Particle Accelerator Physics

Preface to Fourth Edition
Preface to Third Edition
Preface to First Edition, Volume I
Preface to First Edition, Volume II
Contents
Part I Introduction
	1 Introduction to Accelerator Physics
		1.1 Short Historical Overview
		1.2 Particle Accelerator Systems
			1.2.1 Main Components of Accelerator Facilities
			1.2.2 Applications of Particle Accelerators
		1.3 Definitions and Formulas
			1.3.1 Units and Dimensions
			1.3.2 Maxwell\'s Equations
		1.4 Primer in Special Relativity
			1.4.1 Lorentz Transformation
				Lorentz Transformation of Fields
				Lorentz Contraction
				Time Dilatation
			1.4.2 Lorentz Invariance
				Invariance to Lorentz Transformations
				Space-Time
				Four-Velocity
				Four-Acceleration
				Momentum-Energy 4-Vector
				Photon 4-Vector
				Force 4-Vector
				Electro-magnetic 4-Vector
			1.4.3 Spatial and Spectral Distribution of Radiation
				Spectral Distribution
				Spatial Distribution
			1.4.4 Particle Collisions at High Energies
		1.5 Principles of Particle-Beam Dynamics
			1.5.1 Electromagnetic Fields of Charged Particles
				Electric Field of a Point Charge
				Fields of a Charged Particle Beam
			1.5.2 Vector and Scalar Potential
			1.5.3 Wave Equation
				Lienard-Wiechert Potentials
			1.5.4 Induction
			1.5.5 Lorentz Force
			1.5.6 Equation of Motion
			1.5.7 Charged Particles in an Electromagnetic Field
			1.5.8 Linear Equation of Motion
			1.5.9 Energy Conservation
				Poynting Vector
			1.5.10 Stability of a Charged-Particle Beam
		Problems
		References
	2 Linear Accelerators
		2.1 Principles of Linear Accelerators
			2.1.1 Charged Particles in Electric Fields
			2.1.2 Electrostatic Accelerators
				Cascade Generators
				Van de Graaff Accelerator
		2.2 Electric Field Components
			2.2.1 Electrostatic Deflectors
			2.2.2 Electrostatic Focusing Devices
			2.2.3 Iris Doublet
			2.2.4 Einzellens
		2.3 Acceleration by rf Fields
			2.3.1 Basic Principle of Microwave Linear Accelerators
				Synchronicity Condition
		Problems
		References
	3 Circular Accelerators
		3.1 Betatron
		3.2 Weak Focusing
		3.3 Adiabatic Damping
		3.4 Acceleration by rf Fields
			3.4.1 Microtron
			3.4.2 Cyclotron
			3.4.3 Synchro-Cyclotron
			3.4.4 Isochron Cyclotron
			3.4.5 Synchrotron
			3.4.6 Storage Ring
			3.4.7 Summary of Characteristic Parameters
		Problems
		References
Part II Tools We Need
	4 Elements of Classical Mechanics
		4.1 How to Formulate a Lagrangian?
			4.1.1 The Lagrangian for a Charged Particlein an EM-Field
		4.2 Lorentz Force
		4.3 Frenet-Serret Coordinates
		4.4 Hamiltonian Formulation
			4.4.1 Cyclic Variables
			4.4.2 Canonical Transformations
			4.4.3 Curvilinear Coordinates
			4.4.4 Extended Hamiltonian
			4.4.5 Change of Independent Variable
		Problems
		References
	5 Particle Dynamics in Electro-Magnetic Fields
		5.1 The Lorentz Force
		5.2 Fundamentals of Charged Particle Beam Optics
			5.2.1 Particle Beam Guidance
			5.2.2 Particle Beam Focusing
		5.3 Equation of Motion
		5.4 Equations of Motion from the Lagrangian and Hamiltonian
			5.4.1 Equations of Motion from Lagrangian
			5.4.2 Canonical Momenta
			5.4.3 Equation of Motion from Hamiltonian
			5.4.4 Harmonic Oscillator
			5.4.5 Action-Angle Variables
		5.5 Solutions of the Linear Equations of Motion
			5.5.1 Linear Unperturbed Equation of Motion
			5.5.2 Matrix Formulation
			5.5.3 Wronskian
			5.5.4 Perturbation Terms
				Dispersion Function
		Problems
		References
	6 Electromagnetic Fields
		6.1 Pure Multipole Field Expansion
			6.1.1 Electromagnetic Potentials and Fields for Beam Dynamics
			6.1.2 Fields, Gradients and Multipole Strength Parameter
			6.1.3 Main Magnets for Beam Dynamics
				Deflecting Magnets
				Focusing Device
				Synchrotron Magnet
				Higher Order Multipole Magnets
				Vacuum Chamber Material
			6.1.4 Multipole Misalignment and ``Spill-down\'\'
		6.2 Main Magnet Design Criteria
			6.2.1 Design Characteristics of Dipole Magnets
				Excitation Current and Saturation in a Bending Magnet
			6.2.2 Quadrupole Design Concepts
				Pole Profile Shimming
				Excitation Current and Saturation
		6.3 Magnetic Field Measurement
			6.3.1 Hall Probe
			6.3.2 Rotating Coil
				Practical Considerations
		6.4 General Transverse Magnetic-Field Expansion
			6.4.1 Pure Multipole Magnets
			6.4.2 Kinematic Terms
		6.5 Third-Order Differential Equation of Motion
		6.6 Longitudinal Field Devices
		6.7 Periodic Wiggler Magnets
			6.7.1 Wiggler Field Configuration
		6.8 Electrostatic Quadrupole
		Problems
		References
Part III Beam Dynamics
	7 Single Particle Dynamics
		7.1 Linear Beam Transport Systems
			7.1.1 Nomenclature
		7.2 Matrix Formalism in Linear Beam Dynamics
			7.2.1 Driftspace
			7.2.2 Quadrupole Magnet
			7.2.3 Thin Lens Approximation
			7.2.4 Quadrupole End Field Effects
		7.3 Focusing in Bending Magnets
			7.3.1  Sector Magnets
			7.3.2 Fringe Field Effects
			7.3.3 Finite Pole Gap
			7.3.4 Wedge Magnets
			7.3.5 Rectangular Magnet
			7.3.6 Focusing in a Wiggler Magnet
			7.3.7 Hard-Edge Model of Wiggler Magnets
		7.4 Elements of Beam Dynamics
			7.4.1 Building Blocks for Beam Transport Lines
				General Focusing Properties
				Chromatic Properties
				Achromatic Lattices
			7.4.2 Isochronous Systems
		Problems
		References
	8 Particle Beams and Phase Space
		8.1 Beam Emittance
			8.1.1 Liouville\'s Theorem
			8.1.2 Transformation in Phase Space
			8.1.3 Beam Matrix
				Measurement of the Beam Emittance
		8.2 Betatron Functions
			8.2.1 Beam Envelope
		8.3 Beam Dynamics in Terms of Betatron Functions
			8.3.1 Beam Dynamics in Normalized Coordinates
		8.4 Dispersive Systems
			8.4.1 Analytical Solution
			8.4.2 33-Transformation Matrices
			8.4.3 Linear Achromat
			8.4.4 Spectrometer
			8.4.5 Measurement of Beam Energy Spectrum
			8.4.6 Path Length and Momentum Compaction
		Problems
		References
	9 Longitudinal Beam Dynamics
		9.1 Longitudinal Particle Motion
			9.1.1 Longitudinal Phase Space Dynamics
		9.2 Equation of Motion in Phase Space
			9.2.1 Small Oscillation Amplitudes
			9.2.2 Phase Stability
				Large Oscillation Amplitudes
			9.2.3 Acceleration of Charged Particles
		9.3 Longitudinal Phase Space Parameters
			9.3.1 Separatrix Parameters
			9.3.2 Momentum Acceptance
			9.3.3 Bunch Length
			9.3.4 Longitudinal Beam Emittance
			9.3.5 Phase Space Matching
		9.4 Higher-Order Phase Focusing
			9.4.1 Dispersion Function in Higher Order
			9.4.2 Path Length in Higher Order
			9.4.3 Higher Order Momentum Compaction Factor
			9.4.4 Higher-Order Phase Space Motion
			9.4.5 Stability Criteria
		Problems
		References
	10 Periodic Focusing Systems
		10.1 FODO Lattice
			10.1.1 Scaling of FODO Parameters
			10.1.2 Betatron Motion in Periodic Structures
				Stability Criterion
			10.1.3 General FODO Lattice
		10.2 Beam Dynamics in Periodic Closed Lattices
			10.2.1 Hill\'s Equation
			10.2.2 Periodic Betatron Functions
			10.2.3 Periodic Dispersion Function
				Scaling of the Dispersion in a FODO Lattice
				General Solution for the Periodic Dispersion
			10.2.4 Periodic Lattices in Circular Accelerators
				Synchrotron Lattice
				Phase Space Matching
				Dispersion Matching
				Magnet Free Insertions
				Low Beta Insertions
		10.3 FODO Lattice and Acceleration
			10.3.1 Lattice Structure
			10.3.2 Transverse Beam Dynamics and Acceleration
				Analytical Solutions
				Transformation Matrices
				Adiabatic Damping
		Problems
		References
Part IV Beam Parameters
	11 Particle Beam Parameters
		11.1 Definition of Beam Parameters
			11.1.1 Beam Energy
			11.1.2 Time Structure
			11.1.3 Beam Current
			11.1.4 Beam Dimensions
		11.2 Damping
			11.2.1 Robinson Criterion
		11.3 Particle Distribution in Longitudinal Phase Space
			11.3.1 Energy Spread
			11.3.2 Bunch Length
		11.4 Transverse Beam Emittance
			11.4.1 Equilibrium Beam Emittance
			11.4.2 Emittance Increase in a Beam Transport Line
			11.4.3 Vertical Beam Emittance
			11.4.4 Beam Sizes
			11.4.5 Beam Divergence
		11.5 Variation of the Damping Distribution
			11.5.1 Damping Partition and Rf-Frequency
		11.6 Variation of the Equilibrium Beam Emittance
			11.6.1 Beam Emittance and Wiggler Magnets
			11.6.2 Damping Wigglers
		11.7 Robinson Wiggler
			11.7.1 Damping Partition and Synchrotron Oscillation
			11.7.2 Can We Eliminate the Beam Energy Spread?
		11.8 Beam Life Time
			11.8.1 Beam Lifetime and Vacuum
				Elastic Scattering
				Inelastic Scattering
			11.8.2 Ultra High Vacuum System
				Thermal Gas Desorption
				Synchrotron Radiation Induced Desorption
		Problems
		References
	12 Vlasov and Fokker–Planck Equations
		12.1 The Vlasov Equation
			12.1.1 Betatron Oscillations and Perturbations
			12.1.2 Damping
		12.2 Damping of Oscillations in Electron Accelerators
			12.2.1 Damping of Synchrotron Oscillations
			12.2.2 Damping of Vertical Betatron Oscillations
			12.2.3 Robinson\'s Damping Criterion
			12.2.4 Damping of Horizontal Betatron Oscillations
		12.3 The Fokker–Planck Equation
			12.3.1 Stationary Solution of the Fokker–Planck Equation
			12.3.2 Particle Distribution within a Finite Aperture
			12.3.3 Particle Distribution in the Absence of Damping
		Problems
		References
	13 Equilibrium Particle Distribution
		13.1 Particle Distribution in Phase Space
			13.1.1 Diffusion Coefficient and Synchrotron Radiation
			13.1.2 Quantum Excitation of Beam Emittance
		13.2 Equilibrium Beam Emittance
			13.2.1 Horizontal Equilibrium Beam Emittance
			13.2.2 Vertical Equilibrium Beam Emittance
		13.3 Equilibrium Energy Spread and Bunch Length
			13.3.1 Equilibrium Beam Energy Spread
			13.3.2 Equilibrium Bunch Length
		13.4 Phase-Space Manipulation
			13.4.1 Exchange of Transverse Phase-Space Parameters
			13.4.2 Bunch Compression
			13.4.3 Alpha Magnet
		13.5 Polarization of a Particle Beam
		Problems
		References
	14 Beam Emittance and Lattice Design
		14.1 Equilibrium Beam Emittance in Storage Rings
			14.1.1 FODO Lattice
			14.1.2 Minimum Beam Emittance
		14.2 Absolute Minimum Emittance
		14.3 Beam Emittance in Periodic Lattices
			14.3.1 The Double Bend Achromat Lattice (DBA)
			14.3.2 The FODO Lattice
			14.3.3 Optimum Emittance for Colliding Beam Storage Rings
		Problems
		References
Part V Perturbations
	15 Perturbations in Beam Dynamics
		15.1 Magnet Field and Alignment Errors
			15.1.1 Self Compensation of Perturbations
		15.2 Dipole Field Perturbations
			15.2.1 Dipole Field Errors and Dispersion Function
			15.2.2 Perturbations in Open Transport Lines
			15.2.3 Existence of Equilibrium Orbits
			15.2.4 Closed Orbit Distortion
			15.2.5 Statistical Distribution of Dipole Field and Alignment Errors
			15.2.6 Dipole Field Errors in Insertion Devices
			15.2.7 Closed Orbit Correction
			15.2.8 Response Matrix
			15.2.9 Orbit Correction with Single Value Decomposition ( SVD)
				Single Value Decomposition (SVD)
		15.3 Quadrupole Field Perturbations
			15.3.1 Betatron Tune Shift
			15.3.2 Optics Perturbation Due to Insertion Devices
			15.3.3 Resonances and Stop Band Width
			15.3.4 Perturbation of Betatron Function
		15.4 Chromatic Effects in a Circular Accelerator
			15.4.1 Chromaticity
			15.4.2 Chromaticity Correction
			15.4.3 Chromaticity in Higher Approximation
			15.4.4 Non-linear Chromaticity
		15.5 Kinematic Perturbation Terms
		15.6 Perturbation Methods in Beam Dynamics
			15.6.1 Periodic Distribution of Statistical Perturbations
			15.6.2 Periodic Perturbations in Circular Accelerators
			15.6.3 Statistical Methods to Evaluate Perturbations
		15.7 Control of Beam Size in Transport Lines
		Problems
		References
	16 Resonances
		16.1 Lattice Resonances
			16.1.1 Resonance Conditions
			16.1.2 Coupling Resonances
			16.1.3 Resonance Diagram
		16.2 Hamiltonian Resonance Theory
			16.2.1 Non-linear Hamiltonian
			16.2.2 Resonant Terms
			16.2.3 Resonance Patterns and Stop-Band Width
			16.2.4 Half-Integer Stop-Band
			16.2.5 Separatrices
			16.2.6 General Stop-Band Width
		16.3 Third-Order Resonance
			16.3.1 Particle Motion in Phase Space
		Problems
		References
	17 Hamiltonian Nonlinear Beam Dynamics
		17.1 Higher-Order Beam Dynamics
			17.1.1 Multipole Errors
			17.1.2 Non-linear Matrix Formalism
		17.2 Aberrations
			17.2.1 Geometric Aberrations
				Compensation of Nonlinear Perturbations
				Sextupoles Separated by a -I-Transformation
			17.2.2 Filamentation of Phase Space
			17.2.3 Chromatic Aberrations
			17.2.4 Particle Tracking
		17.3 Hamiltonian Perturbation Theory
			17.3.1 Tune Shift in Higher Order
		Problems
		References
Part VI Acceleration
	18 Charged Particle Acceleration
		18.1 Rf-Waveguides and Cavities
			18.1.1 Wave Equation
			18.1.2 Rectangular Waveguide Modes
			18.1.3 Cylindrical Waveguide Modes
				TM-Mode Field Components in Cylindrical Waveguides
		18.2 Rf-Cavities
			18.2.1 Square Cavities
			18.2.2 Cylindrical Cavity
			18.2.3 Energy Gain
			18.2.4 Rf-Cavity as an Oscillator
			18.2.5 Cavity Losses and Shunt Impedance
		18.3 Rf-Parameters
			18.3.1 Synchronous Phase and Rf-voltage
		18.4 Linear Accelerator
			18.4.1 Basic Waveguide Parameters
			18.4.2 Particle Capture in a Linear Accelerator Field
		18.5 Preinjector and Beam Preparation
			18.5.1 Prebuncher
			18.5.2 Beam Chopper
			18.5.3 Buncher Section
		Problems
		References
	19 Beam-Cavity Interaction
		19.1 Coupling Between rf-Field and Particles
			19.1.1 Network Modelling of an Accelerating Cavity
		19.2 Beam Loading and Rf-System
		19.3 Higher-Order Mode Losses in an Rf-Cavity
			19.3.1 Efficiency of Energy Transfer from Cavity to Beam
		19.4 Beam Loading
		19.5 Phase Oscillation and Stability
			19.5.1 Robinson Damping
			19.5.2 Potential Well Distortion
		Problems
		References
Part VII Coupled Motion
	20 Dynamics of Coupled Motion
		20.1 Equations of Motion in Coupled Systems
			20.1.1 Coupled Beam Dynamics in Skew Quadrupoles
			20.1.2 Particle Motion in a Solenoidal Field
			20.1.3 Transformation Matrix for a Solenoid Magnet
		20.2 Betatron Functions for Coupled Motion
		20.3 Conjugate Trajectories
		20.4 Hamiltonian and Coupling
			20.4.1 Linearly Coupled Motion
				Linear Difference Resonance
				Linear Sum Resonance
			20.4.2 Higher-Order Coupling Resonances
			20.4.3 Multiple Resonances
		Problems
		References
Part VIII Intense Beams
	21 Statistical and Collective Effects
		21.1 Statistical Effects
			21.1.1 Schottky Noise
			21.1.2 Stochastic Cooling
			21.1.3 Touschek Effect
			21.1.4 Intra-Beam Scattering
		21.2 Collective Self Fields
			21.2.1 Self Field for Elliptical Particle Beams
				Forces from Space-Charge Fields
			21.2.2 Beam–Beam Effect
			21.2.3 Transverse Self Fields
			21.2.4 Fields from Image Charges
			21.2.5 Space-Charge Effects
				Space Charge Dominated Beams
				Space-Charge Tune Shift
			21.2.6 Longitudinal Space-Charge Field
		21.3 Beam-Current Spectrum
			21.3.1 Longitudinal Beam Spectrum
			21.3.2 Transverse Beam Spectrum
		Problems
		References
	22 Wake Fields and Instabilities
		22.1 Definitions of Wake Field and Impedance
			22.1.1 Parasitic Mode Losses and Impedances
			22.1.2 Longitudinal Wake Fields
				Loss Parameter
			22.1.3 Transverse Wake Fields
			22.1.4 Panofsky-Wenzel Theorem
		22.2 Impedances in an Accelerator Environment
			22.2.1 Space-Charge Impedance
			22.2.2 Resistive-Wall Impedance
			22.2.3 Cavity-Like Structure Impedance
			22.2.4 Overall Accelerator Impedance
			22.2.5 Broad-Band Wake Fields in a Linear Accelerator
		22.3 Coasting-Beam Instabilities
			22.3.1 Negative-Mass Instability
			22.3.2 Dispersion Relation
			22.3.3 Landau Damping
			22.3.4 Transverse Coasting-Beam Instability
		22.4 Longitudinal Single-Bunch Effects
			22.4.1 Potential-Well Distortion
				Synchrotron Oscillation Tune Shift
				Bunch Lengthening
		22.5 Transverse Single-Bunch Instabilities
			22.5.1 Beam Break-Up in Linear Accelerators
			22.5.2 Fast Head-Tail Effect
				Measurement of the Broad-Band Impedance
			22.5.3 Head-Tail Instability
		22.6 Multi-Bunch Instabilities
		Problems
		References
Part IX Synchrotron Radiation
	23 Fundamental Processes
		23.1 Radiation from Moving Charges
			23.1.1 Why Do Charged Particles Radiate?
			23.1.2 Spontaneous Synchrotron Radiation
			23.1.3 Stimulated Radiation
			23.1.4 Electron Beam
		23.2 Conservation Laws and Radiation
			23.2.1 Cherenkov Radiation
			23.2.2 Compton Radiation
		23.3 Electromagnetic Radiation
			23.3.1 Coulomb Regime
			23.3.2 Radiation Regime
		Problems
		References
	24 Overview of Synchrotron Radiation
		24.1 Radiation Sources
			24.1.1 Bending Magnet Radiation
			24.1.2 Superbends
			24.1.3 Wavelength Shifter
			24.1.4 Wiggler Magnet Radiation
			24.1.5 Undulator Radiation
				Back Scattered Photons
				Photon Flux
		24.2 Radiation Power
		24.3 Spectrum
		24.4 Spatial Photon Distribution
		24.5 Fraunhofer Diffraction
		24.6 Spatial Coherence
		24.7 Temporal Coherence
		24.8 Spectral Brightness
			24.8.1 Matching
		24.9 Photon Source Parameters
		Problems
		References
	25 Theory of Synchrotron Radiation
		25.1 Radiation Field
		25.2 Total Radiation Power and Energy Loss
			25.2.1 Transition Radiation
		25.3 Spatial Radiation Distribution
			25.3.1 Radiation Lobes
		25.4 Radiation Field in the Frequency Domain
			25.4.1 Spectral Distribution in Space and Polarization
			25.4.2 Spectral and Spatial Photon Flux
			25.4.3 Harmonic Representation
			25.4.4 Spatial Radiation Power Distribution
		25.5 Asymptotic Solutions
			25.5.1 Low Frequencies and Small Observation Angles
			25.5.2 High Frequencies or Large Observation Angles
		25.6 Angle-Integrated Spectrum
		25.7 Statistical Radiation Parameters
		Problems
		References
	26 Insertion Device Radiation
		26.1 Particle Dynamics in a Periodic Field Magnet
		26.2 Undulator Radiation
			26.2.1 Fundamental Wavelength
			26.2.2 Radiation Power
			26.2.3 Spatial and Spectral Distribution
			26.2.4 Line Spectrum
			26.2.5 Spectral Undulator Brightness
		26.3 Elliptical Polarization
			26.3.1 Elliptical Polarization from Bending MagnetRadiation
			26.3.2 Elliptical Polarization from Periodic InsertionDevices
				Asymmetric Wiggler Magnet
				Elliptically Polarizing Undulator
		Problems
		References
	27 Free Electron Lasers
		27.1 Small Gain Regime
			27.1.1 Energy Transfer
			27.1.2 Equation of Motion
			27.1.3 FEL-Gain
		27.2 High Gain Free Electron Laser
			27.2.1 Electron Dynamics in a SASE FEL
			27.2.2 Electron Source
			27.2.3 Beam Dynamics
			27.2.4 Undulator
		Problems
		References
Correction to: Particle Accelerator Physics
Solutions
	Solutions for Chap. 1
	Solutions for Chap. 2
	Solutions for Chap. 3
	Solutions for Chap. 4
	Solutions for Chap. 5
	Solutions for Chap. 6
	Solutions for Chap. 7
	Solutions for Chap. 8
	Solutions for Chap. 9
	Solutions for Chap. 10
	Solutions for Chap. 11
	Solutions for Chap. 12
	Solutions for Chap. 13
	Solutions for Chap. 14
	Solutions for Chap. 15
	Solutions for Chap. 16
	Solutions for Chap. 17
	Solutions for Chap. 18
	Solutions for Chap. 19
	Solutions for Chap. 20
	Solutions for Chap. 21
	Solutions for Chap. 22
	Solutions for Chap. 23
	Solutions for Chap. 24
	Solutions for Chap. 25
	Solutions for Chap. 26
	Solutions for Chap. 27
A Useful Mathematical Formulae
	A.1 Vector Algebra
		A.1.1 Differential Vector Expressions
		A.1.2 Algebraic Relations
		A.1.3 Differential Relations
		A.1.4 Partial Integration
		A.1.5 Trigonometric and Exponential Functions
		A.1.6 Integral Relations
		A.1.7 Dirac\'s Delta Function
		A.1.8 Bessel\'s Functions
		A.1.9 Series Expansions
		A.1.10 Fourier Series
			Parseval\'s Theorem
			Fourier Transform
		A.1.11 Coordinate Transformations
			Cartesian coordinates
			General Coordinate Transformation
			Cylindrical Coordinates
			Polar Coordinates
			Curvilinear Coordinates
B Physical Formulae and Parameters
	B.1 Physical Constants
	B.2 Relations of Fundamental Parameters
	B.3 Unit Conversions
	B.4 Maxwell\'s Equations
	B.5 Wave and Field Equations
	B.6 Relativistic Relations
		B.6.1 Lorentz Transformation
		B.6.2 Four-Vectors
		B.6.3 Square of the 4-Acceleration
		B.6.4 Miscellaneous 4-Vectors and Lorentz Invariant Properties
	B.7 Transformation Matrices in Beam Dynamics
	B.8 General Transformation Matrix
		B.8.1 Symmetric Magnet Arrangement
		B.8.2 Inverse Transformation Matrix
	B.9 Specific Transformation Matrices
		B.9.1 Drift Space
		B.9.2 Bending Magnets
			Sector Magnet
			Wedge Magnet
			Rectangular Magnet
			Synchrotron Magnet (Sector Type)
			Synchrotron Magnet (Rectangular Type)
		B.9.3 Quadrupole
			Focusing Quadrupole ( k0>0,φ=k l )
			Defocusing Quadrupole (k<0,φ=\"026A30C k\"026A30C )
			Quadrupole Doublet
			Quadrupole Triplet
Index