Introduction to particle accelerators
Walter Scandale
CERN - AT department
Lecce, 17 June 2006
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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
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Inventory of synchrotron components
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Bending magnet
Efficient use of the current -> small gap height Field quality -> determined by the pole shape Field saturation -> 2 Tesla B
Earth= 3 10
-5Tesla
B > 2 Tesla -> use superconducting magnets B
LHC= 8.4 Tesla
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Quadrupole magnet
Vertical focusing
Horizontal defocusing
g=gradient [T/m]
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Alternate gradient focusing
QF QD QF QD QF
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Mechanical analogy for alternate gradient
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Basic 2-D equation of motion
in 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
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Longitudinal stability
Momentum compaction
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Chromaticity and sextupole magnet
Dispersion orbit
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Chromaticity correction and non-linear
resonance
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Emittance
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Synchrotron radiation
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Synchrotron radiation and beam size
Adiabatic damping Synchrotron light emission
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Effect of synchrotron light
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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
Advantage
Collider Fixed target
Bruno Touschek
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Lepton versus hadron colliders
->
->
(At the parton level )
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Lecture II
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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
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LHC features
Technological challenge
(+1)
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Bunch spacing
25 ns - 8.3 m
ε∗ = 3.75 10
-6m
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Maximum B-field
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Cos( θ ) coil
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Superconducting dipole
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Collider luminosity
High L needs:
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Beam-beam interaction
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Head-on
collisions
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LHC luminosity
Performances limitations
Luminosity:
L = event rate
cross section = 1 N
1N
2k f S for equal, round, bi-Gaussian beams: N
1N
2= N
2S --> 4š σσσσ
2εεεε * = σ γ σ γ σ γ σ γ
2222ββββ*
L = N k f
2222∗∗∗∗ γγγγ
4π ε β 4π ε β 4π ε β 4π 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 = r
pN 4 π ε 4 π ε 4 π ε
4 π ε∗∗∗∗ ξ ∗ ξ ∗ ξ ∗ ξ ∗ nb. of interactions Š 0.02
* εεεε L = γγγγ
4πβ 4πβ 4πβ 4πβ
N 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
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LHC insertions
56 m
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High luminosity experiments
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Ion-ion experiment
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