USPAS
Jan 2002 Accelerator School Phys 450B:
Introduction to Accelerator Physics
Instructor : Gerald Dugan
This course will cover the
fundamental physical principles of particle accelerators, with a focus on
circular high-energy colliders. It will include beam optical design, the
single-particle dynamics of transverse motion, lattice design, single particle
acceleration and longitudinal dynamics, synchrotron radiation, nonlinear
effects, linear coupling, emittance growth and beam cooling, wakefields,
impedances,
Office 2010 Professional Plus Key, and collective effects in multiparticle beams.
Prerequsities: Undergraduate courses in electrodynamics and
classical mechanics.
Principal reference:D. A.
Edwards and M. J. Syphers, "An Introduction to the Physics of High Energy
Accelerators",
Office Professional Plus 2007, John Wiley & Sons, Inc., (1993)Other references:
A useful online reference
:
CERN Accelerator College: 5th General Accelerator
school, CERN 94-01 (1994), vol. 1 and vol. 2
Links: and
Other useful references:
Particle Accelerator
Physics I (2nd edition, 1998), by
Helmut Wiedemann
Physics of Collective Beam
Instabilities in High Energy Accelerators (1993),
Office 2010 Standard, By Alexander W. Chao
Course tentative
outline
Lecture #
Pages
Day (App...)
Cum. pages per day
Edwards and Syphers (Chap. #)
Contents
Lecture 1
44
1
44
1
Varieties of accelerators
Particle Sources ,Linear Accelerators,
Circular Accelerators
Accelerator Technologies
Magnets, Radiofrequency Systems,Vacuum systems
Applications of Accelerators
Research
Other applications
Lecture 2
38
1
82
3.1-3.2
Review of basic electrodynamics
Magnetic guide fields used in accelerators
Particle trajectory equations of motion in accelerators
Lecture 3
15
1
97
3.1-3.2
Particle trajectory equations (continued)
Lecture 4
40
2
40
3.1-3.2
Piecewise matrix solutions to the linear trajectory equations
Lecture 5
41
2
81
3.1-3.2
Periodic systems
Twiss parameters and stability
Hill~Os equation and its solution
Courant-Snyder invariant and emittance
Lecture 6
35
2
116
3.2-3.3
Emittance in multi-particle beams
Lattice functions in non-periodic systems
Adiabatic damping
Momentum dispersion
Momentum compaction
Lecture 7
29
3
29
3.4
Lattice design: insertions and matching
Linear deviations from an ideal lattice:
Dipole errors and closed orbit deformations
Lecture 8
38
3
67
3.4
Linear deviations from an ideal lattice:
Dipole errors and closed orbit deformations (continued)
Quadrupole errors and tune shifts
Chromaticity
######tupole Compensation of Chromaticity
Lecture 9
21
3
88
2.1
Single Particle Acceleration:
Standing wave structures
Travelling wave structures
Lecture 10
35
4
35
2.2
Single particle acceleration:
Phase stability
Linear Accelerator Dynamics:
Longitudinal equations of motion:
Small amplitude motion
Longitudinal emittance and adiabatic damping
Large amplitude motion
Lecture 11
38
4
73
2.2
Linear Accelerator Dynamics:
Electron Linacs
Prebunching
Longitudinal dynamics in synchrotrons
Acceleration
Matching and filamentation
Longitudinal `Ogymnastics'O:
Debunching and Bunch rotation
Synchrotron radiation: introduction
Lecture 12
33
4
106
8.1-8.3
Synchrotron radiation: Longitudinal effects
Damping of synchrotron oscillations
Features of synchrotron radiation
Equations for the damping and quantum excitation of synchrotron oscillations:
Energy damping time and equilibrium energy spread
Lecture 13
36
5
36
8.1-8.3, 2.2
Transition Crossing in Proton synchrotrons
Synchrotron radiation: transverse effects
Vertical damping
Horizontal damping and quantum excitation
Equilibrium horizontal emittance
Lecture 14
32
5
68
4.1-4.2
Non-linear transverse motion
Floquet transformation
Harmonic analysis-one dimensional resonances
Two-dimensional resonances
Lecture 15
37
5
105
4.1-4.2
Non-linear transverse motion
Phase-amplitude variables
Second Dorder (quadrupole-driven) linear resonances
Third-order (######tupole-driven) non-linear resonances
Lecture 16
32
6
32
5.1
Linear coupling
Lecture 17
42
6
74
5.1
Linear coupling (continued)
Coupling coefficients for distributions of skew quadrupoles and solenoids
Pretzel Orbits
Motivation and applications
Implications
Long range beam beam effects
######tupole effects and path length changes
Lecture 18
38
6-7
84-28
7.2, 6.1
Beam loss and beam emittance growth
Mechanisms for emittance growth and beam loss
Beam lifetime:
from residual gas interactions; Touschek effect; quantum lifetimes in electron machines; Beam lifetime due to beam-beam collisions
Emittance growth:
from residual gas interactions; intrabeam scattering; random noise sources
Lecture 19
40
7
68
7.3
Beam cooling
Stochastic cooling
Electron cooling
Ionization cooling
Lecture 20
39
7-8
88-19
6.1
Collective effects in multi-particle Beams
Tune shifts and spreads:
Transverse space charge: direct and indirect
Beam-beam interaction
Lecture 21
36
8
55
6.3
Collective effects in multi-particle Beams:Wake functions and impedance
Wake fields and forces
Wake potentials and wake functions
Impedance; relation to wake functions
Longitudinal impedances in accelerators
Lecture 22
38
8
93
6.3
Collective effects in multi-particle beams:
Longitudinal impedances in accelerators
Transverse impedances in accelerators
Parasitic Losses
Lecture 23
41
9
41
6.4
Collective instabilities
Types of instabilities
An instability driven by narrow-band rf cavities: the Robinson instability
Lecture 24
50
9
91
6.4
Collective instabilities
Bunched beam instabilities driven by short-range wakefields:
Head-tail instabilities in synchrotrons
Lecture 25
18
10
18
Collective instabilities;
Rigid beam transverse instability
Lecture 26
36
10
54
Collective instabilities;
Rigid beam transverse multibunch instability
Animations
Lecture 11
Matched
bunch
This animated gif shows the
evolution in longitudinal phase space of a matched bunch in a bucket. The
frames show a snapshot of longitudinal phase space, every 10 turns, for a total
of 100 turns.
Mismatched
bunch: phase error
This animation shows the evolution
in longitudinal phase space of a bunch with a phase error of about 60 degrees.
The evolution is shown at every 5 turns, for a total of 100 turns.
Mismatched
bunch: beta error
This animation shows the evolution
in longitudinal phase space of a bunch with a mismatched longitudinal beta
function (a factor of three mismatch). The evolution is shown at every 5 turns,
for a total of 100 turns.
Bunch
rotation
This animation shows the rotation
in longitudinal phase space of a mismatched bunch. The evolution is shown at
every turn, for a total of 11 turns.
Lecture 12
Energy damping
This animation shows the damping
of both the centroid and the width of an electron beam which is injected
off-energy into a machine, with an energy spread larger than the equilibrium
energy spread.
Lecture 13
Transition
crossing
This animation shows the process
of transition crossing in a proton synchrotron. Longitudinal phase space is
shown on successive turns from turn 10 to turn 30; transition crossing occurs
at turn 20. Note the growth of the energy spread,
Office 2007 Pro Key, and reduction in the bunch
length, as the beam passes through transition
Injection
damping
This animation shows the real
space (x,y) profile of an injected electron beam. The oscillations you see are
the betatron oscillations, which, in this example, have a frequency different
by 20% in the two planes. The oscillations damp to zero with a time constant of
10 time units. The horizontal and vertical beam sizes also damp, with the final
vertical size much smaller than the final horizontal size,
Office Professional 2007 Key, resulting in a flat
beam.
Lecture 17
Pretzel
This animation illustrates
particle-antiparticle collisions using pretzel orbits for collision avoidance
at all but two points in the ring, for arrays of nine bunches. The two colors
represent the preztel orbits of the two species of particle; the dots represent
the bunches.
Office Professional Plus 2007 USPAS P450B Introduc
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