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Introduction to particle

accelerators

Walter ScandaleCERN - AT department

Lecce, 17 June 2006

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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 ofclassical 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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W.Scandale, Introduction to Particle Accelerators 12 June 2005 3 

Inventory of synchrotron components

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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 B Earth = 3 10 -5 Tesla 

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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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

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W.Scandale, Introduction to Particle Accelerators 12 June 2005 8 

Basic 2-D equation of motion

in a dipolar field

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Basic 2D equation of motion

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W.Scandale, Introduction to Particle Accelerators 12 June 2005 10 

Basic 2D equation of motion

FODO structure 

Periodic envelop 

Cos-like trajecto ry 

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-linearresonance

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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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W.Scandale, Introduction to Particle Accelerators 12 June 2005 1

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 tar get 

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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W.Scandale, Introduction to Particle Accelerators 12 June 2005 2 

LHC features

Technological

challenge 

(+1)

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Bunch spacing 25 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-oncollisions 

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LHC luminosity

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W.Scandale, Introduction to Particle Accelerators 12 June 2005 3 

LHC luminosityPerformances limitations

Luminosity:

L = event ratecross section

= 1

N1 N2 k f

S

2

for equal, round, bi-Gaussian beams: N1 N2 = NS --> 4š σσσσ 2

εεεε* =σ γ σ γ σ γ σ γ 2222

ββββ*

∗∗∗∗L =N k f γ γγ γ 

2222

4π ε β4π ε β4π ε β4π ε β∗∗∗∗

protonsin a bunch

no. of bunches

revolution frequency

beam cross section

invariant emittance

Head-on beam-beam:

detuningξ =ξ =ξ =ξ =

rp N

4 π ε4 π ε4 π ε4 π ε∗∗∗∗ξ ∗ξ ∗ξ ∗ξ ∗ nb. of interactions Š 0.02

* εεεεL =

γ γγ γ 

4πβ4πβ4πβ4πβ

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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