Fundamentals of Particle Accelerator Physics

Preface
Acknowledgements
Contents
1 Special Relativity
	1.1 Relativistic Kinematics
		1.1.1 Michelson and Morley's Experiment
		1.1.2 Lorentz-Fitzgerald's Transformations
		1.1.3 Lengths and Time Intervals
		1.1.4 Velocities
	1.2 Relativistic Dynamics
		1.2.1 4-Vectors
		1.2.2 Momentum
		1.2.3 Mass-Energy Equivalence
		1.2.4 Invariant Mass
		1.2.5 Colliders
		1.2.6 Wave-Particle Duality
		1.2.7 Doppler Effect and Angular Collimation
		1.2.8 Forces
		1.2.9 Fields
		1.2.10 Accelerations
2 Low Energy Accelerators
	2.1 Electrostatic Accelerators
		2.1.1 Cockcroft and Walton
		2.1.2 Van de Graaff
	2.2 Electrodynamic Accelerators
		2.2.1 Drift Tube Linacs
		2.2.2 Cyclotron
		2.2.3 Betatron
		2.2.4 Weak Focusing
3 Radiofrequency Structures
	3.1 Principles of Acceleration
		3.1.1 Theorem of E.M. Acceleration
		3.1.2 Pill-Box
	3.2 Periodic Structures
		3.2.1 Travelling Wave
		3.2.2 Standing Wave
		3.2.3 Synchronous Phase
		3.2.4 Transit Time Factor
	3.3 RLC Circuit Model
		3.3.1 Standing Wave
		3.3.2 Travelling Wave Constant Impedance
		3.3.3 Travelling Wave Constant Gradient
		3.3.4 Comparison
		3.3.5 Time Scales in RF Structures
4 High Energy Accelerators
	4.1 General Features
	4.2 Longitudinal Dynamics
		4.2.1 Phase Stability in a Linac
		4.2.2 Adiabatic Damping
		4.2.3 Momentum Compaction
		4.2.4 Transition Energy
		4.2.5 Phase Stability in a Synchrotron
		4.2.6 Constant of Motion
		4.2.7 RF Acceptance
		4.2.8 Stationary Bucket
		4.2.9 Energy Ramp
		4.2.10 Summary
	4.3 Transverse Dynamics
		4.3.1 Multipolar Field Expansion
		4.3.2 Quadrupole Magnet
		4.3.3 Strong Focusing
		4.3.4 Principal Trajectories
		4.3.5 Transfer Matrices
		4.3.6 Periodic Motion
		4.3.7 Betatron Function
		4.3.8 Floquet's Theorem
		4.3.9 Courant-Snyder Invariant
		4.3.10 Phase Space Ellipse
		4.3.11 Floquet's Normalized Coordinates
		4.3.12 Equivalence of Matrices
		4.3.13 Non-Periodic Motion
		4.3.14 Summary
	4.4 Beam Envelope
		4.4.1 Statistical Emittance
		4.4.2 Transverse Beam Matrix
		4.4.3 Transfer of Courant-Snyder Parameters
		4.4.4 Longitudinal Beam Matrix
		4.4.5 Normalized Emittance
		4.4.6 Beam Brightness
5 Hamiltonian Dynamics
	5.1 Single Particle Dynamics
		5.1.1 Lagrange's Equation
		5.1.2 Hamilton's Equations
		5.1.3 Single Particle Hamiltonian
		5.1.4 Hill's Equation
	5.2 Liouville's Theorem
		5.2.1 Statement
		5.2.2 Vlasov's Equation
		5.2.3 Emittance
		5.2.4 Acceleration
	5.3 Poincare'-Cartan Invariants
		5.3.1 Phase Space Hypervolumes
		5.3.2 Eigen-Emittance
		5.3.3 Flat and Round Beam
6 Perturbed Linear Optics
	6.1 Orbit Distortion
		6.1.1 Single Pass
		6.1.2 Closed Orbit
		6.1.3 Amplification Factor
	6.2 Resonances
		6.2.1 Resonance Order
		6.2.2 Sum and Difference Resonance
		6.2.3 Sextupole Resonances and Numerology
	6.3 Linear Chromaticity
		6.3.1 Natural Chromaticity
		6.3.2 Chromaticity Correction
7 Synchrotron Radiation
	7.1 Radiated Power
		7.1.1 Retarded Potentials
		7.1.2 Larmor's Formula
		7.1.3 Schwinger's Formula
		7.1.4 Radiation Emission in a Linac
		7.1.5 Radiation Emission in a Synchrotron
	7.2 Angular Distribution
		7.2.1 Longitudinal Acceleration
		7.2.2 Centripetal Acceleration
	7.3 Spectral Distribution
		7.3.1 Critical Frequency
		7.3.2 Universal Function
		7.3.3 Intensity
		7.3.4 Polarization
8 Equilibrium Distribution
	8.1 Radiation Damping and Quantum Excitation
		8.1.1 Longitudinal Motion
		8.1.2 Horizontal Motion
		8.1.3 Vertical Motion
		8.1.4 Robinson's Theorem
		8.1.5 Radiation Integrals
		8.1.6 Vlasov-Fokker-Planck Equation
	8.2 Lifetime
		8.2.1 Quantum Lifetime
		8.2.2 Dynamic Aperture
		8.2.3 Overvoltage
		8.2.4 Residual Gas Interactions
		8.2.5 Touschek Lifetime
9 Perturbed Distribution
	9.1 Synchro-Betatron Excitation
	9.2 Intrabeam Scattering
		9.2.1 Storage Rings
		9.2.2 Linacs
	9.3 Collective Effects
		9.3.1 Wakefields
		9.3.2 Impedances
		9.3.3 Classification
		9.3.4 Robinson's Instability
10 Light Sources
	10.1 Brilliance
		10.1.1 Practical Meaning
		10.1.2 Optics Matching, Diffraction Limit
		10.1.3 Central Cone
	10.2 Coherence
		10.2.1 Correlation Functions
		10.2.2 Transverse Coherence
		10.2.3 Longitudinal Coherence
		10.2.4 Intensity Enhancement
	10.3 Undulator Spontaneous Radiation
		10.3.1 Central Wavelength
		10.3.2 Spectral Width, Angular Divergence
		10.3.3 Dipole, Wiggler, Undulator
		10.3.4 Harmonic Emission
	10.4 Inverse Compton Scattering
		10.4.1 Thomson Back-Scattering
		10.4.2 Angular and Spectral Distribution
		10.4.3 Compton Back-Scattering
	10.5 Free-Electron Laser
		10.5.1 Resonance Condition
		10.5.2 Pendulum Equation
		10.5.3 Low Gain
		10.5.4 High Gain
		10.5.5 Pierce's Parameter
		10.5.6 Electron Beam Quality
11 Colliders
	11.1 Luminosity
		11.1.1 Discussion: Lifetime, Run Time and Preparation Time
	11.2 Crossing Angle
	11.3 Hourglass Effect
		11.3.1 Discussion: Luminosity of a Compton Source
	11.4 Beam-Beam Tune Shift
	11.5 Beam-Beam Lifetime
Additional Bibliography
Index