Post on 08-Jan-2016
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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
64
65
66
Electron Accelerators
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
Electron Accelerators
X Ray Collimators may be (1) rectangular (conventional)
the transmission through the collimators should be less than 2% of the primary (open) beam
68
Electron Accelerators
X Ray Collimators may be (2) Multi-Leaf collimators (MLC)
the transmission through the collimators should be less than 2% of the primary (open) beam
The transmission between the leaves should be checked to ensure that it is less than the manufacturer’s specification
Siemens MLC
69
Electron Accelerators
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
Components ofHelical Tomotherapy
BinaryMLC
Helical ScanningRing detector at exit side
71
Electron Accelerators
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
Electron Accelerators
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
Electron Accelerators
X Ray Collimators may be (1) rectangular (conventional)
the transmission through the collimators should be less than 2% of the primary (open) beam
75
Electron Accelerators
X Ray Collimators may be (2) Multi-Leaf collimators (MLC)
the transmission through the collimators should be less than 2% of the primary (open) beam
The transmission between the leaves should be checked to ensure that it is less than the manufacturer’s specification
Siemens MLC
76
Electron Accelerators
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
Components ofHelical Tomotherapy
BinaryMLC
Helical ScanningRing detector at exit side
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