Introduction to particle accelerators Walter Scandale CERN - AT department Lecce, 17 June 2006
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 2
Inventory of synchrotron components W.Scandale, Introduction to Particle Accelerators 12 June 2005 3
Bending magnet Efficient use of the current -> small gap height Field quality -> determined by the pole shape Field saturation -> 2 Tesla B Earth = 3 10-5 Tesla B > 2 Tesla -> use superconducting magnets B LHC = 8.4 Tesla W.Scandale, Introduction to Particle Accelerators 12 June 2005 4
Quadrupole magnet Vertical focusing Horizontal defocusing g=gradient [T/m] W.Scandale, Introduction to Particle Accelerators 12 June 2005 5
Alternate gradient focusing QF QD QF QD QF W.Scandale, Introduction to Particle Accelerators 12 June 2005 6
Mechanical analogy for alternate gradient W.Scandale, Introduction to Particle Accelerators 12 June 2005 7
Basic 2-D equation of motion in a dipolar field W.Scandale, Introduction to Particle Accelerators 12 June 2005 8
Basic 2D equation of motion W.Scandale, Introduction to Particle Accelerators 12 June 2005 9
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 10
Longitudinal stability Momentum compaction W.Scandale, Introduction to Particle Accelerators 12 June 2005 11
Chromaticity and sextupole magnet Dispersion orbit W.Scandale, Introduction to Particle Accelerators 12 June 2005 12
Chromaticity correction and non-linear resonance W.Scandale, Introduction to Particle Accelerators 12 June 2005 13
Emittance W.Scandale, Introduction to Particle Accelerators 12 June 2005 14
Synchrotron radiation W.Scandale, Introduction to Particle Accelerators 12 June 2005 15
Synchrotron radiation and beam size Adiabatic damping Synchrotron light emission W.Scandale, Introduction to Particle Accelerators 12 June 2005 16
Effect of synchrotron light W.Scandale, Introduction to Particle Accelerators 12 June 2005 17
Collective effects W.Scandale, Introduction to Particle Accelerators 12 June 2005 18
Instabilities and feedback W.Scandale, Introduction to Particle Accelerators 12 June 2005 19
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Space charge W.Scandale, Introduction to Particle Accelerators 12 June 2005 21
Beam size W.Scandale, Introduction to Particle Accelerators 12 June 2005 22
Fixed target versus collider rings Fixed target Collider Advantage Bruno Touschek W.Scandale, Introduction to Particle Accelerators 12 June 2005 23
Lepton versus hadron colliders -> (At the parton level ) -> W.Scandale, Introduction to Particle Accelerators 12 June 2005 24
Lecture II W.Scandale, Introduction to Particle Accelerators 12 June 2005 25
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 26
LHC features Technological challenge (+1) W.Scandale, Introduction to Particle Accelerators 12 June 2005 27
ε = 3.75 10-6 m Bunch spacing 25 ns - 8.3 m W.Scandale, Introduction to Particle Accelerators 12 June 2005 28
Maximum B-field W.Scandale, Introduction to Particle Accelerators 12 June 2005 29
Cos(θ) coil W.Scandale, Introduction to Particle Accelerators 12 June 2005 30
Superconducting dipole W.Scandale, Introduction to Particle Accelerators 12 June 2005 31
Collider luminosity High L needs: W.Scandale, Introduction to Particle Accelerators 12 June 2005 32
Beam-beam interaction W.Scandale, Introduction to Particle Accelerators 12 June 2005 33
Head-on collisions W.Scandale, Introduction to Particle Accelerators 12 June 2005 34
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LHC luminosity Performances limitations Luminosity: protons in a bunch no. of bunches revolution frequency L = event rate cross section = 1 N1 N2 k f S beam cross section 2 for equal, round, bi-gaussian beams: N1 N2 = N S --> 4š σ 2 2 σ ε* = γ β* invariant emittance L = 2 N k f γ 4π ε β L = γ N N 4πβ * ε * 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 Head-on beam-beam: detuning ξ = ξ nb. of interactions Š 0.02 4 π ε ε W.Scandale, Introduction to Particle Accelerators 12 June 2005 37 rp N
LHC insertions 56 m W.Scandale, Introduction to Particle Accelerators 12 June 2005 38
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High luminosity experiments W.Scandale, Introduction to Particle Accelerators 12 June 2005 42
Ion-ion experiment W.Scandale, Introduction to Particle Accelerators 12 June 2005 43
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