Synchrotron

1

SynchrotronAfter the cyclotron, the next idea was to

constrain the particles to a constant and accelerate them with RF fields Both the B field and the frequency (velocity)

will increaseOliphant (Australia) first developed the

idea but it was classifiedMcMillan first published the idea, named it

the synchrotron, and proposed to build one

Later Oliphant tried to build one in England but ran out of funds and graduate students

In the US, Berkeley (Bevatron) and Brookhaven (Cosmotron) raced to build one BNL won

2

BendingBending in a synchrotron is provided by

dipole magnets

The LHC circumference is ~27 km Packing fraction of ~64% gives ~2.8 km Thus B needed for p=7 TeV is ~8.3 T The use of superconducting magnets using

superfluid He at 1.8K are needed to reach this field Final magnet current is 11850 A

Bending achieved by 1232 15-m dipoles

GeVpTmB 3.0

3

Bending

LHC dipoles

4

Bending

5

Strong FocusingModern accelerators are possible

because of strong focusing Simply a name given to alternating magnetic

field gradients that now are provided by rotated quadrupoles

Invented by Courant, Livingston and Snyder from BNL

But actually patented several years earlier by Christofilos, a Greek elevator engineer! Who went on to develop the first fusion machine at

Livermore even though fusion was classified at the time

Also proposed ELF waves for communication with submarines

6

Strong Focusing

By rotating two quadrupoles through /2 we produce a net focusing effect in the transverse direction

7

Strong FocusingA good analogy comes from optics

Consider two lenses with focal lengths f1 and f2

01

for

111

21

21

2121

ff

d

f

ff

ff

d

fff

8

Strong Focusing In the case of quadrupoles, we define a

strength k

klf

lkxB

xdxdBl

B

lBx

l

f

xα

dx

dB

Bk

z

z

1

analogyby

/

is angle deflection the length of quadrupolea for

is lensa from angle deflection theoptics, in

1

9

Longitudinal Motion In a synchrotron, the particle’s

momentum is incremented on each turn by a precise voltage that will keep pace with the increasing magnetic field

The frequency is just 1/period

sVV sin0

R

cf

2

10

Longitudinal MotionA synchronous particle is one that always

arrives at the desired phase lag s on the flank of the rising RF wave (particle A)

For this to occur the accelerating RF frequency must be an integer multiple of f

h is called the harmonic number Chosen to make RF high in a convenient band

for the cavity and electronics h for the LHC is 35460, RF = 400 MHz The accelerator has 35460 buckets in which a

particle could be located and arrive synchronously

hffRF

11

Longitudinal Motion

Phase stability is what keeps the beam together longitudinally

12

Longitudinal MotionPhase stability is what keeps the

beam together longitudinally

Early particles at N1 get a lower kick and arrive later next turn

Late particles at M1 get a higher kick and arrive earlier next turn

13

Longitudinal Motion

The non-synchronous particle will oscillate about the synchronous one

The longitudinal phase space looks like

E

14

Transverse MotionBeam enters the synchrotron as a bundle

of trajectories spread about an ideal orbit

Unless corrected, the beam particles would naturally leave the beampipe

A restoring field is used that causes the beam to oscillate about the ideal orbit

ds

dzz

ds

dxx

szsx

,

,

15

Transverse MotionStandard LHC lattice cell looks like

16

Transverse MotionThe previous structure is called FODO

Focus – Drift space – Defocus – Drift space

The envelope of oscillations follows a function called (s) (s) has units of length but the units

bear no direct relation to the beam size The particles do not follow (s) but

rather oscillate within them in the form of a modified sinusoid

17

Transverse MotionWe wrote down an expression for the angular

deflection of a particle through a quadrupole

equations s Hill'called are equations These

orbit theof curvature the todue

focusingextra esacknowledg extra term thewhere

01

have weplane horizontal theIn

0

by give is motion of equation theThus

nt displacemea at strength and

length of quadrupolea for

is thisdirection vertical theIn

2

sks

x

zskz

zk

dskzdszd

18

Transverse Motion

In a class on accelerator physics we would proceed to solve these using matrix formalism (Twiss matrix)

Nonetheless you can see that Hill’s equations are reminiscent of harmonic motion except k depends on the position around the accelerator

19

Transverse MotionLet k be a constant (like in the constant

gradient machines like the Cosmotron and Bevatron

noscillatio theof wavelength

local theis then,1

define weif

2sinsinsin

0

000

2

2

ds

d

szzkszz

kzds

zd

20

Transverse Motion Again assuming k is constant

It’s important that Q not be an integer or simple fraction because otherwise the particle will repeat its path in the accelerator and see the same field imperfections The function in an LHC cell varies between 30 and

180 m These will build up into resonances and blow-up

the beam

RQ

Rds

2

2

21

Medical Linac

Block diagram

Pulse modulator

Klystron or magnetron

Bendingmagnet

Electronsource

Accelerating structure

Treatmenthead

22

Medical Linac

23

Treatment Head

24

Important AccessoriesWedgesDynamic wedgesBlocksMultileaf Collimator (MLC)Electronic Portal Imaging (EPID)

25

Electron Accelerators

Wedges3 or more fixed

wedgesauto-wedgedynamic wedge

Modify dose distribution

angle

26

Multileaf Collimator (MLC)

Used to define any field shape for radiation beams

Several variations to the theme: different leaf widths

(1cm to 0.4cm) replaces collimators

or additional to normal collimators

27

Intensity Modulation

Achieved using a Multi Leaf Collimator (MLC)

The field shape is altered step-by-step or dynamically while dose is delivered

MLC pattern 1

MLC pattern 3

MLC pattern 2

Intensitymap

28

IMRTMultiple individual

fields, each of them intensity modulated in two dimensions

Linac based IMRT

29

IMRT

Continuous rotation of a one dimensional fan beam which consists of many beamlets which can be turned on or off

Tomotherapy

30

Components ofHelical Tomotherapy

BinaryMLC

Helical ScanningRing detector at exit side

31

CyclotronThe first circular accelerator was the

cyclotron Developed by Lawrence in 1931 (for $25)

Grad student Livingston built it for his thesis About 4 inches in diameter

32

CyclotronPrinciple of operation

Particle acceleration is achieved using an RF field between “dees” with a constant magnetic field to guide the particles

33

CyclotronPrinciple of operation

c approaches vas cancelt won'

momentum and velocity in vsince relativityby Limited

222

daccelerate is particle the

asconstant remainsfrequency that theNote

for 2

m

eB

mv

eBvvf

e

p

e

mvB

cvmv

qvB

34

CyclotronWhy don’t the particles hit the pole

pieces? The fringe field (gradient) provides vertical

and (less obviously) horizontal focusing

35

CyclotronTRIUMF in Canada has the world’s largest

cyclotron

36

CyclotronTRIUMF

37

CyclotronNSCL cyclotron at Michigan State

38

Cyclotron

39

BetatronSince electrons quickly become

relativistic they could not be accelerated in cyclotrons Kerst and Serber invented the betatron for

this purpose (1940)

Principle of operation Electrons are accelerated with induced

electric fields produced by changing magnetic fields (Faraday’s law)

The magnetic field also served to guide the particles and its gradients provided focusing

40

Betatron

Principle of operation

Bguide = 1/2 Baverage

CoilSteel

Vacuum chamber

<B>B0

41

BetatronPrinciple of operation

orbit

orbit

eRBBeR

p

dt

BdeR

dt

dpF

dt

BdRE

dt

BdRRE

dt

BdA

dt

dEmf

BB

2

2

thenis electron theon force The2

2

2

is betatron theof field Bfor thet requiremen A

2

42

SynchrotronThe next idea was to constrain the

particles to a constant and accelerate them with RF fields Both the B field and the frequency (velocity)

will increaseOliphant (Australia) first developed the

idea but it was classifiedMcMillan scooped the idea, named it the

synchrotron and proposed to build oneLater Oliphant tried to build one but ran

out of funds and graduate students In the US, Berkeley (Bevatron) and

Brookhaven (Cosmotron) raced to build one BNL won

43

BendingRecall from our study of making

momentum measurements

The LHC circumference is ~27 km Packing fraction of ~64% gives ~2.8 km Thus B needed for p=7 TeV is ~8.3 T The use of superconducting magnets using

superfluid He at 1.8K are needed to reach this field Final magnet current is 11850 A

Bending achieved by 1232 15-m dipoles

GeVpTmB 334.0

44

Bending

LHC dipoles

45

Bending

46

Longitudinal Motion

Phase stability is what keeps the beam together longitudinally

47

Longitudinal Motion

The non-synchronous particle will oscillate about the synchronous one

The longitudinal phase space looks like

E

48

Longitudinal Motion In a synchrotron, the particle’s

momentum must be incremented on each turn by a precise voltage that will keep pace with the increasing magnetic field

The frequency is just 1/period

sVV sin0

R

cf

2

49

Longitudinal MotionA synchronous particle is one that always

arrives at the desired phase lag s on the flank of the rising RF wave (particle A)

For this to occur the accelerating RF frequency must be an integer multiple of f

h is called the harmonic number Chosen to make RF high in a convenient band

for the cavity and electronics h for the LHC is 35460, RF = 400 MHz The accelerator has 35460 buckets in which a

particle could be located and arrive synchronously

hffa

50

Transverse MotionBeam enters the synchrotron as a bundle

of trajectories spread about an ideal orbit

Unless corrected, the beam particles would naturally leave the beampipe

A restoring field is used that causes the beam to oscillate about the ideal orbit

ds

dzz

ds

dxx

szsx

,

,

51

Strong FocusingModern accelerators are possible

because of strong focusing Simply a name for alternating

magnetic field gradients that now are provided by rotated quadrupoles

Invented by Courant, Livingston and Snyder from BNL

But actually patented several years earlier by Christofilos, a Greek elevator engineer!Who went on to develop the first fusion

machine at Livermore even though fusion was classified at the time

52

Transverse Motion

53

Strong FocusingA good analogy comes from optics

Consider two lenses with focal lengths f1 and f2

01

for

111

21

21

2121

ff

d

f

ff

ff

d

fff

54

Strong Focusing In the case of quadrupoles, we define a

strength k

klf

lkxB

xdxdBl

B

lBx

l

f

xα

dx

dB

Bk

z

z

1

analogyby

/

is angle deflection the length of quadrupolea for

is lensa from angle deflection theoptics, in

1

55

Strong Focusing

By rotating two quadrupoles through /2 we produce a net focusing effect in the transverse direction

56

Transverse MotionStandard LHC lattice cell looks like

57

Transverse MotionThe previous structure is called FODO

Focus – Drift space – Defocus – Drift space

The envelope of oscillations follows a function called (s) (s) has units of length but the units

bear no direct relation to the beam size The particles do not follow (s) but

rather oscillate within them in the form of a modified sinusoid

58

Transverse MotionWe wrote down an expression for the angular

deflection of a particle through a quadrupole

equations s Hill'called are equations These

orbit theof curvature the todue

focusingextra esacknowledg extra term thewhere

01

have weplane horizontal theIn

0

by give is motion of equation theThus

nt displacemea at strength and

length of quadrupolea for

is thisdirection vertical theIn

2

sks

x

zskz

zk

dskzdszd

59

Transverse Motion

In a class on accelerator physics we would proceed to solve these using matrix formalism (Twiss matrix)

Nonetheless you can see that Hill’s equations are reminiscent of harmonic motion except k depends on the position around the accelerator

60

Transverse MotionLet k be a constant (like in the constant

gradient machines like the Cosmotron and Bevatron

noscillatio theof wavelength

local theis then,1

define weif

2sinsinsin

0

000

2

2

ds

d

szzkszz

kzds

zd

61

Transverse Motion Again assuming k is constant

It’s important that Q not be an integer or simple fraction because otherwise the particle will repeat its path in the accelerator and see the same field imperfections The function in an LHC cell varies between 30 and

180 m These will build up into resonances and blow-up

the beam

RQ

Rds

2

2

62

Medical Linac

Block diagram

Pulse modulator

Klystron or magnetron

Bendingmagnet

Electronsource

Accelerating structure

Treatmenthead

63

Medical Linac

66


Modern accelerators have a lot of treatment options, for example X-rays or electrons (dual

mode) Multiple energies2 X-ray energies5 or more electron

energies

67


X Ray Collimators may be (1) rectangular (conventional)

the transmission through the collimators should be less than 2% of the primary (open) beam

68


X Ray Collimators may be (2) Multi-Leaf collimators (MLC)


The transmission between the leaves should be checked to ensure that it is less than the manufacturer’s specification

Siemens MLC

69


Electron applicators, these may be open sided for modern accelerators using

double scattering foils or scanned beams enclosed for older accelerators using single

scattering foils both types should be checked for

leakage adjacent to the open beam on the sides of the applicators

Varian open sidedelectron cone

70


BinaryMLC


71


Wedges3 or more fixed

wedgesauto-wedgedynamic wedge

Modify dose distribution

angle

72

Multileaf Collimator (MLC)

Used to define any field shape for radiation beams

Several variations to the theme: different leaf widths

(1cm to 0.4cm) replaces collimators

or additional to normal collimators

73


Modern accelerators have a lot of treatment options, for example X-rays or electrons (dual

mode) Multiple energies2 X-ray energies5 or more electron

energies

74


X Ray Collimators may be (1) rectangular (conventional)


75


X Ray Collimators may be (2) Multi-Leaf collimators (MLC)


The transmission between the leaves should be checked to ensure that it is less than the manufacturer’s specification

Siemens MLC

76


Electron applicators, these may be open sided for modern accelerators using

double scattering foils or scanned beams enclosed for older accelerators using single

scattering foils both types should be checked for

leakage adjacent to the open beam on the sides of the applicators

Varian open sidedelectron cone

77


BinaryMLC


78

Plasma AccelerationMost accelerators have gradients of 1-

50 MV/m A 500 GeV ILC (International Linear

Collider) needs to be 10’s of km in length High energy electron circular accelerators

are limited by synchrotron radiation

Plasma accelerators have the potential of 10-100 GV/m PWFA – Plasma Wakefield Acceleration LWFA – Laser Wakefield Acceleration

79

Plasma Acceleration

Idea

80

Plasma Acceleration

Idea

81

Plasma Acceleration

Wakefield principle

82

Plasma AccelerationAcceleration picture

Propagate a relativistic electron or laser beam inside a plasma Beam is used to create the plasma as well – e.g.

from lithium vapor The electrons are displaced transversely Plasma ions attract the displaced electrons

and they start to oscillate A charge density wave is established behind

the beam that creates a very strong electric field (Ez)

Witness electrons can be placed behind the beam at the proper phase and be accelerated

The collective nature of the plasma makes this possible

83

Plasma Acceleration

Acceleration picture Actually what is happening is that

energy is taken (transformed) from the primary beam and given to the witness beam (or to the tail of the primary beam)

A driving beam is always required

84

Plasma AccelerationA simple calculation shows the gradient

strength

m

GeV

cm

nmcE

eEzE

m

neck

cmnn

nee

E

zik

p

zik

p

p

1010

e and

ˆThen

and

10onperturbatidensity plasmawith

Assume

3160

p0

0

0

02

p

3160

0

85

FFTB and FACET

At Stanford, using the SLAC linac FFTB – Final Focus Test Beam facility

Ended in 2006Achieved 50 GeV/m over a metern0~3x1017 e/cm3

FACET – Facility for Accelerator Science and Experimental TestsStarting in 2011Will study both e- and e+ acceleration

86

FFTB and FACET

SLAC linac

87

ILC using PWFA

One still needs to build a colliding beam accelerator though

Synchrotron

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