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, 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 94-01 (1994), vol. 1 and vol. 2

Links:  http://preprints.cern.ch/cernrep/1994/94-01/94-01_v1.html and http://preprints.cern.ch/cernrep/1994/94-01/94-01_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

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’s 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

Sextupole 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 “gymnastics”:

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 –order (quadrupole-driven) linear resonances

Third-order (sextupole-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

Sextupole 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, 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, 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.