Pub. Date:
Springer-Verlag New York, LLC
Particle Accelerator Physics II: Nonlinear and Higher-Order Beam Dynamics / Edition 1

Particle Accelerator Physics II: Nonlinear and Higher-Order Beam Dynamics / Edition 1

by Helmut Wiedemann


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Particle Accelerator Physics II continues the discussion of particle accelerator physics beyond the introductory Particle Accelerator Physics I. Aimed at students and scientists who plan to work or are working in the field of accelerator physics. Basic principles of beam dynamics already discussed in Vol.I are expanded into the nonlinear regime in order to tackle fundamental problems encountered in present-day accelerator design and development. Nonlinear dynamics is discussed both for the transverse phase space to determine chromatic and geometric aberrations which limit the dynamic aperture as well as for the longitude phase space in connection with phase focusing at very small values of the momentum compaction. Effects derived theoretically are compared with observations made at existing accelerators.

Product Details

ISBN-13: 9780387575643
Publisher: Springer-Verlag New York, LLC
Publication date: 05/28/1995
Pages: 480
Product dimensions: 6.40(w) x 9.47(h) x 1.24(d)

Table of Contents

1. Hamiltonian Formulation of Beam Dynamics.- 1.1 Hamiltonian Formalism.- 1.1.1 Lagrange Equations.- 1.1.2 Hamiltonian Equations.- 1.1.3 Canonical Transformations.- 1.1.4 Action-Angle Variables.- 1.2 Hamiltonian Resonance Theory.- 1.2.1 Nonlinear Hamiltonian.- 1.2.2 Resonant Terms.- 1.2.3 Resonance Patterns and Stop-Band Width.- 1.2.4 Third-Order Resonance.- 1.3 Hamiltonian and Coupling.- 1.3.1 Linearly Coupled Motions.- 1.3.2 Higher-Order Coupling Resonances.- 1.3.3 Multiple Resonances.- 1.4 Symplectic Transformation.- Problems.- 2. General Electromagnetic Fields.- 2.1 General Transverse Magnetic-Field Expansion.- 2.2 Third-Order Differential Equation of Motion.- 2.3 Periodic Wiggler Magnets.- 2.3.1 Wiggler Field Configuration.- 2.3.2 Focusing in a Wiggler Magnet.- 2.3.3 Hard-Edge Model of Wiggler Magnets.- 2.4 Superconducting Magnet.- Problems.- 3. Dynamics of Coupled Motion.- 3.1 Conjugate Trajectories.- 3.2 Particle Motion in a Solenoidal Field.- 3.3 Transverse Coupled Oscillations.- 3.3.1 Equations of Motion in Coupling Systems.- 3.3.2 Coupled Beam Dynamics in Skew Quadrupoles.- 3.3.3 Equations of Motion in a Solenoid Magnet.- 3.3.4 Transformation Matrix for a Solenoid Magnet.- 3.3.5 Betatron Functions for Coupled Motion.- Problems.- 4. Higher-Order Perturbations.- 4.1 Kinematic Perturbation Terms.- 4.2 Control of the Central Beam Path.- 4.3 Dipole Field Errors and Dispersion Function.- 4.4 Dispersion Function in Higher Order.- 4.4.1 Chromaticity in Higher Approximation.- 4.4.2 Nonlinear Chromaticity.- 4.5 Perturbation Methods in Beam Dynamics.- 4.5.1 Periodic Distribution of Statistical Perturbations.- 4.5.2 Statistical Methods to Evaluate Perturbations.- Problems.- 5. Hamiltonian Nonlinear Beam Dynamics.- 5.1 Higher-Order Beam Dynamics.- 5.1.1 Multipole Errors.- 5.1.2 Nonlinear Matrix Formalism.- 5.2 Aberrations.- 5.2.1 Geometric Aberrations.- 5.2.2 Filamentation of Phase Space.- 5.2.3 Chromatic Aberrations.- 5.2.4 Particle Tracking.- 5.3 Hamiltonian Perturbation Theory.- 5.3.1 Tune Shift in Higher Order.- Problems.- 6. Charged Particle Acceleration.- 6.1 Accelerating Fields in Resonant rf Cavities.- 6.1.1 Wave Equation.- 6.1.2 Waveguide Modes.- 6.1.3 rf Cavities.- 6.1.4 Cavity Losses and Shunt Impedance.- 6.1.5 Determination of rf Parameters.- 6.2 Beam-Cavity Interaction.- 6.2.1 Coupling Between rf Field and Particles.- 6.2.2 Beam Loading and rf System.- 6.2.3 Higher-Order Mode Losses in an rf Cavity.- 6.2.4 Beam Loading in Circular Accelerators.- 6.3 Higher-Order Phase Focusing.- 6.3.1 Path Length in Higher Order.- 6.3.2 Higher-Order Phase Space Motion.- 6.3.3 Stability Criteria.- 6.4 FODO Lattice and Acceleration.- 6.4.1 Transverse Beam Dynamics and Acceleration.- 6.4.2 Adiabatic Damping.- Problems.- 7. Synchrotron Radiation.- 7.1 Theory of Synchrotron Radiation.- 7.1.1 Radiation Field.- 7.2 Synchrotron Radiation Power and Energy Loss.- 7.3 Spatial Distribution of Synchrotron Radiation.- 7.4 Synchrotron Radiation Spectrum.- 7.4.1 Radiation Field in the Frequency Domain.- 7.4.2 Spectral Distribution in Space and Polarization.- 7.4.3 Angle-Integrated Spectrum.- Problems.- 8. Hamiltonian Many Particle Systems.- 8.1 The Vlasov Equation.- 8.1.1 Betatron Oscillations and Perturbations.- 8.1.2 Damping.- 8.2 Damping of Oscillations in Electron Accelerators.- 8.2.1 Damping of Synchrotron Oscillations.- 8.2.2 Damping of Vertical Betatron Oscillations.- 8.2.3 Robinson’s Damping Criterion.- 8.2.4 Damping of Horizontal Betatron Oscillations.- 8.3 The Fokker-Planck Equation.- 8.3.1 Stationary Solution of the Fokker-Planck Equation.- 8.3.2 Particle Distribution Within a Finite Aperture.- 8.3.3 Particle Distribution in the Absence of Damping.- Problems.- 9. Particle Beam Parameters.- 9.1 Particle Distribution in Phase Space.- 9.1.1 Diffusion Coefficient and Synchrotron Radiation.- 9.1.2 Quantum Excitation of Beam Emittance.- 9.1.3 Horizontal Equilibrium Beam Emittance.- 9.1.4 Vertical Equilibrium Beam Emittance.- 9.2 Equilibrium Energy Spread and Bunch Length.- 9.3 Phase-Space Manipulation.- 9.3.1 Exchange of Transverse Phase-Space Parameters.- 9.3.2 Exchange of Longitudinal Phase-Space Parameters.- 9.4 Polarization of Particle Beam.- Problems.- 10. Collective Phenomena.- 10.1 Statistical Effects.- 10.1.1 Schottky Noise.- 10.1.2 Stochastic Cooling.- 10.1.3 Touschek Effect.- 10.1.4 Intra-Beam Scattering.- 10.2 Collective Self Fields.- 10.2.1 Transverse Self Fields.- 10.2.2 Fields from Image Charges.- 10.2.3 Space-Charge Effects.- 10.2.4 Longitudinal Space-Charge Field.- 10.3 Beam-Current Spectrum.- 10.4 Wake Fields and Impedance.- 10.4.1 Definitions of Wake Field and Impedance.- 10.4.2 Impedances in an Accelerator Environment.- 10.5 Coasting-Beam Instabilities.- 10.5.1 Negative-Mass Instability.- 10.5.2 Dispersion Relation.- 10.5.3 Landau Damping.- 10.5.4 Transverse Coasting-Beam Instability.- 10.6 Longitudinal Single-Bunch Effects.- 10.6.1 Potential-Well Distortion.- 10.7 Transverse Single-Bunch Instabilities.- 10.7.1 Beam Break-Up in Linear Accelerators.- 10.7.2 Fast Head-Tail Effect.- 10.7.3 Head-Tail Instability.- 10.8 Multi-Bunch Instabilities.- Problems.- 11. Insertion Device Radiation.- 11.1 Particle Dynamics in an Undulator.- 11.2 Undulator Radiation.- 11.3 Undulator Radiation Distribution.- 11.4 Elliptical Polarization.- Problems.- References.- Suggested Reading.- Author Index.

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