Contemporary Accelerator PhysicsWorld Scientific, 2004 - 310 страници 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 BalescuOCoLenard 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. Contents: Hamiltonian Formulation of Single Particle Dynamics; Linear Betatron Motion; Nonlinear Resonances of Betatron Oscillations; Canonical Perturbation Theory; Special Methods in Accelerator Theory; Transfer Maps; Statistical Description of Charged Particle Beams; Statistical Description of Non-Integrable Hamiltonian Systems; The Vlasov Equation; Nonlinear Waves and Turbulence in Intense Beams. Readership: Graduate students, academics and researchers in accelerator & experimental physics." |
Съдържание
Canonical Perturbation Theory | 4 |
Linear Betatron Motion | 17 |
Nonlinear Resonances of Betatron Oscillations 335 | 35 |
Special Methods in Accelerator Theory | 95 |
Transfer Maps | 123 |
Statistical Description of Charged Particle Beams | 171 |
Statistical Description of Non Integrable Hamiltonian Systems | 207 |
The Vlasov Equation | 227 |
Nonlinear Waves and Turbulence in Intense Beams | 263 |
Bibliography | 301 |
| 307 | |
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accelerators and storage action-angle variables amplitude angle variable betatron betatron motion betatron oscillations betatron tune canonical transformation canonical variables charged particle beams coefficients collision integral coordinates defined derivative design orbit differential equation distribution function eigenvalues equations of motion evolution expression first-order follows Fourier Hamilton-Jacobi equation Hamilton's equations Hamiltonian harmonic Henon map Hill's equation invariant J₁ k₁ kinetic linear magnetic field microscopic phase space momenta momentum multiple nonlinear resonance obtain paragraph parameter periodic perturbation equations phase space phase space density RG equation RG method right-hand-side of equation second order sextupole sin² solution solved storage rings straightforward symplectic matrix synchro-betatron synchronous particle Taking into account theory tion transfer matrix Tzenov vector potential Vlasov equation w₁ written zero θα ән ӘР дЈк др дт მე მთ მუ