An Introduction toAn Introduction to Particle Accelerators

Erik Adli, University of Oslo/CERN, University of Oslo/CERNNovember, 2007

Erik.Adli@cern.ch

v1.32

ReferencesReferencesBibli h• Bibliography:

– CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992

– LHC Design Report [online]LHC Design Report [online]– K. Wille, The Physics of Particle Accelerators, 2000

• Other referencesOther references– USPAS resource site, A. Chao, USPAS January 2007– CAS 2005, Proceedings (in-print), J. Le Duff, B, Holzer et al.– O. Brüning: CERN student summer lecturesg– N. Pichoff: Transverse Beam Dynamics in Accelerators, JUAS January 2004– U. Am aldi, presentation on Hadron therapy at CERN 2006– Various CLIC and ILC presentations– Several figures in this presentation have been borrowed from the above

references, thanks to all!

Part 1

Introduction

Particle accelerators for HEPParticle accelerators for HEP•LHC: the worldLHC: the world biggest accelerator, both in energy and size (as big as ( gLEP)

•Under construction at CERN todayat CERN today

•End of magnet installation in 2007

•First collisions expected summer 20082008

Particle accelerators for HEPParticle accelerators for HEPThe next big thing. After LHC, a Linear Collider of over 30 km length, g ,will probably be needed (why?)

Others acceleratorsOthers accelerators

Hi i ll h i d i i f f l d l• Historically: the main driving force of accelerator development was collision of particles for high-energy physics experiments

• However, today there are estimated to be around 17 000 particle accelerators in the world, and only a fraction is used in HEP

• Over half of them used in medicine

• Accelerator physics: a disipline in itself, growing field

• Some examples:

Medical applicationsMedical applications

Th• Therapy– The last decades: electron accelerators

(converted to X-ray via a target) are used very successfully for cancer therapy)

– Today's research: proton accelerators y pinstead (hadron therapy): energy deposition can be controlled better, but huge technical challenges

• ImagingIsotope production for PET scanners– Isotope production for PET scanners

Advantages of proton / ion therapyAdvantages of proton / ion-therapy

( Slide borrowed from U. Am aldi )( )

Proton therapy accelerator centreProton therapy accelerator centre

HIBAC in Chiba

( Slide borrowed from U. Am aldi )What is all this? Follow the lectures... :)

Synchrotron Light SourcesSynchrotron Light Sources

th l t t d d i i th f h di ti• the last two decades, enormous increase in the use of synchrony radiation, emitted from particle accelerators

• Can produce very intense light (radiation), at a wide range of frequencies (visible or not)

• Useful in a wide range of scientific applications

Outline of presentationOutline of presentation

Part 1: Intro + Main parameters + Basic ConceptsPart 2: Longitudinal Dynamicsg yPart 3: Transverse DynamicsCase: LHCPart 4: Intro to synchrotron radiationPart 4: Intro to synchrotron radiationPart 5: The road from LEP via LHC to CLICCase: CLIC

Main Parameters

Main parameters: particle typeMain parameters: particle type

d i l• Hadron collisions: compound particles– Mix of quarks, anti-quarks and gluons: variety of processes– Parton energy spreadgy p– Hadron collisions ⇒ large discovery range

• Lepton collisions: elementary particlesLepton collisions: elementary particles– Collision process known– Well defined energy

L lli i i i– Lepton collisions ⇒ precision measurement

“If you know what to look for, collide leptons, if not collide hadrons”

Main parameters: particle typeMain parameters: particle type

Discovery Precision

S S / LHC LEP / LCSppS / LHC LEP / LC

Main parameters: particle energyMain parameters: particle energy

N h i b f d t l b d i• New physics can be found at larger unprobed energies

• Energy for particle creation: centre-of-mass energy, ECMgy p gy CM

• Assume particles in beams with parameters m, E, E >> mc2

– Particle beam on fixed target:

C

mE=CME

E2E– Colliding particle beams:

• ⇒ Colliding beams much more efficient

E2ECM =

Main parameters: luminosityMain parameters: luminosity

Hi h i t h !• High energy is not enough !

• Cross-sections for interesting processes are very small (~ pb = 10−36 cm² ) !g p y ( p )– σ(gg → H) = 23 pb [ at s2

pp = (14 TeV)2, mH = 150 GeV/c2 ]

σL=R– We need L >> 1030 cm-2s-1 in order to observe a significant amount of

interesting processes!

• L [cm-2s-1] for “bunched colliding beams” depends on– number of particles per bunch (n1, n2)– bunch transverse size at the interaction point (σ σ )– bunch transverse size at the interaction point (σx, σy )– bunch collision rate ( f)

nnf 21=Lyx

fσπσ4

Main parameters: LEP and LHCMain parameters: LEP and LHCLEP LHCLEP LHC

Particle type(s) e+ and e- p, ions (Pb, Au)

Collision energy (Ecm) 209 GeV (max) p: 14 TeV at p (~ 2-3 TeV mass reach, depending on physics)on physics)Pb: 1150 TeV

Luminosity (L) Peak: 1032 cm-2s-1

Daily avg last years: 1031 cm-2s-1

Peak: 1034 cm-2s-1

(IP1 / IP5)

Integrated: ~ 1000 pb-1

(per experiment)

Capabilities of particle acceleratorsCapabilities of particle accelerators

A d HEP ti l l t l t ti l k i th• A modern HEP particle accelerator can accelerate particles, keeping them within millimeters of a defined reference trajectory, and transport them over a distance of several times the size of the solar system

HOW?

HOW?HOW?I thi t ti t t l i thi b t d i• In this presentation we try to explain this by studying:

– the basic components of an accelerator– the physical mechanisms that determines the particle motion– how particles (more or less) follow a specified path, even if our accelerator is not

designed perfectly

• At the end, we use what we have learned in a case-study: the LHC

Part 2

Basic concepts

An acceleratorAn accelerator

• Structures in which the particles will move • Structures to accelerate the particles• Structures to steer the particles• Structures to measure the particles

Lorentz equationLorentz equation

Th t i t k f l t• The two main tasks of an accelerator– Increase the particle energy– Change the particle direction (follow a given trajectory, focusing)

• Lorentz equation:

FFBEBEFrrrrrrrrr

)(

F ⊥ F d k th ti l

BE FFBvqEqBvEqF rr+=×+=×+= )(

• FB ⊥ v ⇒ FB does no work on the particle– Only FE can increase the particle energy

• FE or FB for deflection? v ≈ c ⇒ Magnetic field of 1 T (feasible) same bending power as en electric field of 3⋅108 V/m (NOT feasible)

– FB is by far the most effective in order to change the particle direction

Acceleration techniques: DC fieldAcceleration techniques: DC field

Th i l t l ti th d DC lt• The simplest acceleration method: DC voltage

• Energy kick: ΔE=qV

• Can accelerate particles over many gaps: electrostatic accelerator

• Problem: breakdown voltage at ~10MVProblem: breakdown voltage at 10MV

• DC field still used at start of injector chain

Acceleration techniques: RF fieldAcceleration techniques: RF field

O ill ti RF ( di f ) fi ld• Oscillating RF (radio-frequency) field

• “Widerøe accelerator”, after the pioneering work of the Norwegian Rolf Wid (b h f h i Vi Wid )Widerøe (brother of the aviator Viggo Widerøe)

• Particle must sees the field only when the field is in the accelerating y gdirection

– Requires the synchronism condition to hold: Tparticle =½TRF vTL )2/1(=

• Problem: high power loss due to radiation

Principle of phase focusingPrinciple of phase focusing

...what happens to particles with energies slightly off the nominal values...?

Acceleration techniques: RF cavitiesAcceleration techniques: RF cavities

• Electromagnetic power is stored in a resonant volume instead of• Electromagnetic power is stored in a resonant volume instead of being radiated

• RF power feed into cavity, originating from RF power generators, lik Kl tlike Klystrons

• RF power oscillating (from magnetic to electric energy), at the d i d fdesired frequency

• RF cavities requires bunched beams (as opposed to ti b )coasting beams)

– particles located in bunches separated in space

Acceleration techniques: Pill Box cavityAcceleration techniques: Pill-Box cavity

Id l li d i l it• Ideal cylindrical cavity:

• Solution for E and H are oscillating modes (of increasing frequency)

• The fundamental mode normally used for acceleration is named TM010 with the following features:

– Ez is constant in space along the axis of acceleration, z, at any instant– λ010 = 2.6a, l < 2 a

• Acceleration efficiency of cavity depends on the transit-time factor– Ratio of “actual energy gain”, versus “energy gain if the field was constant in time“

vl

VeTVe

dzEe

dztEe

EET

z

const

var ωθθ

θω====

ΔΔ=

∫∫

,2/

)2/sin(ˆ

ˆ

ˆ

)cos(ˆ

– Example: l = λ / 2 gives θ=π and T=0.64

dzEe zconst ∫

From pill box to real cavitiesFrom pill-box to real cavities

(from A. Chao)

LHC cavity module ILC cavity

Why circular accelerators?Why circular accelerators?

• Technological limit on the electrical field in an RF cavity (breakdown)

• Gives a limited ΔE per distance

• ⇒ Circular accelerators, in order to re-use the same RF cavity, y

• This requires a bending field FB in order to follow a circular trajectory (later slide)slide)

The synchrotronThe synchrotron

A l ti i f d b RF iti• Acceleration is performed by RF cavities

• (Piecewise) circular motion is ensured by a guide field FB

• FB : Bending magnets with a homogenous field

][112 TBqBv• In the arc section:

• RF frequency must stay locked to the revolution frequency of a particle

]/[][3.0][11 F 1

B cGeVpTBm

pqBvm ≈⇔=⇒= −

ρρρ

q y y q y p(later slide)

• Almost all present day particle accelerators are synchrotronsp y p y

Digression: other accelerator typesDigression: other accelerator types

C l t• Cyclotron: – constant B field– constant RF field in the gap increases energy– radius increases proportionally to energy– limit: relativistic energy, RF phase out of synch– In some respects simpler than the synchrotron,

and often used as medical accelerators

• Synchro-cyclotrony y– Cyclotron with varying RF phase

• BetatronBetatron– Acceleration induced by time-varying magnetic field

• The synchrotron will be the only type discussed in this course• The synchrotron will be the only type discussed in this course

Particle motionParticle motion

• We separate the particle motion into:– longitudinal motion: motion tangential to the reference trajectory along the

accelerator structure uaccelerator structure, us

– transverse motion: degrees of freedom orthogonal to the reference trajectory, u uux, uy

• us, ux, uy are unit vector in a moving coordinate system, following the particleparticle

?

Part 3

L i di l d iLongitudinal dynamicsand acceleration

L it di l D i d f f d t ti l t th f t j tLongitudinal Dynamics: degrees of freedom tangential to the reference trajectoryus: tangential to the reference trajectory

RF accelerationRF acceleration

• We assume a cavity with an oscillating RF-field: )sin(ˆ tEE RFzz ω=

• In this section we neglect the transit-transit factor– we assume a field constant in time while the particle passes the cavity

• Work done on a particle inside cavity:

)sin(ˆ)sin(ˆ tVqdztEqdzEqFdzW RFRFzz ωω ==== ∫∫∫ )()( qqq RFRFzz ∫∫∫

Synchrotron with one cavitySynchrotron with one cavity

• The energy kick of a particle, ΔE, depends on the RF phase seen, φ

ˆˆ

• We define a “synchronous particle”, s, which always sees the same phase i h i

φω sinˆ)sin(ˆ VqtVqWE RF ===Δ

φs passing the cavity⇒ ωRF =h ωrs ( h: “harmonic number” )

• E.g. at constant speed, a synchronous particle circulating in the synchrotron, assuming no losses in accelerator, will always see φs=0

Non synchronous particlesNon-synchronous particles

A h ti l P h d t ki k ΔE• A synchronous particle P1 sees a phase φs and get a energy kick ΔEs

• A particle N1 arriving early with φ= φs−δ will get a lower energy kick

• A particle M1 arriving late with φ= φs+δ will get a higher energy kick

R b i h t h b h ith h b f• Remember: in a synchrotron we have bunches with a huge number of particles, which will always have a certain energy spread!

Frequency dependence on energyFrequency dependence on energy

I d t th ff t f t l /hi h ΔE d t t d th• In order to see the effect of a too low/high ΔE, we need to study the relation between the change in energy and the change in the revolution frequency (η: "slip factor")

pdpfdf rr

//=η

• Two effects:1. Higher energy ⇒ higher speed (except ultra-relativistic)

Rcfr π

β2

=

2. Higher energy ⇒ larger orbit “Momentum compaction”

Momentum compactionMomentum compaction

I i / ill l d t l bit• Increase in energy/mass will lead to a larger orbit

RdR /• We define the “momentum compaction factor” as:pdpRdR

//=α

• α is a function of the transverse focusing in the accelerator, α=<Dx> / R– ⇒ α is a well defined quantity for a given accelerator

Calculating ηCalculating η

L ith i diff ti ti i• Logarithmic differentiation gives:

β dRddfr

γβββββ

=+=

−=

22

)1( dddpRf

f

r

r

αη

γβββ

−==⇒

=−

+=

2

2

1//

)1

1(

dfdf

p

rr

• For a momentum increase dp/p:

γη 2/ pdp

For a momentum increase dp/p:– η>0: velocity increase dominates ( fr increases )– η<0: circumference increase dominates ( fr decreases )

Phase stabilityPhase stability

• η>0: velocity increase dominates f increases• η>0: velocity increase dominates, fr increases

• Synchronous particle stable for 0º<φs<90º– A particle N1 arriving early with φ= φs−δ will get a lower energy kick, and arrive p 1 g y φ φs g gy ,

relatively later next pass– A particle M1 arriving late with φ= φs+δ will get a higher energy kick, and arrive

relatively earlier next pass

• η<0: stability for 90º<φs<180º

• η=0 is called transition. When the synchrotron reaching this energy, the η y g gy,RF phase needs to be switched rapidly from φs to 180−φs

Longitudinal phase spaceLongitudinal phase-space(from A. Chao)

δ = Δp/p

Phase-space for a harmonic oscillator:

H = p2 / 2 + x2 / 2

Longitudinal phase-space showing the

synchrotron motion

Synchrotron motion: "particles rotate in the phase-space"

Synchrotron oscillationsSynchrotron oscillations

A l i f ll lit d ill ti i• Analysis of small amplitude oscillations gives:

• As result of the phase stability, the energy and phase will oscillate, resulting p y gy p gin longitudinal synchrotron oscillations:

2&&

srsS

ss

Veh φηωφφφ

cosˆ,0)(

2

2

=Ω

=−Ω+

• Equation of an Harmonic Oscillator

ssS pRπ2

Ω

q

• For derivations, please refer to [Wille2000]

Synchrotron: energy rampingSynchrotron: energy ramping

W i h t th f th ti l Wh t d d ?• We now wish to ramp up the energy of the particle. What do we do?

• Each time the synchronous particle passes the cavity it will receive a moment m kickmomentum kick:

• We want the synchronous particle to on the same trajectory (reference trajectory) regardless of particle energy Therefore we require the field and

)2)((sinˆ/)( ss RfVqvEp πφ=Δ=Δ

trajectory) regardless of particle energy. Therefore, we require the field and the particle momentum to increase proportionally:

• Combining gives:

Bqp && ρ=

BRVf && ρπφ⇒Δ )2/1(iˆ• Combining gives:

• Thus, for a given dB/dt profile the synchronous phase is given as:

BqRVqppf ss ρπφ =⇒=Δ )2/1(sin

VqBRq

s ˆ2arcsin

&ρπφ =

• For a given B’ , the synchronous particles will, by definition, see the phase φs

Summary: longitudinal dynamicsSummary: longitudinal dynamicsfor a synchrotron

S t th i h t• Summary: to ramp up the energy in a synchrotron

– Simply ramp up the magnetic field

– With the (automatic) RF frequency modulation the synchronous particle will stay on the reference orbit

– Due to the phase-stability, the particles in the phase-space vicinity of the synchronous particle will be captured by the RF and will also be accelerated at th t d i h t ill tithe same rate, undergoing synchrotron oscillations

?

Part 4

Transverse dynamics

Transverse dynamics: degrees of freedom orthogonal to the reference trajectoryy g g j yux: the horizontal plane

uy: the vertical plane

Bending fieldBending field

Ci l l t d fl ti f d d• Circular accelerators: deflecting forces are needed

BE FFBvEqFrrrrrr

+=×+= )(

• Circular accelerators: piecewise circular orbits with a defined bending radius ρ

– Straight sections are needed for e.g. particle detectors– In circular arc sections the magnetic field must provide the desired bending

radius:

peB=

ρ1

• For a constant particle energy we need a constant B field ⇒ dipole magnets with homogenous field

pρ

• In a synchrotron, the bending radius,1/ρ=eB/p, is kept constant during acceleration (last section)acceleration (last section)

The reference trajectoryThe reference trajectoryW d t t d f th b k i ll ti l l t th f– We need to steer and focus the beam, keeping all particles close to the reference orbit

Reference trajectoryReference trajectory

ρ

Dipole magnets to steer Focus?

cosθ distributionhomogenous field or

Focusing field: quadrupolesFocusing field: quadrupoles• Quadrupole magnets gives linear field in x and y:

Bx = -gyx gyBy = -gx

• However, forces are focusing in one plane and defocusing in the orthogonal plane: Fx = -qvgx (focusing)

F = qvgy (defocusing)Fy = qvgy (defocusing)

Alternating gradient scheme, leading to betatron oscillationsAlternating gradient scheme, leading to betatron oscillations

The LatticeThe Lattice

A l t i d f b di t f i t d• An accelerator is composed of bending magnets, focusing magnets and non-linear magnets (later)

• The ensemble of magnets in the accelerator constitutes the “accelerator lattice”

Stability of a FODO structureStability of a FODO structure

Th li iti t th hi bl f i ff t t h t f l l th• There are limitions to the achievable focusing effect; too short focal length will give overfocusing, and an unstable trajectory:

4/lfstability >⇒

Example: lattice componentsExample: lattice components

Equations of motion: coordinatesEquations of motion: coordinates

C di t t• Coordinate system:

• x, y are small deviations from the reference trajectory– x: deviations in the horizontal plane– y: deviations in the vertical plane

• r = ρ + x

Linear equations of motion ILinear equations of motion I

F l i l h i t th t ti f ti• From classical mechanics we get the exact equations of motion :

gxBerrxm θθ &&&& −−=− )()( 2

• Preferred: x(s) instead of x(t), x’(s) is the slope

gyerym θ&&& −=

• Approximation: (s)xv)((t)x v 222

2

′′≈=⇒≈=dtds

dxdvr &&&

θθpp

• Equations of motions become:

2 dtds

gxBex −−=′′ )(1Equations of motions become:

yegy

gmvr

−=′′

)(

mv

Linear equations of motion IILinear equations of motion II

A i ti 111111 dpx Δ• Approximations: t.o. 2neglecting ),1(111 ),1(111 nd

000 pp

ppppx

xrΔ−≈

Δ+=−≈

+=

ρρρ

• We use the quadrupole strength: pegk /=

• Basic linear trajectory equations: 1)1(0

2

Δ=−−′′ xppxkx

ρρ0''

0

=+kyypρρ

– k: normalized quadrupole strength– 1/ρ: normalized dipole strength– p0 is the reference momentum Δp is the momentum deviationp0 is the reference momentum, Δp is the momentum deviation

Mathematical descriptionMathematical description• The linearized deviations from the reference orbit can be

described by Hill's equation0)( =+′′ xsKx 0)( =+ xsKx

• no field: K(s)=0

• inside a dipole K(s) = 1/ρ2• inside a dipole K(s) = 1/ρ2

• inside a quadrupole K(s)=+\-k

0⇓

=+′′ Kxx⇓

=+′′ xsKx 0)(

)sin()( 0φ+=

⇓

sKAsx ∫=+=

⇓s

s

dtssssx0

)( ),)(sin()()( 0 βφφφεβ

β

Particle motion: general solutions of Hill's equationParticle motion: general solutions of Hill s equation

W h l l t d ti l ti f i l ti l b t d i th• We have calculated particle motion for a single particle by studying the transfer matrices M(s). We now want to find characteristics of the generalaspects of the motion

• Solution of Hill’s equation with K(s) =K → harmonic oscillator0=+′′ Kxx

• The general solution of Hill’s equation with is:)sin()( 0φ+=

⇓

sKAsx

• The general solution of Hill s equation with is:

⇓=+′′ xsKx 0)(

β(s): the "beta

• Oscillating solution but with amplitude and phase-advance dependent on s !

∫=+=s

s

dtssssx0

)( ),)(sin()()( 0 βφφφεβ

function"

Oscillating solution,but with amplitude and phase advance dependent on s !– a “quasi-harmonic” oscillator

The transverse beam sizeThe transverse beam size

• A very important parameter– Vacuum chamber– Interaction point and luminosity

• The transverse beam size is given by the envelope of the particles:

)()(E εβ )()( ssE εβ=L tti

Beam qualityLattice

The beta function βThe beta function, β

• Twiss parameter β(s) ”the beta function” defines the envelope for the• Twiss parameter β(s), the beta function , defines the envelope for the solutions of Hill’s, and thus envelope for the particle motion (Δp=0)

I FODO h b f i i i i h iddl f h F• In a FODO structure the beta function is at maximum in the middle of the F quadrupole and at minimum in the middle of the D quadrupole

• NB: Even if beta function is periodic, the particle motion itself is in general not periodic (after one revolution the initial condition φ0 is altered)

• The beta function should be kept at minimum, β∗, at interaction points to maximize the luminosity

Example: motion in a FODO latticeExample: motion in a FODO lattice

(From CAS 1992)(From CAS 1992)

Transverse phase spaceTransverse phase-space

• The phase space of the horizontal plane is spanned by the two coordinates• The phase-space of the horizontal plane is spanned by the two coordinates [x, x’]

))(sin()()( 0φφβ⇓

+= ssAsx

• ⇒ For a fixed point, s, on the accelerator [x, x’] is a parametric

)))(sin(2

'))((cos()(' 00 φφβφφβ

+++= ssAsx

p , , [ , ] prepresentation of an ellipse

l βε)(E– envelope:– divergence: γε

βε==

)()(

sAsE

• For each turn the particle moves around the ellipse according to its tune (non-integer part)

• The shape of the ellipse depends β(s) and β'(s),and thus the position along the ring

EmittanceEmittance

Th l ti f Hill' f i ti l i d t i d b i iti l diti),)(sin()()( 0φφεβ += sssx

• The solution of Hill's for a given particle is determined by initial conditions [x0, x'0]. An ideal particle will have [x0, x'0] = [0, 0] and x(s) = 0

• A given beam consists of particles of various amplitude and angle. At a certain point s, the particles will fill the phase-space ellipse

• As long as a particle is inside the phase-space ellipse, it will remain there, and the area of the ellipse is constant (Liouville's theorem)

• ε is called the beam emittance (horizontal / vertical)

constantarea == πε

– very important parameter for beam quality

• Small emittance strongly desired:– Keep beam envelope and beam divergence small– Keep luminosity high

RMS transverse beam sizeRMS transverse beam size

• In reality: what is often quoted is the RMS emittance, and the RMS beam size,

RMS itt lti h• RMS emittance εrms: resulting phase-space ellipse contains one σ of particles

RMS beam si e )()( ss βεσ• RMS beam size: )()( ss rmsβεσ =

Beam quality Lattice

Conclusion: transverse dynamicsConclusion: transverse dynamics

W h t di d th t ti f i l l t d• We have now studied the transverse optics of a circular accelerator and we have had a look at the optics elements,

– the dipole for bending– the quadrupole for focusing– (sextupole for chromaticity correction – not discussed here)

• All optic elements (+ more) are needed in a high performance accelerator, like the LHC

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IntermezzoIntermezzoNorske storheter innen akseleratorfysikk

Rolf Wideröe Bjørn WiikProfessor og direktør ved

Odd DahlKjell Johnsen

Europas nest største akseleratorsenter (DESY i Hamburg)

Pioneer både for betatronprinsippet og for lineære akseleratorer Leder av CERN PS prosjektet

(en viktig del av LHC-Involvert i en rekke CERNkomplekset den dag i dag) Involvert i en rekke CERN-prosjekter, leder av ISR og CERN's gruppe for akseleratorforskning

Case: LHC

LHCLHC

LHC: wrt to earlier slidesLHC: wrt. to earlier slides

t t lli i• proton-proton collisions⇒ two vacuum chambers, with opposite bending field

• RF cavities⇒ bunched beams

• Synchrotron with alternating-gradient focusing

S d ti l tti t d d ti RF iti• Superconducting lattice magnets and superconducting RF cavities

• Regular FODO arc-section with sextupoles for chromaticity correction

• Proton chosen as particle type due to low synchrotron radiation

• Magnetic field-strength limiting factor for particle energy

LHC injector systemLHC injector system

LHC i ibl f l ti• LHC is responsible for accelerating protons from 450 GeV up to 7000 GeV

• 450 GeV protons injected into LHC from the SPS

• PS injects into the SPS

• LINACS injects into the PS

• The protons are generated by a Duoplasmatron Proton Source

LHC layoutLHC layout

• circumference = 26658 9 m• circumference = 26658.9 m

• 8 interaction points, 4 of which contains detectors where the beams intersectdetectors where the beams intersect

• 8 straight sections, containing the IPs, around 530 m long

• 8 arcs with a regular lattice structure, containing 23 arc cells

• Each arc cell has a FODO structure, 106.9 m long

LHC beam transverse sizeLHC beam transverse size

mmtyparc 3.0≈= εβσ

mIP μεβσ 17* ≈=

beta in drift space:

β(s) = β* + (s-s*)2 / β∗radnmmmtyp ×≈=≈ 5.0,55.0,180 * εββ

LHC cavitiesLHC cavities

• Superconducting RF cavities (standing wave, 400 MHz)• Each beam: one cryostats with 4+4 cavities each• Located at LHC point 4

LHC main parametersLHC main parametersat collision energy

Particle type p, PbProton energy Ep at collision 7000 GeVgy p

Peak luminosity (ATLAS, CMS)

10 x 1034 cm-2s-1

CMS)Circumference C 26 658.9 mB di di 2804 0Bending radius ρ 2804.0 mRF frequency fRF 400.8 MHz# particles per bunch np 1.15 x 1011

# bunches nb 2808# bunches nb 2808

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Part 5

Synchrotron radiation

1) Synchrotron radiation1) Synchrotron radiation

• Charged particles undergoing acceleration emit electromagnetic radiation

• Main limitation for circular electron machines– RF power consumption becomes too high

• The main limitation factor for LEP...– ...the main reason for building LHC !

• However, synchrotron radiations is also useful (see later slides)

Show RAD2D hereShow RAD2D here

(anim)(anim)

Characteristic of SR: powerCharacteristic of SR: power

Characteristics of SR: distributionCharacteristics of SR: distribution

El t t f di ti di t ib t d "H t di l "• Electron rest-frame: radiation distributed as a "Hertz-dipole"

ψ2sin∝dPS

• Relativist electron: Hertz dipole distribution in the electron rest frame but

ψsin∝Ωd

• Relativist electron: Hertz-dipole distribution in the electron rest-frame, but transformed into the laboratory frame the radiation form a very sharply peaked light-cone

Characteristics of SR: spectrum

B d t (d t h t l b

Characteristics of SR: spectrum

• Broad spectra (due to short pulses as seen by an observer)

• But, 50% of power contained within a well defined "critical frequency"defined critical frequency

Summary: advantages of Synchrotron RadiationSummary: advantages of Synchrotron Radiation1. Very high intensity2. Spectrum that cannot be covered easy with

other sourcesother sources3. Critical frequency easily controlled

Typical SR centreTypical SR centre

Accelerator + Users Some applications of Synchrotron Radiation:•material/molecule analysis (UV, X-ray)•crystallography•Archaeology

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ReferencesReferencesBibli h• Bibliography:

– CAS 1992, Fifth General Accelerator Physics Course, Proceedings, 7-18 September 1992

– LHC Design Report [online]LHC Design Report [online]– K. Wille, The Physics of Particle Accelerators, 2000

• Other referencesOther references– USPAS resource site, A. Chao, USPAS January 2007– CAS 2005, Proceedings (in-print), J. Le Duff, B, Holzer et al.– O. Brüning: CERN student summer lecturesg– N. Pichoff: Transverse Beam Dynamics in Accelerators, JUAS January 2004– U. Am aldi, presentation on Hadron therapy at CERN 2006– Various CLIC and ILC presentations– Several figures in this presentation have been borrowed from the above

references, thanks to all!