Measurements of Beam Energy - CERN · ANKA, PAC03 A.-S. Müller Energy Measurements Œ Introduction...

Forschungszentrum Karlsruhein der Helmholtz-Gemeinschaft

Measurements of Beam Energy

Anke-Susanne Müller

Institut für Synchrotronstrahlung (ISS), Forschungszentrum KarlsruheLaboratorium für Applikationen der Synchrotronstrahlung (LAS), Uni Karlsruhe

A.-S. Müller Energy Measurements page 1

Outline

IntroductionÜ Why do we need to know the beam energy?

Methods of energy calibrationÜ classical: spectrometersÜ exotic: from particle/nuclear physics processesÜ photon based measurementsÜ energy measurements from central frequencyÜ best precision: resonant depolarisationÜ energy from energy losses

Applications and resultsÜ Beam parametersÜ LEP energy calibration

Summary

A.-S. Müller Energy Measurements – Introduction page 2

What for?

Example 1 (LEP):For precise measurements of Zmass/width and cross sectionsa beam energy needs to beknown

Example 2 (LEP2):E0 for determination of mW

Example 3 (Syn. Light Sources):for insertion devices: εγ ∝ E2

1% ∆E/E Ü 2% ∆εγ/εγ

Example 4 (e.g. Tandem):For resonances in nuclear phy-sics in “ion beam on fixed target”configurations

The LEP experiments have measured the shape of the Z resonance :

0

5

10

15

20

25

30

35

87 88 89 90 91 92 93 94 95

√s [GeV]

σha

d[n

b]

Hadrons

1990

1991

1992

1993

Nν=3

Nν=2

Nν=4

“most precise measurementof the number 3”

LEP Electroweak Working Group


For Optics Measurements

abs(

K) /

m-2

quadrupole family

from magnet current assuming 2.500 GeVfrom magnet current assuming 2.477 GeVfrom LOCO

2.00

2.05

2.10

2.15

0 1 2 3 4 5 6

Measurements of quadrupole gradients show systematic offset relativeto the model if the beam energy is wrong ....

This effects both lepton and hadron accelerators....

ANKA, PAC03


Beam EnergyDetermination using

Spectrometers

A.-S. Müller Energy Measurements – Spectrometers page 5

Spectrometer

Spectrometers measure the particle momentum by preciselydetermining the angle of deflection in a dipole magnet

θ ∝1

E0

∫Bds

Ingredients:Ü beam position (O(1µm)) at entrance and exit of analysing magnetÜ magnetic field (O(10−5) or better)

Single pass systemsÜ position measurement with position sensitive detector at the beam

stop (possible attenuation)

Storage ringsÜ no beam stop therefore position measurement with beam position

monitors following the deflection


The LEP Spectrometer

position measurementwith 1 µm

magnetic fields∆B/B = O(10−5)

final energy resolution:∆E/E = O(10−4)

Q18 Q17

Copper "Absorbers"

Stretched-Wire Position Monitor

PickupsSteel "Injection" Dipole

0 10 m


The LEP Spectrometer II

Pickup positions monitored with a stretched wire system (beware ofthermal effects due to synchrotron radiation etc.)

Take into account the local magnetic field of the earth and fields gene-rated by close-by power lines

Jurassic Limestone Block

Stretched WirePosition Sensors


Beam Energy from ParticlePhysics Processes

A.-S. Müller Energy Measurements – Particle Physics page 9

Radiative Returns to the Z

X-check Ecm using ofthe type e+e− → Zγ,Z → ff where thefermion f is a quark,electron, muon orτ-lepton

From knowledge of mZ

at LEP1 invert problemand deduce initialcollision energy of event

∆E/E = O(3 · 10−4)

√s′ /GeV

Eve

nts

√s′ /GeV

Eve

nts

√s′ /GeV

Eve

nts

√s′ /GeV

Eve

nts

(a) qq_(γ) (b) µ+µ−(γ)

(c) τ+τ−(γ) (d) e+e−(γ)

OPAL dataSignal2f bkg4f bkg+ 2γ bkg

0

1000

2000

3000

4000

5000

6000

7000

50 100 150 200 050

100150200250300350400450

50 100 150 200

0255075

100125150175200225250

50 100 150 200

10

10 2

10 3

50 100 150 200

G. Abbiendi et al., Phys. Lett. B (604) 2004.

A.-S. Müller Energy Measurements – Particle Physics page 10

Beam Energy from PhotonBased Methods

A.-S. Müller Energy Measurements – Photon Based Methods page 11

SR Spectrum

The spectrum of synchrotron radiation has a strong dependence onthe electron beam energy

measure synchrotronphoton spectrum

determine εc

measure B

derive E0

Ü the uncertainty ∆E/E

is of O(10−3)

10−3 10−2 10−1 100 10110−3

10−2

10−1

100

ξ = ω / ωc

Rel

ativ

e Po

wer

50 %

~ 1.3 (ξ)1/2 e−ξ

~ 2.1 ξ1/3

εc [eV] = 665 E2 [GeV2] B[T]


SR Spectrum II

Measure photon spectrum fordifferent absorber (Al)thicknesses

Integrated spectra allow toreconstruct synchrotronradiation spectrum

Critical energy εc follows from fitaccording to e−ε/εc

E. Tegeler, G. Ulm, NIM A (266) 1988.


Compton Back Scattering I

Laser photons of energy ε1 scatter with electrons of energy E0

according to relativistic kinematics, resulting in the final photonenergy ε2

ε2 = ε1

1 − β cos φ

1 − β cos θ + ε1(1 − cos (θ − φ))/E0

For head-on collisions (φ = π) and observation in direction ofelectron beam (θ = 0)

εmax2 = ε1 4γ2 1

1 + 4γε1/(mec2)

Ü determine end of spectrum εmax2 at a detector (e.g. HPGe)

Relative uncertainty ∆E/E ∝ ∆εmax2 /εmax

2 is of O(10−4)

PSfrag replacements

φ θE0ε1

ε2


Compton Back Scattering II

Measurement at BESSY I (800 MeV)

laser off

laser on

difference

Ü E0 = 796.88(12) MeV

R. Klein et al., NIM A (384) 1997.


Beam Energy fromMeasurements of the

Central Frequency

A.-S. Müller Energy Measurements – Central Frequency page 16

Central Frequency and Momentum

The speed of particles relative to c

can be written as

β =C frev

c=

C fRF

hc

To simultaneously determine p andC, measure frev for two particletypes with different Z/m in thesame machine (e+/p, p/Pb53+)

Momentum can be written as

p ≈ mpc

√

√

√

√

fRF,p

2∆fRF

[

(

mi

Zmp

)2

− 1

]

Ü for high energies difficult since∆f ∝ (mi/Zmp)2/p2

Ü maximise mi/Zmp (Pb53+)

∆p/p is of O(10−4)

fRF - 200 390 000 (Hz)

Q

Proton

4179 +- 1

4321 +- 1

0.12

0.14

0.16

0.18

0.2

3800 4000 4200 4400 4600fRF - 200 390 000 (Hz)

Q

Proton

4179 +- 1

4321 +- 1

0.12

0.14

0.16

0.18

0.2

3800 4000 4200 4400 4600

fRF - 200 380 000 (Hz)

Q

Pb53+

7985 +- 1

8119 +- 2

0.12

0.14

0.16

0.18

0.2

7400 7600 7800 8000 8200 8400 8600

J. Wenninger, SPS 2003: 449.16(14) GeV

A.-S. Müller Energy Measurements – Central Frequency page 17

Beam Energy fromMeasurements of the

Energy Loss

A.-S. Müller Energy Measurements – Energy Loss Measurements page 18

Energy from Energy Loss

U0

/ MeV

E0 / GeV

LEP

0

500

1000

1500

2000

2500

40 50 60 70 80 90

Energy loss per turn andparticle:

U0 =4π

3

rc

(mc2)3

E40

ρ

Ü high sensitivity on E!

Quantities that depend onU0 are e.g. radiation dam-ping, ∆xD and Qs

Circumference / m Energy / GeV U0 / MeV

ANKA 110 2.5 0.6ESRF 844 6.0 4.9LEP 26700 94.5 2576


Energy from Coherent Damping

Coherent damping at LEPÜ composed of radiation and head-tail damping:

1/τcoh = 1/τ0 + 1/τhead−tail

1

τ0

=1

2

U0 frev

E0

Jx ∼ E30

1

τhead−tail∝

σsQ′

E0

Ib

Synchrotron radiation dampingÜ due to emission of synchrotron γ

and RF gains

Head-tail dampingÜ depends on chromaticity and

bunch current

Beware of filamentation! p

p p0

∆ γp

∆pRF

p1


Energy from Coherent Damping II

-2

0

100 150 200 250 300 350 400 450 500 550 600

-2

0

100 150 200 250 300 350 400 450 500 550 600

-2

0

100 150 200 250 300 350 400 450 500 550 600

-0.1

0

0.1

100 150 200 250 300 350 400 450 500 550 600

Turn

x / mm

Turn

x / mm

Turn

x / mm

Turn

xData-xFit / mm

Turn

x / mm

Turn

x / mm

Turn

x / mm

Turn

x / mm

75 µA

205 µA

320 µA

450 µA

-2

0

2

4

6

0 200 400 600 800 1000

-2

0

2

4

6

0 200 400 600 800 1000

-2

0

2

4

6

0 200 400 600 800 1000

-2

0

2

4

6

0 200 400 600 800 1000


Energy from Coherent Damping III

Measure for different chromaticities Ü contribution from head-taildamping varies, radiation damping stays the same as long as the ener-gy stays the same (warning: better be finished before the tide turns....)

Energy loss from comparisonto MAD:U0 = UMAD

0 τMAD0 /τmeas

0

Sources of uncertaintyÜ Jx and central frequencyÜ energy / frequency shifts

due to tides

Finally:8 Energy uncertainty O(1%)

Ü not sufficiently precise forE-calibration but still quiteinteresting Ibunch / µA

E0 = 45.625 GeV

-2

0

2

4

6

8

10

12

14

16

18

100 200 300 400 500

τ-1 )

10

( /

T

3re

v

Q’ < 0

Q’ > 0


Qs and RF Voltage

first pointed out by H. Burkhardt and A. Hofmann as a means todetermine the energy loss at LEP

Synchrotron tune Qs depends on total RF voltage and beam energy

Q4s =

(

αch

2πE

)2

e2 V2RF −

(

Cγ

ρE4 + K

)2

∼

a

E2+ bE6

X-calibrate at “low”energies with RDP anduse method to extrapolateto energies where RDPdoesn’t work

Energy resolution:∆E/E = O(10−4)

Qs

VRF / MV

Enom = 50.005 GeV

Enom = 55.293 GeV

Enom = 60.589 GeV

Enom = 80.000 GeV0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

250 500 750 1000 1250 1500 1750 2000 2250 2500

energy

calibration

determination


Beam Energy fromResonant Depolarisation

A.-S. Müller Energy Measurements – Resonant Depolarisation page 24

Transverse Polarisation

Polarisation build-up by emission ofsynchrotron radiation:

Ü asymmetry in spin flip probabilityleads to transverse polarisation

Ü max. polarisation is given by sizeof asymmetry term:

8/5√

3 ≈ 92.4%

Polarisation level increasesexponentially with build up time

τp =8

5√

3

1

α

(

m0c2

hc

)2ρ3

cγ5

(

R

ρ

)

Ü typical for electrons: severalminutes to a few hours

Ü LEP: 340′, ANKA: 10′

P(t) = P0

(

1 − e−t/τp)

4:00 4:20 4:40

0

5

10

15

Pasymp,τ (%) = 11.5 ± .3

04-Nov-1996 day time (h)

LEP PolTeam

Ebeam = 50 GeV / optics: 90/60


Spin Motion

The motion of the spin vector ~s of a relativistic electron in thepresence of electric and magnetic fields ~E and ~B is described by theThomas-BMT (Bargmann, Michel, Telegdi) equation:

d~s

dt= ~ΩBMT × ~s

The spin precession frequency ~ΩBMT can be written as

~ΩBMT = −e

γm0

[

(1 + aγ) ~B⊥ + (1 + a) ~B‖ −

(

aγ +γ

1 + γ

)

~β ×~E

c

]

a = (ge − 2)/2 = 0.001159652193(10)

The average over all particles of the number of spin oscillations perrevolution is defined as the spin tune

ν = fspin/frev =(ge − 2)/2

m0c2E0


Resonant Depolarisation

l (Tm)bx

-0.0002

0 1 2 3

0.0002

PP

PP

n0

0.14 mrad

Turns

Horizontal magn. field Bx

modulated with fdep is appliedto the beam

For a certain phase relationbetween the kicks of thedepolariser and the spin tunethe small spin rotations addup coherently from turn toturn and the polarisation isdestroyed

Ü resonance condition forspin rotations

fdep = (k ± [ν]) · frev, k ∈ N

To determine the spin tune, the frequencyof the depolariser field is slowly variedwith time over a given frequency range

Ü beam energy from γ = ν/a

Ü precision: ∆E/E ≈ 10−6 − 10−5


Polarisation and Loss Rate

To detect a change in polarisation, a polarimeter is needed

Touschek cross-section depends on electron beam polarisationÜ use particle loss rate as a measure for polarisation level

Set up a beam loss monitor in a Touschek sensitive region (low β fol-lowed by large Dx) and monitor fast loss rate changes

Test detector sensitivity andsetup by moving tune fromand to a resonance (knownimpact on life time / loss rate)

Touschek polarimtery evenworks for machines that arenot limited by the Touschekeffect

loss

rate

/ kH

z

time / s

0.5

0.75

1

1.25

1.5

0 50 100 150

PSfrag replacements

Q2

Q2Q2

Q2

Q2Q2


Simple Polarimeter

E.g. with scintillators wrapped inlead sheets to suppress the con-tribution of synchrotron radiationto the count rate

Alterntive: Pb-Glass block withphoto multiplier

Photo multiplier pulses are con-verted to NIM signals and coun-ted using a custom made inter-face to a Linux PC


LEP Energy Calibration

Beam Energy / GeV

Pol

ariz

atio

n / %

0

20

40

60

40 50 60 70

Absolute measurement of polarisation level with Compton scattering:Ü Circ. polarized laser light collides with beamÜ Measure vert. profile of γs in Si-W calorimeterÜ P⊥ ∝ vert. shift of γ profiles for the two pol. statesÜ RDP works for P > 5 % ⇒ extrapolation methods necessary for

higher E0


LEP Polarimeter

Si-W calorimeter

Movableabsorber (Pb)

Detectors

Synchrotronlight monitor

γ

3 mradLIR

Nd-YAG laser (100 Hz)

Focussing mirrorfor positronmeasurement

Focussinglense

Laser pulse

Electronbunch(11 kHz)

Electrondetector

Soleil-Babinetcompensator

Rotating/2 plateλ

Mirror

Mirror

Mirror

Optical bench

BackscatteredPhotons

Positrondetector

Positronbunch(11 kHz)

313 m 313 m

Laser polarimeter

Expander


Depolarisation Scansre

lativ

e ch

ange

in lo

ss r

ate

depolariser frequency [MHz]

depolarisation on Ebeam

depolarisation on Qs side band

-0.1

-0.05

0

0.05

0.1

1.64 1.65 1.66 1.67 1.68 1.69 1.7

scan the depolariser frequencyacround the suspected beamenergy equivalent

get fdep from a fit

r = a −∂rI

∂tt +

∆r

1 + exp

− t−td

σd

depolarisation can also occur onsynchrotron side bands

due to the single particlenature of the depolarisati-on process, this happens atfdep/frev = [ν] ± Qinc

s

rela

tive

chan

ge in

loss

rat

e

depolariser frequency [MHz]

-0.05

0

0.05

1.68 1.69 1.7


Some RDP Applications∆E

/ E

∆fRF / fRF0

-0.01

-0.005

0

-0.2 0 0.2 0.4 0.6 0.8x 10

-4

inco

here

nt Q

s

coherent Qs

22

24

26

28

30

21 22 23 24 25 26 27 28 29 30

Measure αc using RDP scans fordifferent fRF:

∆fRF

fRF= αc1 δ + αc2 δ2

Relative precision ∆α/α ≈ 10−3

Measure simultaneously inc. (RDP)and coh. (stripline etc.)

The coh./inc ratio is a measure forbunch lengthening with current(A. Hofmann, 1994)

Qcohs

Qincs

= 1 − λIbunch


The Moon


LEP and the Moon

Moon ecliptic

Earth Rotation Axis

∆R < 0 ∆R > 0

ε M

ε E

= 5 oεε ME = 22oTides affect both the oceansand the earth crust

Local radius change ∆R dueto mass M at distance d withzenith angle θ:

∆R ∝M

d3(3 cos2 θ − 1)

Some facts:Ü Sun tides are 50 % weaker than Moon tidesÜ Full Moon tides at equator ∆R ≈ ± 50 cmÜ Geneva region: vertical motion ≈ ± 12.5 cmÜ Change in LEP circumference of ≈ ± 0.5 mm

J. Wenninger


Circumference and Energy

Impact on LEP beam energy becauseÜ length of actual orbit L is determined by the frequency of the RF

systemÜ change in circumference ∆C Ü beam has to move off-centre

through the magnetsÜ additional bending field in the quadrupoles changes the beam

energy

E ∝∮

Bds

Resulting change in beam energy:

∆E

E= −

1

αc

(fRF − fcRF)

fRF

= −1

αc

∆C

C


LEP and the Moon II

∆ E

[MeV

]

November 11th, 1992

Daytime23:00 3:00 7:00 11:00 15:00 19:00 23:00 3:00

-5

0

5

Beam energy measurement with RDP during full moon compared to aprediction by a geological model

(L. Arnaudon et al.: Effects of Terrestrial Tides on the LEP Be-

am Energy. NIM A357, pages 249–252, 1995. )


Continuous E-monitoring

Flux LoopNMR probe

beampipe

DipoleFlux Loop

continuous monitoring of the beam energy by measurements of thebending field using E0 ∝

∮dsB

NMR probes and and flux loop cables

field measurements calibrated for low beam energies with RDP andthen used for extrapolation to high beam energies


Impact of Civilisation

Noisy period Calm period

16:00 18:00 20:00 22:00 00:00 02:00 04:00 06:00

46474

46478

46482

46486

46490

46494

46498

Time of day

Bea

m E

nerg

y / M

eV

Measurements of theLEP dipole field withNMR probes in someof the bendingmagnets yieldvariations of the beamenergy since

E0 ∝∮

dsB

correlation with humanactivity?


The TGV

photo by S. Ingolstadt


Vagabond CurrentsV

olta

ge o

n ra

ils [V

]

Railway Tracks

TGV

Gen

eve

Mey

rin

Zim

eysa

17.11.1995

Vol

tage

on

beam

pipe

[V]

LEP Beam Pipe

Time

Ben

ding

B fi

eld

[Gau

ss]

LEP NMR

-7

0

-0.024

-0.02

-0.016

-0.012

746.28

746.30

746.32

746.34

746.36

16:50 16:55

Lake

Lem

an

Versoix

SPS Bellevue

Genthod

Lausanne

1 km

Zimeysa Meyrin

Cornavin

La Versoix

Belleg

arde

Airport

Russin

St. Jean

Vernier

IP 1

IP 7

IP 6

IP 8

IP 2

IP 3

IP 4IP 5

LEP

DC railway 1500VAC railway 15000VRiverEarth current

Earth current

power station

about 20 % of current does not flowback to power station over the railwaytracks

in France some lines use DC currents:lower voltages ⇒ higher currents


LEP Energy: A Closer Look

The energy model of LEP:

Ebeam(t) = (Einitial + ∆Edipole(t))

· (1 + Ctide(t)) · (1 + Corbit) · (1 + CRF(t))

· (1 + Chcorr(t)) · (1 + CQFQD(t))

Term Physical Effect O(∆E) [MeV]

∆Edipole magnet temperature, parasitic currents on the vacu-um chamber etc.

10

Ctide tidal deformations (quadrupole contribution) 10Corbit Circumference changes due to rainfall / under-

ground water table height10

CRF RF frequency change (∼ 100 Hz) to reduce σx byincreasing Jx

100

Chcorr horizontal correctors change∮

Bds and ∆L 10CQFQD stray fields of power supply cables 1


Historical Problem

The problems with electrical trains close to physics institutes are notexactly a recent discovery...

Journal article in 1895:

Central-Zeitung für Optik und Mechanik, XVI. Jg., No. 13, Page 151

“Nachtheile physikalischer Institute durch elektrische Bahnen”

(which roughly translates to “Disadvantages for Physics Institutes fromElectrical Trains”)

What happened:During first tests with electrical trams (instead of the horse-powered mo-dels) in Berlin it became clear that vagabond currents severely disturbedthe delicate electrometers


Summary

Beam energy is an important parameter forcontrol room and experiment

A variety of methods exists, chooseaccording to design precision and energy range

To achieve highest precision, a combinationof several measurements might be needed

Once achieved, the high precision measure-ments might have some surprises in store....

Advice: plan for long shifts...

8

4

4

4

¢

A.-S. Müller Energy Measurements – Summary page 44

Measurements of Beam Energy - CERN · ANKA, PAC03 A.-S. Müller Energy Measurements Œ Introduction...

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