This book offers a concise and coherent introduction to accelerator physics and technology at the fundamental level but still in connection to advanced applications ranging from high-energy colliders to most advanced light sources, i.e., Compton sources, storage rings and free-electron lasers. The book is targeted at accelerator physics students at both undergraduate and graduate levels, but also of interest also to Ph.D. students and senior scientists not specialized in beam physics and accelerator design, or at the beginning of their career in particle accelerators.
The book introduces readers to particle accelerators in a logical and sequential manner, with paragraphs devoted to highlight the physical meaning of the presented topics, providing a solid link to experimental results, with a simple but rigorous mathematical approach. In particular, the book will turn out to be self-consistent, including for example basics of Special Relativity and Statistical Mechanics for accelerators. Mathematical derivations of the most important expressions and theorems are given in a rigorous manner, but with simple and immediate demonstration where possible.
The understanding gained by a systematic study of the book will offer students the possibility to further specialize their knowledge through the wide and up-to-date bibliography reported. Both theoretical and experimental items are presented with reference to the most recent achievements in colliders and light sources. The author draws on his almost 20-years long experience in the design, commissioning and operation of accelerator facilities as well as on his 10-years long teaching experience about particle accelerators at the University of Trieste, Department of Engineering and of Physics, as well as at international schools on accelerator physics.
Author(s): Simone Di Mitri
Series: Graduate Texts in Physics
Publisher: Springer
Year: 2023
Language: English
Pages: 275
City: Cham
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
