introduction to particle accelerators · introduction to particle accelerators walter scandale cern...

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

W.Scandale, Introduction to Particle Accelerators 12 June 2005 7

Mechanical analogy for alternate gradient

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

Basic 2-D equation of motionin a dipolar field

W.Scandale, Introduction to Particle Accelerators 12 June 2005 9

Basic 2D equation of motion

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

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

W.Scandale, Introduction to Particle Accelerators 12 June 2005 13

Chromaticity correction and non-linear resonance

W.Scandale, Introduction to Particle Accelerators 12 June 2005 14

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

W.Scandale, Introduction to Particle Accelerators 12 June 2005 19

Instabilities and feedback

W.Scandale, Introduction to Particle Accelerators 12 June 2005 20

W.Scandale, Introduction to Particle Accelerators 12 June 2005 21

Space charge

W.Scandale, Introduction to Particle Accelerators 12 June 2005 22

Beam size

W.Scandale, Introduction to Particle Accelerators 12 June 2005 23

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

W.Scandale, Introduction to Particle Accelerators 12 June 2005 35

W.Scandale, Introduction to Particle Accelerators 12 June 2005 36

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

W.Scandale, Introduction to Particle Accelerators 12 June 2005 39

W.Scandale, Introduction to Particle Accelerators 12 June 2005 40

W.Scandale, Introduction to Particle Accelerators 12 June 2005 41

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

W.Scandale, Introduction to Particle Accelerators 12 June 2005 44

W.Scandale, Introduction to Particle Accelerators 12 June 2005 45

W.Scandale, Introduction to Particle Accelerators 12 June 2005 46

W.Scandale, Introduction to Particle Accelerators 12 June 2005 47

W.Scandale, Introduction to Particle Accelerators 12 June 2005 48

W.Scandale, Introduction to Particle Accelerators 12 June 2005 49