Preface
Preface to the first edition
1 Introduction
I Historical Developments
I.1 Natural Accelerators
I.2 Electrostatic Accelerators
I.3 Induction Accelerators
I.4 Radio-Frequency (RF) Accelerators
I.5 Colliders and Storage Rings
I.6 Synchrotron Radiation Storage Rings
II Layout and Components of Accelerators
II.1 Acceleration Cavities
II.2 Accelerator Magnets
II.3 Other Important Components
III Accelerator Applications
III.1 High Energy and Nuclear Physics
III.2 Solid-State and Condensed-Matter Physics
III.3 Other Applications
Exercise
2 Transverse Motion
I Hamiltonian for Particle Motion in Accelerators
I.1 Hamiltonian in Frenet-Serret Coordinate System
I.2 Magnetic Field in Frenet-Serret Coordinate System
I.3 Equation of Betatron Motion
I.4 Particle Motion in Dipole and Quadrupole Magnets
Exercise
II Linear Betatron Motion
II.1 Transfer Matrix and Stability of Betatron Motion
II.2 Courant-Snyder Parametrization
II.3 Floquet Transformation
II.4 Action-Angle Variable and Floquet Transformation
II.5 Courant-Snyder Invariant and Emittance
II.6 Stability of Betatron Motion: A FODO Cell Example
II.7 Symplectic Condition
II.8 Effect of Space-Charge Force on Betatron Motion
Exercise
III Effect of Linear Magnet Imperfections
III.1 Closed-Orbit Distortion due to Dipole Field Errors
III.2 Extended Matrix Method for the Closed Orbit
III.3 Application of Dipole Field Error
III.4 Quadrupole Field (Gradient) Errors
III.5 Basic Beam Observation of Transverse Motion
III.6 Application of quadrupole field error
III.7 Transverse Spectra
III.8 Beam Injection and Extraction
III.9 Mechanisms of emittance dilution and diffusion
Exercise
IV Off-Momentum Orbit
IV.1 Dispersion Function
IV.2 Η-Function, Action, and Integral Representation
IV.3 Momentum Compaction Factor
IV.4 Dispersion Suppression and Dispersion Matching
IV.5 Achromat Transport Systems
IV.6 Transport Notation
IV.7 Experimental Measurements of Dispersion Function
IV.8 Transition Energy Manipulation
A. γT jump schemes
B. Flexible momentum compaction (FMC) lattices
C. Other similar FMC modules
D. FMC in double-bend (DB) lattices
IV.9 Minimum (Η) Modules
Exercise
V Chromatic Aberration
V.1 Chromaticity Measurement and Correction
V.2 Nonlinear Effects of Chromatic Sextupoles
V.3 Chromatic Aberration and Correction
V.4 Lattice Design Strategy
Exercise
VI Linear Coupling
VI.1 The Linear Coupling Hamiltonian
VI.2 Effects of an isolated Linear Coupling Resonance
VI.3 Experimental Measurement of Linear Coupling
VI.4 Linear Coupling Correction with Skew Quadrupoles
VI.5 Linear Coupling Using Transfer Matrix Formalism
Exercise
VII Nonlinear Resonances
VII.1 Nonlinear Resonances Driven by Sextupoles
VII.2 Higher-Order Resonances
VII.3 Nonlinear Detuning from Sextupoles
VII.4 Betatron Tunes and Nonlinear Resonances
Exercise
VIII Collective Instabilities and Landau Damping
VIII.1 Impedance
VIII.2 Transverse Wave Modes
VIII.3 Effect of Wakefield on Transverse Wave
VIII.4 Frequency Spread and Landau Damping
Exercise
IX Synchro-Betatron Hamiltonian
Exercise
3 Synchrotron Motion
I Longitudinal Equation of Motion
I .1 The Synchrotron Hamiltonian
I .2 The Synchrotron Mapping Equation
I .3 Evolution of Synchrotron Phase-Space Ellipse
I .4 Some Practical Examples
I .5 Summary of Synchrotron Equations of Motion
Exercise
II Adiabatic Synchrotron Motion
II.1 Fixed Points
II.2 Bucket Area
II.3 Small-Amplitude Oscillations and Bunch Area
II.4 Small-Amplitude Synchrotron Motion at the UFP
II.5 Synchrotron Motion for Large-Amplitude Particles
II.6 Experimental Tracking of Synchrotron Motion
Exercise
III RF Phase and Voltage Modulations
III.1 Normalized Phase-Space Coordinates
III.2 RF Phase Modulation and Parametric Resonances
III.3 Measurements of Synchrotron Phase Modulation
III.4 Effects of Dipole Field Modulation
III.5 RF Voltage Modulation
III.6 Measurement of RF Voltage Modulation
Exercise
IV Nonadiabatic and Nonlinear Synchrotron Motion
IV.1 Linear Synchrotron Motion Near Transition Energy
IV.2 Nonlinear Synchrotron Motion at γ≈γT
IV.3 Beam Manipulation Near Transition Energy
IV.4 Synchrotron Motion with Nonlinear Phase Slip Factor
IV.5 The QI Dynamical Systems
Exercise
V Beam Manipulation in Synchrotron Phase Space
V.1 RF Frequency Requirements
V.2 Capture and Acceleration of Proton and Ion Beams
V.3 Bunch Compression and Rotation
V.4 Debunching
V.5 Beam Stacking and Phase Displacement Acceleration
V.6 Double rf Systems
V.7 The Barrier RF Bucket
Exercise
VI Fundamentals of RF Systems
VI.1 Pillbox Cavity
VI.2 Low Frequency Coaxial Cavities
VI.3 Beam Loading
VI.4 Beam Loading Compensation and Robinson Instability
Exercise
VII Longitudinal Collective Instabilities
VII.1 Longitudinal Spectra
VII.2 Collective Microwave Instability in Coasting Beams
VII.3 Longitudinal Impedance
VII.4 Microwave Single Bunch Instability
Exercise
VIII Introduction to Linear Accelerators
VIII.1 Historical Milestones
VIII.2 Fundamental Properties of Accelerating Structures
A. Transit time factor
B. Shunt impedance
C. The quality factor Q
VIII.3 Particle Acceleration by EM Waves
A. EM waves in a cylindrical wave guide
B. Phase velocity and group velocity
C. TM modes in a cylindrical pillbox cavity
D. A1varez structure
E. Loaded wave guide chain and the space harmonics
F. Standing wave, traveling wave, and coupled cavity linacs
G. HOMs
VIII.4 Longitudinal Particle Dynamics in a Linac
VIII.5 Transverse Beam Dynamics in a Linac
Exercise
4 Physics of Electron Storage Rings
I Fields of a Moving Charged Particle
I.1 Non-relativistic Reduction
I.2 Radiation Field for Particles at Relativistic Velocities
I.3 Frequency and Angular Distribution
I.4 Quantum Fluctuation
Exercise
II Radiation Damping and Excitation
II.1 Damping of Synchrotron Motion
II.2 Damping of Betatron Motion
II.3 Damping Rate Adjustment
II.4 Radiation Excitation and Equilibrium Energy Spread
II.5 Radial Bunch Width and Distribution Function
II.6 Vertical Beam Width
II.7 Radiation Integrals
II.8 Beam Lifetime
Exercise
III Emittance in Electron Storage Rings
III.1 Emittance of Synchrotron Radiation Lattices
A. FODO cell lattice
B. Double-bend achromat (Chasman-Green lattice)
C. Minimum (Η)-function lattice
D. Minimizing emittance in a combined function DBA
E. Three-bend achromat
III.2 Insertion Devices
III.3 Beam Physics of High Brightness Storage Rings
Exercise
5 Special Topics in Beam Physics
I Free Electron Laser (FEL)
I.1 Small Signal Regime
I.2 Interaction of the Radiation Field with the Beam
I.3 Experiments on High Gain FEL Generation
Exercise
II Beam-Beam Interaction
II. 1 The beam-beam force
II.2 The Coherent Beam-Beam Effects
II.3 Nonlinear Beam-Beam Effects
II.4 Experimental Observations and Numerical Simulations
II.5 Beam-Beam Interaction in Linear Colliders
Exercise
A Basics of Classical Mechanics
I Hamiltonian Dynamics
I.1 Canonical Transformations
I.2 Fixed Points
I.3 Poisson Bracket
I.4 Liouville Theorem
I.5 Floquet Theorem
II Stochastic Beam Dynamics
II.1 Central Limit Theorem
II.2 Langevin Equation of Motion
II.3 Stochastic Integration Methods
II.4 Fokker-Planck Equation
B Numerical Methods and Physical Constants
I Fourier Transform
1.1 Nyquist Sampling Theorem
1.2 Discrete Fourier Transform
1.3 Digital Filtering
1.4 Some Simple Fourier Transforms
II Model Independent Analysis
II.1 Model Independent Analysis
II.2 Independent Component Analysis
II.3 Accelerator Modeling
III Cauchy Theorem and the Dispersion Relation
III.1 Cauchy Integral Formula
III.2 Dispersion Relation
IV Useful Handy Formulas
IV.1 Generating functions for the Bessel functions
IV.2 The Hankel transform
IV.3 The complex error function
IV.4 A multipole expansion formula
IV.5 Cylindrical Coordinates
IV.6 Gauss' and Stokes' theorems
IV.7 Vector Operation
V Maxwell's equations
V.1 Lorentz Transformation of EM fields
V.2 Cylindrical waveguides
V.3 Voltage Standing Wave Ratio
VI Physical Properties and Constants
Bibliography
Index
Symbols and Notations
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