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Introduction to particle accelerators Walter Scandale CERN - AT department Lecce, 17 June 2006
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 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
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Quadrupole magnet
Vertical focusingHorizontal defocusing
g=gradient [T/m]
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Alternate gradient focusing
QF QF QFQD QD
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Mechanical analogy for alternate gradient
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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
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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
AdvantageColliderFixed 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 spacing25 ns - 8.3 m
ε∗ = 3.75 10-6 m
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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 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
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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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