condition      105
Continued fraction      47
Continuity equation      245 253
Continuous medium      182
Correlation function      181
Correlation time      182
Coulomb logarithm      199
Courant — Snyder invariant      28
Crossing rate      54
Current Velocity      269
Damping coefficient      296
Dark soliton      276
Debye radius      191
Debye sphere      228
Degeneration      44
Density condensate      263
Density wave      263
Design orbit      1 2 15
Dielectric function      256
Dielectric susceptibility      295
Difference resonances      39
Diffusion coefficient      198 216 220 225
Dispersion equation      285
Dispersion function      14 285 295
dispersion relation      258 268
Dissipative system      32
Distortion      69 155
Distortion of torus      64
Distribution function      172
Drift coefficient      198
Dynamic aperture      156
Effective energy      42
Effective Hamiltonian      42
Effective potential      42
Eigenvalue      131
Eigenvector      131
Electric susceptibility      233
Elliptic integral      44
Emittance      30
Envelope equation      31 248 250
envelope function      265
Equations for characteristics      242
Evolution operator      182
Evolution time      44
Fixed point      56 92
Floquet’s theorem      21
Fluctuation spectrum      291
Fokker — Planck equation      216 225
Fold catastrophe      43
Formal series      63 78
Fresnel’s integral      53
Fresnet — Serret formulas      3
Frobenius — Perron operator      217 220
Fundamental solution      19
Gamma-operator      82
Gauge transformation      277
Generalized Courant — Snyder invariant      155
Generalized kinetic equation      185 204
Generating function      7 29
Generator      101
Gibbs ensemble      174 180 188
Ginzburg — Landau equation      291
Green’s function      66
Gross — Pitaevskii equation      277
Group velocity      260 287 296
Hamilton — Jacobi equation      63 236
Hamiltonian      3
Hamiltonian flow      172
Hamilton’s equations      4
Heaviside function      242
Henon map      148
Hessian matrix      230
Hilbert space      221
Hill’s equation      21 106
Hydrodynamic equations      254
Hydrodynamic turbulence      299
Hydrodynamics      244
Implicit map      161
Integral equation      80
Invariant curve      69
Invariant torus      39 66
Involution      39
Isolated resonance      39
Jacobian matrix      279
Jaynes principle      187
Kam theorem      39
Kick map      127 167
Kinetic equation for waves      298
Kinetic form of Fokker — Planck equation      218
Kolmogorov spectrum law      299
Kronecker’s delta-symbol      22
Lagrange’s equations      6
Lagrangian      2
Lagrangian variables      252 278
Lagratigian description      254
Landau collision integral      185 200
Landau contour      257
Landau damping      255
Langevin equation      204 217
Liapunov exponent      120
Libration      57
Lie algebra      138
Lie bracket      105
Lie group      99
Liouville equation      173 209 219
Liouville operator      217 219
Liouville’s theorem      21
Lorentz force      175
Lorentz gauge      176
Manakov integrability      276
MAP      123
Mathieu equation      111
Matrix element      221
Melnikov — Arnold integral      59
Method of multiple scales      95
Microscopic phase space density      175 292
Modulational diffusion      215
Moivre’s formula      28
Momentum compaction factor      15
Multiple scale Fourier transformation      282
Multiple scales      102 115
Natural coordinate system      2
Nonlinear Fokker — Planck operator      197
Nonlinear Landau damping      291
Nonlinear optics      276
Nonlinear resonance      35 67 111 117 157
Nonlinear Schrodinger equation      276
Nonlinear tune shift      87
Nonlinear tuneshift      115
Nonlinearity coefficient      209
Nonlinearity parameter      75
Normalized emittance      33
Octupole      11
One-turn map      128 167
Orthogonal matrix      142
Pade approximation      78
Parametric resonance      70 266 273
Particle-wave interaction      291
Pendulum      75 90
Pendulum frequency      58
Pendulum motion      56
Periodic crossing      54
Perveance      241 278
Phase advance      26 264
Phase slip coefficient      15
Phase space      21
phase velocity      261
Plasmon      299
Plemelj formula      119
Poincare return map      123
Poincare section      123
Poincare — Dulac normal form      24
Poisson bracket      28 230 278
Poisson equation      233 242
Polar decomposition      143
Primary resonance      119
Projection operator      85 209
Quadrupole      10
Quadrupole perturbation      68
Random force      217
Reductive perturbation method      95
Regularized RG map      154
Relaxation length      228
Relaxation time      182 203 228
Renormalization group      95
Renormalization group reduction      211 270
Renormalization transformation      88 91 100 109 152 165
Resonance      35 109
Resonance bandwidth      39
Resonance condition      39
Resonance detuning      39 112
Resonance order      39
Resonant Hamiltonian      40
Resonant mode coupling      213
Reversibility      173
RG equation      99 102 109 110 114 119 152 165 212 214
RG map      153 165
RG method      95 96 106 112 117 149 211
Rotation      57
Rotation map      127
Ruelle resonance      220
Secondary resonance      73 91
Secular equation      132 168
Secular perturbation theory      73
Secular term      100
Secularity      73
Separatrix      57 75
Separatrix mapping      61
Sextupole      11
Sextupole perturbation      111
Small denominator      67
Small-scale fluctuation      192
Smooth focusing      266
Solitary wave      263
Solvability condition      104
Space charge      240
Stability criterion      47
Stable island      225
Stationary point      52 75
Stochastic layer      61
Stochasticity parameter      220
Successive linearization      46
Sum resonance      39
Symmetric matrix      138
Symplectic      16 21
Symplectic group      131
Symplectic map      128
Symplectic matrix      128 142
Symplectic symmetry      153
Synchro-betatron formalism      11
Synchro-betatron resonance      36
Synchronous particle      12
Synchrotron magnet      11
Synchrotron motion      1
Taylor expansion      83
Theory of envelopes      95
Thermal speed      245
Three-wave interaction      292 297
Transfer map      127
Transfer matrix      19
Translation operator      86
Translational group      101
Tune modulation      62
Turbulence      291
Turbulence spectrum      299
Twiss parameters      25
Two resonance model      88
Unified kinetic equation      201
Vlasov equation      227 232 242 255 278
Vlasov limit      185
Vlasov — Maxwell equations      229
Volterra series      63 79
wronskian      20
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