Fundamentals of Particle Accelerator Physics

Description

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. 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