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The Large Hadron Collider
Machine, Experiments, Physics
Accelerator physics and the LHC
Johannes Haller
Thomas Schörner-Sadenius
Hamburg University
Summer Term 2009
SETTING THE STAGE
“Everyman’s accelerator”: Television set!
deflection
From there it is a long way to the LHC …
… we will make it short!
diagnostics
source
acceleration
… but accelerators have come a long way: Thompson
watched scintillations of particles on screens in glass
pipes  “cathode rays”. Deflection of electrons with
E,B fields!
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“Livingston plot”:
– About a decade in energy per time decade! Trend
also for the future? Costs? Space?
– What about cosmic accelerators? Astroparticle
physics?
– Caveat: Plot not precise – many machines run at
different energies with different particles …
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MOTIVATION, BASICS
Basics of all beam-accelerating/–steering elements:
   dp
– Lorentz force: 
Remember: Quantum mechanics, relativity
– DeBroglie: connection between
h
wave length (resolution power)

p
and particle momentum:
– Einstein: Wish for ever-higher
E  mc2
center-of-mass energies
Want accelerators with ever higher energies to
investigate ever smaller constituents of nature
and to find new, heavy objects.
F  q ( E  v  B) 
– For the simple case of a perpendicular B field:
mv 2
mv p
 qvB  B 

r
qr
qr
– Which fields for particle deflections? E or B?
 chose
p  0.3GeV / c q  e r  1m
magnetic fields!
B  1T E  300MV / m
Basics of accelerators: Electrodynamics, Maxwell:
 
D  
 
B  0
 

  E  B
   
 B  j  D
Electric and magnetic fields are used to accelerate,
collect and guide clouds of particles through an
accelerator. We will discuss:
- History of accelerators
- Dipols, quadrupoles, sextupoles, …, focusing
- Optical lattices
- Accelerations
-…
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Circular or linear accelerators?
- Linear: + Only focussing elements required.
– One acceleration only!
+ No synchrotron losses!
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- Circular: + Repeated acceleration!
1E
E   
– More complex layout.
Rm
– Synchroton losses
Particle types?
- Electrons: high synchrotron losses
ideal point sources
well-known initial states.
- Protons: necessary B field rises with m (if r const)!
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SYNCHROTRON RADIATION
Emission is tangential to the orbit and collimated
in narrow cone:
Power radiated from relativistic particle under
centripetal acceleration:
e 2c
1
E4
PS 


60 (m0c 2 ) 4 R 2
Energy lost per orbit:
2R e 2
1
E4
W   PS dt  PS



c
30 m0c 2 4 R
Difference electron/proton
for same energy,radius:

– Electron with v~c:
Ps ,e
Ps , p

m4p
4
e
m
 1.13 1013
E 4 [GeV 4 ]
W  8.85 10
MeV
 [km]
5
– Proton with v~c:
W  7.8 10
6
E 4 [TeV 4 ]
MeV
 [km]
– Numbers:
electrons in LEP: 3 GeV/turn
protons in LHC: 6.7 keV/turn
Issues of radiation protection of humans,
experiments, electronics, …
At LHC: Radiation will be visible to the eye!
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COLLIDER VERSUS FIXED-TARGET
Then the collider:
Consider the following two scenarios (for protons):
– 450 GeV is the maximum SppS energy at CERN!
 p1  p2 2  E1  E2 2   p1  p 2 2 
2
2
 2 E   900 GeV 
2
s  ECM
  p1  p2 
2
2 m
 ???
m s1   
Let’s do the calculation: First fixed-target:
 p1  p2 2  E1  E2 2   p1 2 

 E12  E22  2 E1 E2  p12 


 m 2  p12  m 2  2 E1m  p12 
 2m 2  2 E1m 
 2m( E1  m) 
 2m 2 (  1)  29 GeV 
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 If technically possible build colliders!
- Fixed-target experiments today used if strong
boosts wanted, for example to produce beams of
certain particles (pions, kaons, neutrinos, …) or
if asymmetry required (BABAR) …
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ACCELERATION 1: OVERVIEW
Acceleration involves several steps:
– Power generation in klystrons
 generation of very intense,
high-frequency electromagnetic fields.
– Transport of this energy from the klystron
to the accelerator
 wave guides
– Power transmission from electromagnetic
wave to particles
 accelerating resonating cavities
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ACCELERATION 2: POWER GENERATION
Today, acceleration happens with high-frequency RF
EM fields. The necessary power is generated in
klystrons (field amplifiers):
– Low-current electron beam is accelerated and
cut into bunches by applying HF fields in first
resonating cavity.
– Bunched electrons induce high-power HF fields in
second cavity that can then be transferred to
accelerating cavities in the accelerator ring.
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ACCELERATION 3: POWER TRANSFER
Power is brought to the cavities in wave guides:
– Behaviour of these (and of accelerating cavities)
dictated by wave equation:
One can show (B parallel, E perpendicular to wall):
– General solution of wave equation:
f x ( x)  A sin( k x x) B cos( k x x)
 2 
 
 
2
E  c E  0  E r   k E r   0
With wave number:
k

c

f y ( y )  C sin( k y y ) D cos( k y y )
Applying boundary conditions for E,B fields:
2
k x a  m
k y b  n

Considering, for simplicity, only z direction and
assuming:
E x  0 E y  E0 sin(
… one can show that a solution is given by
kz2  k 2  kx2  ky2  k 2 
2
2
m,n specify the mode of the guide. Example TE10:
E z x, y,z  f x x f y y f z z
Ez  E0 eikz z
 m   n 
k 
 

a

  b 
2
c
f x f y

fx fy
x ikz z
)e
a
Ez  0
Special case: rectangular wave guide:

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ACCELERATION 4: ACCELERATING CAVITIES
Accelerating cavities: Particles accelerated by `riding’
on standing EM wave:
– General solution of wave equation:






W (r , t )  A exp i t  k r  B exp i t  k r
Alternative (historic): alternating positive and
negative electric fields:

– If wave completely reflected, then A=B:
 


W (r , t )  2 A cos k r exp it 
– Stable standing wave with constant
amplitude if for cavity of length l:
(n integer)
 Length l has to match RF
Frequency and particle
momentum.
ln
z
2
– Drift tubes alternatingly connected to poles of HF.
– Acceleration between tubes.
– Drift lengths, energy and frequencies need to be
tuned.
– No continuous particle flow! Bunched operation!
– Efficient for light particles (synchrotron radiation)
– Today also with resonating cavities (ILC).
– Energy after n drift tubes:
En  nqU 0 sin 
(Phase ψ between particles and field).
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PARTICLE STEERING (1)
Focusing (simple approach):
Dipole magnets:
– B field perpendicular  force perpendicular to
velocity v and B field!
B  p qR
Dipoles define beam momentum!
Quadrupole magnets: More complicated field shape:
Gradient for particles in x and y, no field on axis
 focusing / defocusing action!
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 Combine two quadrupoles to have net focusing in
two dimensions: The FODO structure!
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PARTICLE STEERING (2)
Dipole and Qaudrupole magnets:
– provide stable trajectory for particles with nominal
momentum
Sextupole magnets:
– Correct trajectories of off-momentum particles.
Multipole magnets (up to 10 or 12 poles)
– Used to compensate field imperfections of the
dipoles. Improve beam quality and lifetime.
From these elements a “lattice” is build up – aim for
regular structures for easy-to-understand machine:
Formalism for description: multipole expansion:
- use Lorentz force, B=(Bx,By,0), v=(0,0,vs), path
length s and
mv2
e
1
 qvB 
By ( x, y, s) 
r
p
R( x, y, s)
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Develop B field in vicinity of orbit (x,y << R):
2
3
dB y
e
e
1 d By 2 1 d By 3
B y ( x)  ( B y 0 
x
x 
x  ...)
p
p
dx
2! dx 2
3! dx 3
1
1
1
  kx  mx2  x 3  ...
R
2!
3!
Dipole:
deflection
Quadrupole
Focusing
Sextupole
trajectory
Octupole
trajectory
With multipoles I influence the path in great
details. Use mainly dipoles and quadrupoles
(“linear optics”, easy to calculate).
Description of lattice / behaviour of beams: Matrix
formalism:
– 6 quantities to describe beam particles: x,x’,y,y’,s,δ
– Each optical element corresponds to one 6*6 matrix
acting on the 6-vector of the particle. Describe ring
by product of “transfer” matrices:
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 x( s ) 
 x(0) 

  M N  ...  M 2  M 1 



x
(
s
)
x
(
0
)




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PARTICLE FOCUSING (1)
(Weak) transverse focusing:
– Particles tend to leave orbit horizontally and/or
vertically (Coulomb repulsion, starting conditions).
– In horizontal plane deflecting dipoles have weak
focusing action: Consider particle with distance x to
beam:
Constant gradient:
B field weaker towards
larger r, r component!
 Trajectory is bent towards orbit! Focusing! But
oscillations!
– Vertically slightly more difficult:
 constant gradient scheme for magnets with
large dipole gaps: Small Br component.
 Particles perform oscillations around orbit!
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More efficient: strong focusing and “alternating
gradient scheme”:
- constant gradient: dipoles opened towards outside.
- Idea Livingston et al: Open some dipoles towards
inside  different focusing effect  also smaller
dipole gaps and thus higher fields possible.
- First used at AGS and CERN PS (30 GeV).
- Still one step further: FFAG: Gradient spiraling
around orbit  not pursued.
- Today: Focusing with multipoles (FODO!).
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PARTICLE FOCUSING (2)
Strong focusing with two quadrupoles in action:
Longitudinal focusing and phase stability:
– Particles not all in sync with accelerating phase.
– Solution: On–time particles should not arrive on
the peak:
Particle late/slow
 larger U, acceleration
Particle early/fast:
 Smaller U, acceleration
For not too large amplitudes: harmonic oscillation
around orbit and phase: synchrotron oscillations!
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PARTICLE FOCUSING (3), BEAM CHARACT.
Stochastic cooling:
… just a few buzz words:
- Nobel prize S. v.d. Meer 1984
– β function: Measure for beam diameter; strictly
- Active correction to wandering bunches.
speaking: β(s) is s-dependent amplitude of
- “Nobel prize for finding out that the diameter is less particle oscillations along the orbit.
then the circumference …”
– Emittance ε: Measure for the divergence of the
- especially important for anti-protons!
beam (beam quality).
– Acceptance: A=min(d2(s)/β(s)),
d=Strahlrohrdurchmesser, space for the beam at
the narrowest position in s.
– Enveloppe E:
E(s)   (s)
– Luminosity: Measure for beam intensity in cm-2s-1.
L f
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4  x  x* y  y*
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EXAMPLES OF ACCELERATORS (1)
Betatron:
- Vacuum pipe with electrons serves as second
transformator winding
Cyclotron:
– constant B field, but r~v  orbit timeτ=const.
– Particles run on spirals, on each orbit two
acceleration steps.
– Maximum energy 33 MeV at 2 T (protons).
 

  E  B
- Variable flux in magnet yoke  variable B
field  variable E field for acceleration.
- Also guiding field grows with the flux.
- Only ¼ of oscillations useable.
- Maximum energy limited by synchrotron radiation,
~100 MeV.
– relativistic effects: m γm.    eB m
 adapt frequency: synchro-cyclotron.
– Also iso-cyclotron: adapt B field with radius.
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CYCLOTRON IN ACTION
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EXAMPLES OF ACCELERATORS (2)
Synchrotron:
– With realistic fields and energies E > 1 GeV radius
for single magnets gets too large.
– Idea: Keep R constant and increase E and B in
synchronised way.
mv mc 2v
E
r
 2 
qB
qc B qcB
(v  c)
– Particles travel along orbit many 106 times
 importance of focusing
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– finally combine two synchrotrons  collider!
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OVERVIEW OF HEP ACCELERATORS
Collider
Start/end
Beams
Max. energy
[GeV]
Circumference or
length [km]
PETRA (DESY)
1978-86
e +e –
23.4
2.304
SLC (SLAC)
1989-99
e +e –
50
1.45 + 1.47
LEP (CERN)
1989-2000
e +e –
104
26.7
ILC (?)
20??-??
e +e –
500?
15+15 (?)
KEKB (KEK)
1999-??
e +e –
8 x 3.5
3.0
PEP-II (SLAC)
1999-??
e +e –
9 x 3.1
2.2
HERA (DESY)
1991-2007
ep
27.5 x 820/920
6.3
SppS (CERN)
1981-1990
ppbar
315
6.9
TEVATRON
(FNAL)
1987-2009/10
ppbar
1000
6.28
LHC (CERN)
2008-??
pp
7000
26.7
????
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DESY ACCELERATORS
Hermes
H1
ZEUS
Petra/DESY
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FERMILAB AND SLAC ACCELERATORS
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CERN ACCELERATORS
LEP, LHC
Spp
S
ISR
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PS
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LHC ACCELERATOR SYSTEM
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LHC
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LHC REALISATION
Enveloppe of the LHC:
- Regular pattern in the arcs.
- Straight sections: max. focusing at IR:
LHC RF system:
– operates at 400 MHz.
– 16 SC cavities, 8 per beam.
– peak accelerating voltage: 16 MV / beam
(for comparison: LEP at 104 GeV: 3600 MV)
reason: synchrotron loss: LEP: 3 GeV / turn
LHC: 6.7 keV / turn
LHC dipoles:
- Collision point beam size (rms, defined by β* )
- CMS & ATLAS: 16 μm, LHCb: 22-160 μm,
- ALICE: 16 μm (ions), >160 μm (p)
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LHC: REALISATION
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LHC IMPRESSIONS
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LHC IMPRESSIONS – AND AN ACCIDENT
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LHC IMPRESSIONS – AND AN ACCIDENT
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LHC IMPRESSIONS – AND AN ACCIDENT
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LHC IMPRESSIONS – AND AN ACCIDENT
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LHC DETAILS
Increase with respect to existing accelerators :
In :
• A factor 2 in magnetic field
– We
• A factor 7 in beam energy
• A factor 200 in stored energy
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POWER IN THE LHC
Comparison:
– Energy of A380 at 700 km/h corresponds to energy
stored in the LHC magnet system!
– Sufficient to heat up and melt 12 tons of copper!
Energy in the beams:
– corresponds to 90 kg of TNT
– 8 litres of gasoline
– 15 kg of chocolate
 It’s how easy the energy is
released that matters !
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HISTORY AND STATUS OF THE LHC
History:
– 1982: First studies for LHC project
– 1983: Z/W discovery at SppS
– 1989: Start of LEP operation
– 1994: Approval of CERN project by CERN Council
– 1996: Final decision to start LHC construction
– 1996: LEP operation > 80 GeV (W factory)
– 2000: Final year of LEP operation
– 2001: CERN financial crisis: 1B CHF missing 
extension of LHC program
– 2002: Removal of LEP equipment
– 2003: Start of LHC installation
– 2005: Start of hardware commissioning
– 2007: Magnet failure  6 months delay
– 2008: Beam commissioning
- 10 September 2008: First beams
- 19 September 2008: Helium leak
- Expected restart: October 2010.
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THINGS NOT COVERED (IN DETAIL)
… due to time constraints or lack of interest:
– Interlock
– Quenching and machine protection
– Beam dumping
– Superconductivity
– Collimation and lifetime
– Commissioning and operation
– Interaction region layout
– Comparison to Tevatron
– Preacceleration and injection
– old accelerator principles as cascade accelerators
(Cockcroft-Walton), “Band-Generator”, …
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Applications of accelerators:
– Cancer therapy
– TV, monitors
– production of radio-active substances
(radio chemistry).
– material sciences
–…
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LITERATURE
Some literature on accelerators (for HEP):
 E. Wilson, “An Introduction to Particle Accelerators”,
Oxford 2001
 H. Wiedemann, “Particle Accelerator Physics” I & II,
Springer 1993/1995
 K. Wille, Physik der Teilchenbeschleuniger,
Teubner 1992 (auch auf Englisch)
 Particle Data Group, Phys. Rev. D66 (2002) 010001-1,
http://pdg.lbl.gov
 SLAC Linear Accelerator Center,
http://www2.slac.stanford.edu/vvc/accelerators/
 CERN,
http://public.web.cern.ch/Public/ACCELERATORS/accintro.html
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