Instructor : Gerald Dugan
This course will cover the
fundamental physical principles of particle accelerators, with a focus on
circular highenergy colliders. It will include beam optical design, the
singleparticle 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, 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", John Wiley & Sons, Inc., (1993)Other references:
A useful online reference
:
CERN Accelerator School: 5th General Accelerator
school, CERN 9401 (1994), vol. 1 and vol. 2
Links: http://preprints.cern.ch/cernrep/1994/9401/9401_v1.html and http://preprints.cern.ch/cernrep/1994/9401/9401_v2.html
Other useful references:
Particle Accelerator
Physics I (2nd edition, 1998), by
Helmut Wiedemann
Physics of Collective Beam
Instabilities in High Energy Accelerators (1993), By Alexander W. Chao
Course tentative outline
Lecture # 
Pages 
Day (App...) 
Cum. pages per day 
Edwards and Syphers (Chap. #) 
Contents 
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 

38 
1 
82 
3.13.2 
Review of basic electrodynamics Magnetic guide fields used in accelerators Particle trajectory equations of motion in accelerators 

15 
1 
97 
3.13.2 
Particle trajectory equations (continued) 

40 
2 
40 
3.13.2 
Piecewise matrix solutions to the linear trajectory equations 

41 
2 
81 
3.13.2 
Periodic systems Twiss parameters and stability HillÕs equation and its solution CourantSnyder invariant and emittance 

35 
2 
116 
3.23.3 
Emittance in multiparticle beams Lattice functions in nonperiodic systems Adiabatic damping Momentum dispersion Momentum compaction 

29 
3 
29 
3.4 
Lattice design: insertions and matching Linear deviations from an ideal lattice: Dipole errors and closed orbit deformations 

38 
3 
67 
3.4 
Linear deviations from an ideal lattice: Dipole errors and closed orbit deformations (continued) Quadrupole errors and tune shifts Chromaticity Sextupole Compensation of Chromaticity 

21 
3 
88 
2.1 
Single Particle Acceleration: Standing wave structures Travelling wave structures 

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 

38 
4 
73 
2.2 
Linear Accelerator Dynamics: Electron Linacs Prebunching Longitudinal dynamics in synchrotrons Acceleration Matching and filamentation Longitudinal ÒgymnasticsÓ: Debunching and Bunch rotation Synchrotron radiation: introduction 

33 
4 
106 
8.18.3 
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 

36 
5 
36 
8.18.3, 2.2 
Transition Crossing in Proton synchrotrons Synchrotron radiation: transverse effects Vertical damping Horizontal damping and quantum excitation Equilibrium horizontal emittance 

32 
5 
68 
4.14.2 
Nonlinear transverse motion Floquet transformation Harmonic analysisone dimensional resonances Twodimensional resonances 

37 
5 
105 
4.14.2 
Nonlinear transverse motion Phaseamplitude variables Second Ðorder (quadrupoledriven) linear resonances Thirdorder (sextupoledriven) nonlinear resonances 

32 
6 
32 
5.1 
Linear coupling 

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 Sextupole effects and path length changes 

38 
67 
8428 
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 beambeam collisions Emittance growth: from residual
gas interactions; intrabeam scattering; random noise sources 

40 
7 
68 
7.3 
Beam cooling Stochastic cooling Electron cooling Ionization cooling 

39 
78 
8819 
6.1 
Collective effects in multiparticle Beams Tune shifts and spreads: Transverse space charge: direct and indirect Beambeam interaction 

36 
8 
55 
6.3 
Collective effects in
multiparticle Beams:Wake functions and impedance Wake fields and forces Wake potentials and wake functions Impedance; relation to wake functions Longitudinal impedances in accelerators 

38 
8 
93 
6.3 
Collective effects in multiparticle beams: Longitudinal impedances in accelerators Transverse impedances in accelerators Parasitic Losses 

41 
9 
41 
6.4 
Collective instabilities Types of instabilities An instability driven by narrowband rf cavities: the Robinson instability 

50 
9 
91 
6.4 
Collective instabilities Bunched beam instabilities driven by shortrange wakefields: Headtail instabilities in synchrotrons 

18 
10 
18 

Collective instabilities; Rigid beam transverse instability 

36 
10 
54 

Collective instabilities; Rigid beam transverse multibunch instability 
Animations
Lecture 11
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.
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.
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.
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.
This animation shows the damping
of both the centroid and the width of an electron beam which is injected
offenergy into a machine, with an energy spread larger than the equilibrium
energy spread.
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, and reduction in the bunch
length, as the beam passes through transition
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, resulting in a flat
beam.
This animation illustrates
particleantiparticle 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.