Engines of Discovery
R.S. Orr
Department of Physics
University of Toronto
Berkley 1930
1 MeV
Geneva 20089

14 TeV
Birth of Particle Physics and Accelerators
• 1909
Geiger/Marsden MeV a backscattering - Manchester
• 1919
Rutherford disintegrates Nitrogen
• 1927
Rutherford demands accelerator development
Particle accelerator studies - Cavendish
• 1929
Cockcroft and Walton start high voltage experiments
• 1932
The goal achieved:
-
Manchester
Cockcroft + Walton split Li nucleus
Cockcroft-Walton Generator
665 kV
Ising – 1924
Resonant Accelerator Concept
Wideroe - 1928
Alternating (radio frequency) fields allow higher voltages
• The acceleration occurs in the electric field between cylindrical drift tubes.
• The RF power must be synchronised with the motion of the electrons, so that
acceleration occurs in every gap.
Linear Accelerator = LINAC
Recirculation Concept - Cyclotron
Radio frequency
alternating voltage
D-shaped RF cavities
time t =0
Hollow metal
drift tubes
time t =½ RF period
• Orbit radius increases with momentum
• Orbital Frequency independent of momentum
• Particle motion and RF in phase
Lawrence:
4” – 80 keV
11” - 1.2 MeV
Equilibrium Orbit
Constant revolution frequency
f rev
v
v eB
eB



2  2  mv 2  m
Magnetic rigidity
mv p
B 

e
e
Orbit Stability
Slight Displacement from Equilibrium Orbit
Particle Lost
Vertical and Horizontal Focusing
Vertical Orbit Stability in Lawrence’s Cyclotron
Cross Section Thru Ds
Electrostatic Focusing Lens
Orbital Stability in a Cyclotron
SHIMS
q
F  v B
c
Betatron Oscillations
Horizontal
R
Bz  Bz0  
r
 mv
2
R
Fx 
e
 vBz0  0
c
 mv
2
r
Fx  
n
e
 vBz
c
 mv 2 x
R
R
1  n 
v
x 
1 n
R
n 1
Vertical
Field Index
m
Equilibrium Orbit
Simple Harmonic
dt 2
m
d2y
dt 2
m
Weak Focusing
 n
d2y
dt
Stable Oscillations around
Equilibrium orbit
e
 vBx
c
Bx Bz

0
z
x
Centrifugal = Lorentz
on equilibrium orbit
Restoring Force
d2y
2
Bz e
v  Fz
R c
 n m
z  n
v2
R
v2
R2
n 1
2
0
This machine is just
a model for a bigger
one, of course
This machine is just
a model for a bigger
one, of course
1931
104 Volts
1953
109 Volts
This machine is just
a model for a bigger
one, of course
1932
106 Volts
1960
1010 Volts
Invention of the Synchrotron
Marcus Oliphant
– later to become
Governor of South Australia
Synchrotron Ring Schematic
Bending magnets
Accelerating
cavity
• Increase magnetic field
during acceleration.
• Constant orbital radius
Vacuum
tube
Focusing magnets
 1

 1
 f

0
 1
1
L




1


1   0 1   

 f
 1
 L

 f2

0

1 

0

1 


L
 L

1

L


f


L
 L
  f 2 1 f 


f
Net Focusing
• FODO Lattice
• Strong Focusing
Strong Focusing
• Field Index set by Pole Face Shape
• Weak, n = 0.5
• Strong, n = 3500
• Strong Focusing = Alternating Gradient
• “Combined Function” Magnet
Enormous Cost Saving
Strong Focusing Magnet
Weak Focusing Magnet
•
•
•
•
Strong Focusing = Alternating Gradient
Reduce amplitude of betatron oscillations
Reduce diameter of vacuum pipe
Reduce Aperture of Magnets
• 35 GeV (CERN PS, AGS) costs same as 7 GeV (NIMROD)
TRAJECTORY
BEAM ENVELOPE
2
d Y
ds
2
 K  s Y  0
Y  s   A  s  cos   s    

Y  s     s  cos   s    

d 2
ds
2
 K  s 
1
3
 s  2 s
Amplitude of betatron oscillations
angle
• Single Particle Phase Space
• Beam Envelope
position
Shape of phase space changes along accelerator lattice
Area constant -> Liouville
• Real Accelerator
• Non-linear
Successive turns around accelerator lattice
A
B
C
• B is synchronous with RF phase
• A too energetic to be in phase
• B not energetic enough to be in phase
 Es n1   Es n  eV sin s
 1
1 
 2  2 
     

Closed Oscillations in Phase
(non relativistic)
Synchronous particle
Change in transit time around lattice
 Es n1   Es n  eV sin s
n1  n 
 c
2
2
v Es
En1
Synchronous Particle
Non-Synchronous Particle
En1  En  eV  sin   sin s 
• Symplectic Mapping
• Preserves Phase Space
Unconfined motion = “lost” particles
Stable oscillations
Trapped by RF
Synchronous particle
Transformed “s” into “Φ”
position around lattice
Particle orbits in energy-phase
separatrix
 Es n1   Es n  eV sin s
d  c
E
 2
dn
v Es
2
d E
 eV  sin   sin s 
dn
Non-linear equations
Describing deviation in phase and energy from synchronous orbit
H
Initial condition
 cos    sin s 
separatrix
RF Bucket
2
1  d   c
constant = Η = 
  2
2  dn 
v Es
2
 cos    sin s 
CERN Seen from the Air
• Tunnels of CERN accelerator complex
superimposed on a map of Geneva.
• Accelerator is 50 m underground
• 25 km in circumference
Superconducting Magnet
8 Tesla
•In order to accelerate protons to high energy, must
bend them in circular accelerator
•7 TeV momentum needs intense magnetic field
LHC 2002
LHC 2003
Dipole Cold Masses
Ph. Lebrun
ATLAS Plenary Meeting
18 February 2005
Infrastructure completed in 2003
Underground
Dipole-dipole interconnect
March 2006
Descent of the Last Magnet, 26 April 2007
300 m underground at 2 km/h!
RF Modules
Refrigeration Units at 1.8 K
Point 8
QSCC QSCA QSCB QSCC
Shaft
QSRA QSRB
Cavern
QURA
QUIC
QURC
Sector 7-8
QURC
Sector 8-1
Tunnel
Air Liquide
Surface
Storage
IHI Linde
Cryogenic Distribution
Point 8
QSCC QSCA QSCB QSCC
Shaft
QSRA QSRB
Surface
Storage
Cavern
QURA
QUIC
Sector 7-8
QURC
Sector 8-1
Tunnel
QURC
DFBA Electrical Feed Box
Connection to
magnets
x 16
Vacuum equipment VAA
Current lead chimneys
Sh
uff
lin
gm
13kA leads
Hi
gh
SHM/HCM
interconnect
2 per LHC Point
6kA leads
od
ule
cu
rre
Jumper cryo
connection to QRL
nt
m
od
ule
13
k
A&
Supporting beam
6k
Al
ea
ds
6kA leads
Removable door
HCM/LCM
interconnect
600A leads
Lo
w
cu
rre
nt
mo
du
le
6k
A
&6
00
Al
ea
ds
1.9K
4.5K
13 kA HTS Current Leads
6 kA current leads with water-cooled cables
Lyn Evans – EDMS docment no. 970483
45
Beam 2 first beam – D-Day
46
Beam on turns 1 and 2
Courtesy R. Bailey
47
No RF, debunching in ~ 25*10 turns, i.e.
roughly 25 mS
Courtesy E. Ciapala
48
First attempt at capture, at exactly the wrong
injection phase…
Courtesy E. Ciapala
49
Capture with corrected injection phasing
Courtesy E. Ciapala
50
Capture with optimum injection phasing,
correct reference
Courtesy E. Ciapala
51
LHC longitudinal bunch profile Beam 2
52
H wire scan
Lyn Evans – EDMS document no. 970483
53
Kick response compared with
theoretical optics
54
Alors, c’est fini!
Et maintenant?
• Storage Ring
• Stable phase = 0
• No acceleration
Synchrotron (phase) oscillations
d 2 
dn2
d 2 
dn
2
  c 2eV


cos s    0
2
 v E

s


  2 s    0
 0 ;
 0 ;
   t 
   t 
; cos s  0
; cos s  0