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Introduction to particle accelerators
Walter Scandale
CERN - AT department
Lecce, 17 June 2006
W.Scandale, Introduction to Particle Accelerators 12 June 2005 2
Introductory remarks
Particle accelerators are black boxes producing � either flux of particles impinging on a fixed target� or debris of interactions emerging from colliding particles
In trying to clarify what the black boxes are one can� list the technological problems� describe the basic physics and mathematics involved
Most of the phenomena in a particle accelerator can be described in terms of classical mechanics and electro-dynamics, using a little bit of restricted relativity
However there will be complications:� in an accelerator there are many non-linear phenomena (stability of motion, chaotic
single-particle trajectories)� there are many particles interacting to each other and with a complex surroundings� the available instrumentation will only provide observables averaged over large
ensembles of particles
In two hours we can only fly over the problems just to have an overview of them
W.Scandale, Introduction to Particle Accelerators 12 June 2005 3
Inventory of synchrotron components
W.Scandale, Introduction to Particle Accelerators 12 June 2005 4
Bending magnet
Efficient use of the current -> small gap heightField quality -> determined by the pole shapeField saturation -> 2 Tesla BEarth = 3 10-5 Tesla
B > 2 Tesla -> use superconducting magnets BLHC = 8.4 Tesla
W.Scandale, Introduction to Particle Accelerators 12 June 2005 5
Quadrupole magnet
Vertical focusingHorizontal defocusing
g=gradient [T/m]
W.Scandale, Introduction to Particle Accelerators 12 June 2005 6
Alternate gradient focusing
QF QF QFQD QD
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Mechanical analogy for alternate gradient
W.Scandale, Introduction to Particle Accelerators 12 June 2005 8
Basic 2-D equation of motionin a dipolar field
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Basic 2D equation of motion
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Basic 2D equation of motion
FODO structure
Periodic envelop
Cos-like trajectory
Sin-like trajectory
Multi-turn trajectory
W.Scandale, Introduction to Particle Accelerators 12 June 2005 11
Longitudinal stability
Momentum compaction
W.Scandale, Introduction to Particle Accelerators 12 June 2005 12
Chromaticity and sextupole magnet
Dispersion orbit
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Chromaticity correction and non-linear resonance
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Emittance
W.Scandale, Introduction to Particle Accelerators 12 June 2005 15
Synchrotron radiation
W.Scandale, Introduction to Particle Accelerators 12 June 2005 16
Synchrotron radiation and beam size
Adiabatic damping Synchrotron light emission
W.Scandale, Introduction to Particle Accelerators 12 June 2005 17
Effect of synchrotron light
W.Scandale, Introduction to Particle Accelerators 12 June 2005 18
Collective effects
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Instabilities and feedback
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Space charge
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Beam size
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Fixed target versus collider rings
AdvantageColliderFixed target
Bruno Touschek
W.Scandale, Introduction to Particle Accelerators 12 June 2005 24
Lepton versus hadron colliders
->
->
(At the parton level )
W.Scandale, Introduction to Particle Accelerators 12 June 2005 25
Lecture II
W.Scandale, Introduction to Particle Accelerators 12 June 2005 26
LHC lay-out
C = 26658.90 m
Arc = 2452.23 m
DS = 2 x 170 m
INS = 2 x 269 m
Free space
for detectors: ± 23 m
W.Scandale, Introduction to Particle Accelerators 12 June 2005 27
LHC features
Technological challenge
(+1)
W.Scandale, Introduction to Particle Accelerators 12 June 2005 28
Bunch spacing25 ns - 8.3 m
ε∗ = 3.75 10-6 m
W.Scandale, Introduction to Particle Accelerators 12 June 2005 29
Maximum B-field
W.Scandale, Introduction to Particle Accelerators 12 June 2005 30
Cos(θ) coil
W.Scandale, Introduction to Particle Accelerators 12 June 2005 31
Superconducting dipole
W.Scandale, Introduction to Particle Accelerators 12 June 2005 32
Collider luminosity
High L needs:
W.Scandale, Introduction to Particle Accelerators 12 June 2005 33
Beam-beam interaction
W.Scandale, Introduction to Particle Accelerators 12 June 2005 34
Head-on collisions
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W.Scandale, Introduction to Particle Accelerators 12 June 2005 37
LHC luminosityPerformances limitations
Luminosity:
L = event rate cross section �
= 1 �
N1 N2 k f �
S
2for equal, round, bi-Gaussian beams: N1 N2 = N
S --> 4š σσσσ 2
εεεε* = σ γσ γσ γσ γ2222
ββββ*
∗∗∗∗L = N k f γγγγ
2222
4π ε β4π ε β4π ε β4π ε β∗∗∗∗
protons in a bunch
no. of bunches
revolution frequency
beam cross section
invariant emittance
Head-on beam-beam:
detuning ξ = ξ = ξ = ξ = rp N4 π ε4 π ε4 π ε4 π ε∗∗∗∗
ξ ∗ ξ ∗ ξ ∗ ξ ∗ nb. of interactions Š 0.02
* εεεεL =
γγγγ
4πβ4πβ4πβ4πβN N
* ²t
Transverse beam density: • head-on beam-beam • space-charge in the injectors • transfers dilution
Beam current: • long range beam-beam • collective instability • synchrotron radiation • stored beam energy
W.Scandale, Introduction to Particle Accelerators 12 June 2005 38
LHC insertions
56 m
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W.Scandale, Introduction to Particle Accelerators 12 June 2005 42
High luminosity experiments
W.Scandale, Introduction to Particle Accelerators 12 June 2005 43
Ion-ion experiment
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