Post on 29-Sep-2018
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
A.-S. Müller Energy Measurements – Introduction page 3
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
A.-S. Müller Energy Measurements – Introduction page 4
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
A.-S. Müller Energy Measurements – Spectrometers page 6
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
A.-S. Müller Energy Measurements – Spectrometers page 7
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
A.-S. Müller Energy Measurements – Spectrometers page 8
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]
A.-S. Müller Energy Measurements – Photon Based Methods page 12
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.
A.-S. Müller Energy Measurements – Photon Based Methods page 13
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
A.-S. Müller Energy Measurements – Photon Based Methods page 14
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.
A.-S. Müller Energy Measurements – Photon Based Methods page 15
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
A.-S. Müller Energy Measurements – Energy Loss Measurements page 19
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
A.-S. Müller Energy Measurements – Energy Loss Measurements page 20
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
A.-S. Müller Energy Measurements – Energy Loss Measurements page 21
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
A.-S. Müller Energy Measurements – Energy Loss Measurements page 22
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
A.-S. Müller Energy Measurements – Energy Loss Measurements page 23
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 25
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 26
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 27
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 28
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 29
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 30
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 31
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 32
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 33
The Moon
A.-S. Müller Energy Measurements – Resonant Depolarisation page 34
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 35
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 36
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. )
A.-S. Müller Energy Measurements – Resonant Depolarisation page 37
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 38
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?
A.-S. Müller Energy Measurements – Resonant Depolarisation page 39
The TGV
photo by S. Ingolstadt
A.-S. Müller Energy Measurements – Resonant Depolarisation page 40
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 41
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 42
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
A.-S. Müller Energy Measurements – Resonant Depolarisation page 43
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