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Challenges for Polarimetry at the ILC
Moritz Beckmann, Anthony Hartin, Jenny List
DESY - FLC
EUCARD Workshop“Spin optimization at Lepton accelerators”
Mainz, GermanyFebruary 12, 2014
Outline
• Introduction• Polarimetry in the ILC beam delivery system• Spin transport
• Results• Beamline simulation• Collision effects
• Polarization measurement at the disrupted beam• Beamline design in view of the polarization measurement• Impact of the laser spot size at the downstream polarimeter
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 2 / 26
ILC Beam Delivery System (BDS)
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 3 / 26
Laser Compton Polarimeter (Principle)
dipole magnetspolarized laser
scattered e±
e± beam
detector
• Laser: Compton scattering e± γ → e± γ• Scattering cross section depends on Pz
• Magnet chicane separates scattered e± from beam• Pz is determined from scattered electrons
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 4 / 26
Polarimetry at the ILC
150 m~1 650 m
upstream polarimeter IP
downstream polarimeter
e± beamlines
• Two Compton polarimeters per beam to measure Pz• Upstream polarimeter undisturbed by collision effects• Downstream polarimeter assesses collision effects• 0.25 % systematic uncertainty (goal)
• What do these measurements tell us about thelongitudinal polarization at the IP?
→ spin transport simulation
• Aim to understand spin transport to 0.1 %
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 5 / 26
Polarimetry at the ILC
150 m~1 650 m
upstream polarimeter IP
downstream polarimeter
e± beamlines
• Two Compton polarimeters per beam to measure Pz• Upstream polarimeter undisturbed by collision effects• Downstream polarimeter assesses collision effects• 0.25 % systematic uncertainty (goal)
• What do these measurements tell us about thelongitudinal polarization at the IP?→ spin transport simulation
• Aim to understand spin transport to 0.1 %
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 5 / 26
Spin Precession
• Spin precession in electromagnetic fields:T-BMT equation
• For ~B⊥ only:
ϑspin = b(E) · ϑorbit
b(E ) = aγ + 1 = g−22 ·
Em + 1
≈ 568 for 250 GeV-electrons
• Dipole magnets, no beam energy spread:spin vectors precess uniformly, |~P| conserved
B
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 6 / 26
Spin Fan-Out in Quadrupole Magnets
PP'P
quadrupole magnets
For illustration purposes, the second quadrupole is stronger. Two-dimensional
betatron oscillations are not taken into account here.
• Different precession angles after first quadrupole⇒ polarization |~P| decreases
• |~P| recovered by second quadrupoleMoritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 7 / 26
Beam-Beam Collision Effects
e e Pairs+ _
BeamstrahlungA. Vogel
Bunches focus each other by their electromagnetic fields:
• Spin fan-out (like in quadrupole magnets)
• Spin flip by emission of beamstrahlung(Sokolov-Ternov effect)
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 8 / 26
Spin Transport Simulation Framework
UP IP DP
beam-beam collisionGuinea-Pig++
data analysis
polarimeter measurement
polarimeter measurement
beamline layout
particle / spin transport along the BDS Bmad
beam parameters
• Developed a beamline simulation (based on Bmad)
• Simulate 40 000 (macro)particles per bunch, generated frombeam parameters at the beginning of the BDS
• Interfaced directly to the simulation of the collisions(Guinea-Pig++)
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 9 / 26
Results
•√s = 500 GeV
• Beam parameters according to Reference Design Report(RDR, 2007)
• Collision effects also for beam parameters according toTechnical Design Report (TDR, 2013)
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 10 / 26
Spin Transport in the BDS: Basic Configuration
distance s along BDS [m]0 500 1000 1500 2000 2500 3000 3500
po
lari
zati
on
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
UP IP DP
-ezP|P|
UP/DP: up-/downstream polarimeter
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 11 / 26
Spin Transport in the BDS: Basic Configuration
distance s along BDS [m]3400 3450 3500 3550
po
lari
zati
on
0.799
0.7995
0.8
]-3
rela
tive
ch
ang
e [1
0
-1
-0.5
0
IP DP
-e
zP|P|
extractionline
quadrupoles
dipole chicanes
DP: downstream-polarimeter
• Quadrupoles cause spin fan-out
• Changes in Pz well below 0.1 % without collisions
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 12 / 26
Factors affecting the spin transport (without collisions)
contribution uncertainty[10−3]
Beam and polarization alignment 0.72(∆ϑbunch = 50µrad, ∆ϑpol = 25 mrad)Random misalignments (10µm) 0.43Variation in beam parameters (few %) 0.03Bunch rotation (crab cavities) < 0.01Detector solenoid 0.01Synchrotron radiation 0.005
Total (quadratic sum) 0.85
Now: e+e− beam collisions
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 13 / 26
Spin Transport after Collision
distance s along BDS [m]3400 3450 3500 3550
zlo
ng
. po
lari
zati
on
P
0.76
0.77
0.78
0.79
0.8
]-3
rela
tive
ch
ang
e [1
0
-40
-20
0
IP DP
-e
no collisionlumi-weightedafter collisionmeasurable
no collisionlumi-weightedafter collisionmeasurable
DP: downstream-polarimeter
• Luminosity-weighted (•): Pz of the colliding particles
• Larger angular divergence / energy spread after collision
• Large spin fan-out in extraction line quadrupoles
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 14 / 26
Spin Transport after Collision
distance s along BDS [m]3400 3450 3500 3550
zlo
ng
. po
lari
zati
on
P
0.76
0.77
0.78
0.79
0.8
]-3
rela
tive
ch
ang
e [1
0
-40
-20
0
IP DP
-e
no collisionlumi-weightedafter collisionmeasurable
no collisionlumi-weightedafter collisionmeasurable
DP: downstream-polarimeter
• Extraction line design: restore luminosity-weighted Pz(•) at the downstream polarimeter
• Employ spin fan-out: focus beam at downstreampolarimeter with half divergence angle w. r. t. the IP
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 15 / 26
Spin Transport after Collision
distance s along BDS [m]3400 3450 3500 3550
zlo
ng
. po
lari
zati
on
P
0.76
0.77
0.78
0.79
0.8
]-3
rela
tive
ch
ang
e [1
0
-40
-20
0
IP DP
-e
no collisionlumi-weightedafter collisionmeasurable
no collisionlumi-weightedafter collisionmeasurable
DP: downstream-polarimeter
θx θy ⇒ ∆Pz ∝ θx2
∆P lumz ≈ 1
4∆Pz ∝(θx
2
)2
Idea: |R22(IP→ DP)| = 0.5 ⇒ P lumz = PDP
z
Further reading: SLAC-PUB-4692, SLAC-PUB-8397
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 16 / 26
Laser and Particle Bunch at the Downstream Polarimeter
after collisionwithoutcollision
laser spote± beam
~mm ~cm0.04mm
~cm
• Without collision: entire beam exposed to laser
• After collision: center of beam exposed to lasersample of scattered electrons representative?
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 17 / 26
Downstream Measurement
• Downstream polarimeter located in magnet chicane⇒ particle position correlated with energy (dispersion)
-0.4 -0.3 -0.2 -0.1 0-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
0.015
1
10
210
310
410
510
610
particle energy [GeV]160 180 200 220 240ve
rt. p
arti
cle
po
siti
on
y [
mm
]
-20
-10
0
10 Laser spot size
• Laser spot size at Compton-IP only ∼ 0.1 - 1 mm
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 18 / 26
Downstream Measurement
• Beamstrahlung correlates energy and Pz⇒ Pz correlated with particle position⇒ Selective measurement, measurement bias
-0.015 -0.01 -0.005 0
zlo
ng
. po
lari
zati
on
P
0.75
0.76
0.77
0.78
0.79
0.8
vert. particle position y [mm]-15 -10 -5 0
laser spot size
• Measurable longitudinal polarization := average Pz ofparticles within a given (laser spot) radius
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 19 / 26
Spin Transport for Different Beam Parameters
0 20 40 60
zlo
ng
. po
lari
sati
on
P
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
no energy spread/lossRDR TDR TDR* RDR TDR TDR*
before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
DP: downstream polarimeter
• No energy spread/loss: no discrepancy between measurement() and average Pz () at downstream polarimeter
• RDR → TDR: stronger focussing ⇒ higher collision intensity⇒ larger spin fan-out in collision and afterwards
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 20 / 26
Spin Transport for Different Beam Parameters
0 20 40 60
zlo
ng
. po
lari
sati
on
P
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
no energy spread/lossRDR TDR TDR* RDR TDR TDR*
before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
DP: downstream polarimeter
• No energy spread/loss: no discrepancy between measurement() and average Pz () at downstream polarimeter
• RDR → TDR: stronger focussing ⇒ higher collision intensity⇒ larger spin fan-out in collision and afterwards
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 20 / 26
Spin Transport for Different Beam Parameters
0 20 40 60
zlo
ng
. po
lari
sati
on
P
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
no energy spread/lossRDR TDR TDR* RDR TDR TDR*
before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
DP: downstream polarimeter
Extraction line design: restore P lumz (•) at downstream pol. ()
• Design (|R22| = 0.5) assumes Dx 1DRDRx = 0.17 DTDR
x = 0.3
• More beamstrahlung (not accounted for by design)
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 21 / 26
Spin Transport for Different Spin Configurations
DP
TDR*
R22=-0.5
P'
P
P
P'
IP
TDRafter collision
T-BMT
T-BMT
assumingθ
spin= (aγ+1)·θ
orbit
at the beginning
assumingθ
spin= (aγ+1)·θ
orbit
at the beginning
For illustration only. All angles exaggerated. Beamstrahlung effects neglected.
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 22 / 26
Spin Transport for Different Spin Configurations
0 20 40 60
zlo
ng
. po
lari
sati
on
P
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
no energy spread/lossRDR TDR TDR* RDR TDR TDR*
before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
DP: downstream polarimeter
TDR* with respect to TDR:
• All spin vectors parallel before collision, bunch focussed(45µrad divergence angle)
• Mostly same behaviour in collision (N, •, H), but differentvalue at downstream polarimeter ()
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 23 / 26
Spin Transport for Different Beam Parameters
0 20 40 60
zlo
ng
. po
lari
sati
on
P
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
no energy spread/lossRDR TDR TDR* RDR TDR TDR*
before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
DP: downstream polarimeter
• Polarization varies by several % along the extraction line
• Discrepancies between P lumz and Pz at the downstream pol.
(•, , ) in the range 0.1− 0.4 %;discrepancies cancel partially, but only coincidentally
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 24 / 26
Conclusions
• Cross-calibration (without collisions) to precision of < 0.1 %
• Polarization vector alone not sufficient anymore to describespin configuration of beam:• Spin fan-out becomes relevant due to higher measurement
precision, higher energy and more intensive collisions• How well do we know the initial spin configuration?→ “cradle-to-grave” simulation
• Extraction line design (restore P lumz at downstream pol.):
• Works as foreseen for low-intensity collisions X• TDR beam parameters: higher intensity → larger discrepancies• Beamstrahlung not taken into account; Dx no longer 1• Disrupted beam lets knowledge of the laser spot size/position
at the downstream polarimeter become crucial for themeasurement precision
• Larger laser-spot? Drawbacks: required laser power,low-energy tail undesired in polarimeter
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 25 / 26
Conclusions
• Cross-calibration (without collisions) to precision of < 0.1 %
• Polarization vector alone not sufficient anymore to describespin configuration of beam:• Spin fan-out becomes relevant due to higher measurement
precision, higher energy and more intensive collisions• How well do we know the initial spin configuration?→ “cradle-to-grave” simulation
• Extraction line design (restore P lumz at downstream pol.):
• Works as foreseen for low-intensity collisions X• TDR beam parameters: higher intensity → larger discrepancies• Beamstrahlung not taken into account; Dx no longer 1• Disrupted beam lets knowledge of the laser spot size/position
at the downstream polarimeter become crucial for themeasurement precision
• Larger laser-spot? Drawbacks: required laser power,low-energy tail undesired in polarimeter
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 25 / 26
Thanks for your attention!
Further reading:
• DESY-THESIS-13-053http://www-library.desy.de/preparch/desy/thesis/desy-thesis-13-053.pdf
• Publication in preparation
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 26 / 26
Backup Slides
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 27 / 26
Differences RDR - TDR
Parameter symbol RDR TDR
Bunches per train 2 625 1 312Horizontal bunch size σx [nm] 639 474Vertical bunch size σy [nm] 5.7 5.9Beam energy spread (e−/e+) σE/E [10−3] 1.4/1.0 1.24/0.7
e+e− luminosity L [1038 m−2 s−1] 2 1.47incl. waist shift 1.8
Beamstrahlung parameter Υglobal 0.048 0.062
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 28 / 26
Thomas-Bargmann-Michel-Telegdi (T-BMT) Equation
d
dt~S =
(~ΩB + ~ΩE
)× ~S
~ΩB =− q
mγ
((1 + aγ) ~B − a ~p · ~B
(γ + 1)m2c2~p
)
=− q
mγ
((1 + aγ) ~B⊥ + (1 + a) ~B‖
)
~ΩE =q
mγ· 1
mc2
(a +
1
1 + γ
)~p × ~E
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 29 / 26
Compton Scattering
0 50 100 150 200 2500.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
σC
om
pto
n[m
barn
/ G
eV
]
Compton−scattered Electron Energy [GeV]
λPe = +1(same)
λPe = −1
(opposite)
0 100 200 300 400 5000
5
10
15
20
25
30
Com
pton
End
poin
t Ene
rgy
[GeV
]Beam Energy [GeV]
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 30 / 26
Polarimeter Chicane (upstream)
• Constant magnetic field• Dispersion (depending on beam energy): 1-11 cm• Scattering for every bunch per bunch train• Energy spectrum is polarization-dependent• Energy distribution → spatial distribution• Cherenkov gas detector counts electrons per channel
+e /e
+e /e IP
16.1m
8 m
16.1m
CherenkovDetector
125 GeV
25 GeV
50 GeV
Magnetic Chicane
250 GeV
24 c
m
45.6 GeV
inout
LaserIP
8.1m
Dipole 2 Dipole 3
8.1m
Dipole 4Dipole 1
P11P10 P12P1 P2 P3
P5P4 P6 P7 P8 P9
total length: 74.6 m
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 31 / 26
Polarimeter Chicane (downstream)
• Constant magnetic field• Dispersion (depending on beam energy): 1-11 cm• Scattering for 3 bunches per bunch train• Energy spectrum is polarization-dependent• Energy distribution → spatial distribution• Cherenkov gas detector counts electrons per channel
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 32 / 26
Polarimeter Detector
e
PMLED (calibration)
Cherenkov photons
2
10 c
m
10 x 10 mmcross section:
15 cm
Al−
tube
s
beam
aluminum tubes
xy
z
photodetectors
LEDs
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 33 / 26
Compton Polarimeters: Systematic Errors
Goal: relative systematic error on measurement < 0.25 %(SLD polarimeter: 0.5 %)
• Detector linearity: contribution of ∼ 0.1− 0.2 % (goal)
• Laser polarization: ∼ 0.1 % X• Analyzing power: ∼ 0.1 % (UP: X, DP: ?)
• Detector alignment: can be determined from data (X)0.5 mm precision sufficient
• Alignment of magnets negligible compared to detector XField inhomogeneities? to be investigated
• Disrupted electron beam at downstream polarimeter:• Dependence on laser-spot size and position: ??• Beam energy spread no concern for small laser-spot sizes
thanks to dispersion X
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 34 / 26
Polarization Measurement at the IP
-1Luminosity fb0 200 400 600 800 1000 1200
% e
rror
pol
ariz
atio
n
0
0.2
0.4
0.6
0.8
1 pol- pol 80% e+30% e
positron Blondel
electron Blondelpositron Fitelectron Fit
-1Luminosity fb0 200 400 600 800 1000 1200
% e
rror
pol
ariz
atio
n
0
0.2
0.4
0.6
0.8
1 pol- pol 80% e+60% e
positron Blondel
electron Blondelpositron Fitelectron Fit
I. Marchesini
Blondel scheme:
|P lumiz (e±)| =
√(σ−+ + σ+− − σ−− − σ++)(±σ−+ ∓ σ+− + σ−− − σ++)
(σ−+ + σ+− + σ−− + σ++)(±σ−+ ∓ σ+− − σ−− + σ++)
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 35 / 26
Polarization Measurement at the IP
I. Marchesini
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 36 / 26
Polarization Measurement at the IP
I. Marchesini
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 37 / 26
Quadrupole Magnet
S
NS
N
S
N S
N
Black arrows: magnetic field linesBlue arrows: forces on an incoming electron beam
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 38 / 26
Bunch Rotation at the IP
• Collision under crossing angle of 14 mrad
• Maximize luminosity: rotate bunches using crab cavities
• Time-dependent transverse deflection of particles
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 39 / 26
Downstream Pol.: Dispersion w/o Collision
-0.008 -0.006 -0.004 -0.002 0 0.002 0.004
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2-310×
1
10
210
310
410
510
particle energy [GeV]248 248.5 249 249.5 250 250.5 251ve
rt. p
arti
cle
po
siti
on
y [
mm
]
-0.2
-0.1
0
0.1
0.2
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 40 / 26
Downstream Pol.: Dispersion after Collision
-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
1
10
210
310
410
510
610
particle energy [GeV]160 180 200 220 240ve
rt. p
arti
cle
po
siti
on
y [
mm
]
-20
-10
0
10
-0.05 -0.04 -0.03 -0.02 -0.01 0
-0.4
-0.2
0
0.2
0.4
-310×
1
10
210
310
410
510
particle energy [GeV]238 240 242 244 246 248 250ve
rt. p
arti
cle
po
siti
on
y [
mm
]
-0.5
0
0.5
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 41 / 26
Downstream Measurement
Longitudinal polarization vs. energy at the downstreampolarimeter, after collision
-0.3 -0.2 -0.1 0
lon
g. p
ola
riza
tio
n
0.66
0.68
0.7
0.72
0.74
0.76
0.78
0.8
particle energy [GeV]160 170 180 190 200 210 220 230 240 250
(E)zP
zaverage P
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 42 / 26
0 50
zlo
ng
. po
lari
zati
on
P
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
UP before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
-e
no CCnoCCL no BS,SR
no SRref. WS WSL TDRϒ
0 20 40 60 80
|P
enti
re p
ola
riza
tio
n |
0.79
0.795
0.8 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
-e
no CCnoCCL no BS,SR
no SRref. WS WSL TDRϒ
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 43 / 26
0 50
zlo
ng
. po
lari
zati
on
P
0.296
0.297
0.298
0.299
0.3 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
UP before collision lumi-weighted after collision DP DP measurable (r=0.1/0.2/0.5/1.0 mm)
+e
no CCnoCCL no BS,SR
no SRref. WS WSL TDRϒ
0 20 40 60 80
|P
enti
re p
ola
riza
tio
n |
0.296
0.297
0.298
0.299
0.3 ]-3
rela
tive
ch
ang
e [1
0
-15
-10
-5
0
+e
no CCnoCCL no BS,SR
no SRref. WS WSL TDRϒ
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 44 / 26
Why Polarization?
Electroweak processes: cross sections depend on Pze. g. W+W− pair production
I. Marchesini
Polarized beams
• provide new observables
• can be used to enhance/suppress processes
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 45 / 26
The International Linear Collider (ILC)
• e+e− collider as complement to LHC
•√s ≤ 500 GeV, upgradable to 1 TeV
• Longitudinally polarized beams: |Pz(e−)| = 80 %
Longitudinally polarized beams:
|Pz(e+)| = 30 to 60 %
Moritz Beckmann DESY-FLC EUCARD Workshop Mainz 2014 46 / 26