1

Accelerator Physics Accelerator Physics Aspects Aspects LHCbLHCb

Elena.Wildner@cern.ch CERN SL/AP

Layout Crossing Scheme Luminosity Collision Scheme Electron Cloud Impedances Official Schedule

2

Layout of the LHC

3

Layout of IR8

Dispersion Suppressor TripletMatching

4

A few definitions L o n g i t u d i n a l e m i t t a n c e :

tEl 4T r a n s v e r s e e m i t t a n c e :

)/( 2, TTnT

L u m i n o s i t y :

tNNkfNL

nTTT

rev

,2

2 144

Beam transverse density,proportional to the beam-beam parameter

Proportional to the beam currentnT

p Nr

,4

Inversely proportional to *

Beam-Beam Parameter:

5

A few definitions

Head-on + Long range

nT

p Nr

,4

Beam-Beam Tune Shift Parameter:

Spread of the transverse oscillation frequencies High order transverse resonances and a tune shift It is limited by the space between dangerous

resonances Difficult to compensate for: all particles do not have

the same tune shift Independent of * Its nominal value is 0.0035

6

Crossing Angle

Crossing angle:

*,

Tnn

Beam envelope defined at n

Avoid unwanted bunch collisions Must be larger than the divergence of the beam

envelope Limited by the excursions of the beam trajectories

(aperture limitations in the triplet) In the expression for the luminosity there is a

reduction factor for the crossing angle (0.1)

7

Beam Separation and crossing scheme Spectrometer magnet

compensation: 3 correction magnets to make local bump

Horizontal crossing Vertical separation when not in

collision

Spectrometer

Correctors

End of triplet

Correctors

D2

D1

IP

8

Beam Separation and crossing scheme

Limitations by Aperture Accomodate spectrometer -> 11.22m shift towards IP7 Beam Separation 2 mm tot= spec + ext tot=345 rad / 75 rad depending on spectrometer

polarity spec=135 rad positive or negative ext =210 rad constant Crossing scheme only one direction Ramping of spectrometer magnet important to permit

both polarities of spectrometer (limitations at injection)

9

Beam Separation and crossing scheme

=1m

10mm

10mm

1mm

0.5mm

10

Optics IR8

Beam Size =Sqrt (*gamma)

=70m, =10m

=400m

=160m, =50

11

10 20 30 40 50

73

74

75

76

77

78

Nominal

Luminosity vs *

Wanted luminosity range for LHCb 1-5 1032 cm-2 s-1

Tunability 1m < * < 35m

Luminosity requirements fulfilled dynamically by varying *

Limited to 35m

5 1032

1 1032

50% of Nominal

10 % of Nominal

12

Luminosity Lifetime

Scattering from residual gas ignored (10-12 torr) The beam-beam effect and the intrabeam scattering produce

emittance increase but this is compensated by synchrotron radiation damping. The net result is a decrease of emittance.

We are left with the formula above giving a lifetime of 26 hours Beam-gas induced lost rate into the pipe at the triplet under

study

Initial Beam Intensity Lifetimefrom the collisions

xkLN

0

Number of Interaction pointsTotal cross section (10-25 cm2)

13

Luminosity Life Time

No Beam-Beam Blow up No synchrotron radiation damping decreases L = 11hours

Synchrotron radiation (theory) constant L = 25hours

Synchrotron radiation (theory) decreases because of beam

blow up (SppS Collider) L = 10hours Run on Beam-beam limit

14

Collision scheme

Distance between IPs = 891 half buckets: collision scheme has to repeat from one IP to the other

“Holes” (empty buckets) due to injection kickers SPS and LHC, dump Kicker LHC

There are 2808 filled buckets out of 3564 according to following scheme: {[(72b+8e)*3+30e]*2+[(72b+8e)*4+31e]}*3{[(72b+8e)*3+30e]*3+81e}

“Pacman” bunches: do not encounter bunches of the other beam in one or several parasitic collision points

“Superpacman” bunches: as “pacman” but not even at the collision point

15

Filling scheme

(72b+8e)*3+30e+81e

(72b+8e)*3+30e

(72b+8e)*4+31e

16

Horizontal orbit offsets

Horizontal offset at IP1, in IP8 the situation is similar, need to scale so that the spread 1/10 of the beam size

Zooming up

Effects coming from the very start of train where there is a “big hole”

Effects coming from the “small holes”

17

Collision scheme IP8 shifted by 3 half buckets which means 124 extra

superpacman bunches in IP8 Double bunch spacing no encounters in IP8

Triple spacing means less luminosity (bunch current has to be increased by 31/2 to keep luminosity constant)

Bunch offsets within +-0.1 at collision point, small effects

IP8

18

Longitudinal Impedance Longitudinal impedance can cause longitudinal

instabilities of the beam The geometry of an element is crucial All elements in the machine are optimized to give a

minimum contribution to the impedance budget. Longitudinal impedance budget is very tight No feedback system in the LHC for longitudinal

instabilities A longitudinal feedback system is technically very

difficult and expensive The evaluation of the LHCb experimental beam pipe

longitudinal impedance is done by Nikhef. Has to fit into total budget of the LHC!

Examples of critical geometries

Sharp edges not good

19

Transverse Impedance

A transverse feedback system is required in the LHC to cure the effect of transverse impedance (resistive wall instability).

Aluminum, copper and beryllium are good materials (stainless steel not so good).

Transverse impedance should not exceed budget because of emittance conservation (feedback capabilities are limited)

20

Higher Order Modes Depends on the geometry of the object Frequencey spectrum of loss factor should not

overlap, bunch spectrum Different positioning of the vertex detector gives

different resonance conditions All positions of the detector have to be evaluated Heating up change resonance conditions, cooling

down etc. Pumping effect.

Different situations should be carefully evaluated

21

Electron Cloud

Photons, protons, electrons from gas ionization

Critical dimensions of chamber Heat Load Vacuum

22

Electron Cloud

Scale different

SEY=1.2Boxes open, xb=12cm, yb=3cm

SEY=2.8Boxes closed, xb=6mm, yb=6mm

23

Official Schedule

First Beam 01/02/2006

First Collisions 01/04/2006 L *=0.5=5 1032cm -2 s-1

Shut Down 01/05-31/07/2006

Physics Run 01/08/2006-28/02/2007 L *=0.5>= 2 1033cm -2 s-1

24

People who Contributed

Optics: Oliver Brüning Crossing Scheme: Werner Herr, Oliver Brüning Electron Cloud: Frank Zimmermann, Oliver Brüning Impedance: Daniel Brandt, Oliver Brüning Lattice files: Elena Wildner Aperture: Bernard Jeanneret Beam-Beam: H.Grote

25

LHC general parameters Energy at collision 7 TeV Energy at injection 450 GeV

Dist. aperture axes (1.9 K) 194 mm Luminosity 1 E34 cm ²s ¹ Beam beam parameter 3.6 E-3 DC beam current 0.56 A Bunch spacing 7.48 m Bunch separation 24.95 ns Number of particles per bunch 1.1 E11 Norm. transv. emittance (r.m.s.) 3.75 µm Total crossing angle 300 µrad

Luminosity lifetime 10 hEnergy loss per turn 7 keVCritical photon energy 44.1 eV

Total radiated power per beam 3.8 kW Stored energy per beam 350 MJ

Filling time per ring 4.3 min

26

Transverse Parameters

Parameter Injection Collision Unit

Energy 0.450 7 TeVRelativistic factor (gamma) 479.6 7460.6Magnetic rigidity 1501 23349 T mDipole field 0.535 8.33 TTransverse physical emittance 7.82 0.503 nmNorm. transv. emittance (r.m.s.) 3.75 3.75 µmMaximum beta value in arc (H/V) ~180 ~180 mMax. beam size, arc (H/V) (r.m.s.) 1.20 0.303 mmBeam size at IP1 and IP5 (r.m.s.) - 15.9 µmMaximum beta value in insertions - 4705 mTransv. intrabeam scattering growth time 45 100 h

27

Longitudinal ParametersParameter Injection Collision Unit

Energy 0.450 7 TeVRevolution frequency 11.2455 11.2455 kHzRF frequency 200.395 (*) 400.790 MHzRF harmonic number 17820 35640RF tuning range 10 10 kHzRF voltage 3 16 MVFrequency slip factor (eta) 3.43 3.47 E-4Energy gain/turn (20 min. ramping) - 485 (**) keVRF power per beam - 257 (**) kWSynchrotron frequency 29 24 HzBucket area 2.38 7.63 eVsLongitudinal emittance (2 r.m.s.) 1 2.5 eVsEnergy spread (r.m.s.) 0.285 0.105 E-3Bunch duration (r.m.s.) 0.62 0.28 nsBunch separation 24.95 24.95 nsStored energy per beam - 350 MJLong. intrabeam scattering growth time 33 60 hSynchrotron radiation energy loss per turn - 7 keVLongitudinal damping time - 25.8 hRF component of batch current 1.20 1.25 ADC beam current 0.56 0.56 A

(*) At injection the 400MHz RF system is used as a second harmonic system in addition withv=0.75MV(**) During acceleration