development of a rogowski coil beam position monitor for...
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Development of a Rogowski coil Beam Position Monitor for Electric Dipole Moment
measurements at storage rings
PHD defense talk
Physics Institute III B | Nuclear Physics Institute (IKP-II)
Fabian Trinkel
15th December 2017
Content
1 of 23
• Motivation for Electric Dipole Moment (EDM) measurements
• Spin dynamics in storage rings
• EDM measurement at the accelerator facility COSY
• Beam position measurements
1. Common Beam Position Monitors (BPMs) at COSY
2. Development of a Rogowski coil BPM
3. Estimation of a deuteron EDM limit for a measurement at COSY
• Summary and future developments
Fabian Trinkel | III Physikalisches Institut B
Baryogenesis: Why does the universe contains more matter than antimatter?
2 of 23 Fabian Trinkel | III Physikalisches Institut B
Early Universe
Sakharov* conditions:
1. Baryon number violating interactions
2. Thermal non-equilibrium
3. Violation of 𝑪, 𝑪𝑷 symmetry
Possible sources:
• Strong 𝑪𝑷 violation (SM)
• Electroweak 𝑪𝑷 violation (SM)
Today
Anti-
matter Matter
Big Bang
Symmetry between matter and antimatter
Ryan K
ald
ari
, 2006, N
AS
A W
ikip
edia
Measurement
(WMAP)
Cosmological SM
Expectation
(𝜂𝐵−𝜂𝐵 ) 𝜂𝛾 6.14 ± 0.25 ⋅ 10−10 10−18
*Andrej Sakharov 21 May 1921 – 14 December 1989
Electric Dipole Moments (EDMs) as a new source of 𝑪𝑷 violation
• ℋ = −𝝁 ⋅ 𝐵 − 𝒅 ⋅ 𝐸
𝑷: ℋ = −𝝁 ⋅ 𝐵 + 𝒅 ⋅ 𝐸
𝑻: ℋ = −𝝁 ⋅ 𝐵 + 𝒅 ⋅ 𝐸
• Permanent EDMs of light hadrons are
𝑇-violating
– 𝑪𝑷𝑻 theorem ⇒ 𝑪𝑷 violation
• Standard Model expectation:
𝑑 ≈ 10−31e ⋅ cm (Estimated by the
neutron EDM limit) A. Knecht, 2008, Wikimedia
𝝁 = 𝒈 ⋅𝑒
2𝑚 𝒔 𝒅 = 𝜼 ⋅
𝑒
2𝑚𝑐 𝒔
3 of 23 Fabian Trinkel | III Physikalisches Institut B
: MDM
𝒅: EDM
𝐸 𝐵 𝒅
𝒅
𝒅
𝐸 𝐵
𝐸 𝐵
𝑷
𝑻
𝒔
𝒔
𝒔
EDM measurement at the accelerator facility COSY (COoler SYnchrotron)
4 of 23
Polarised
Source
Polarimeter
Electron
Cooler
Stochastic
Cooling
RF Wien Filter
(Stripline design)
Fabian Trinkel | III Physikalisches Institut B
COSY facts
Provides polarized protons
and deuterons
Circumference 184 m
Momentum 3.7 GeV/c
Intensity 109 to 1010
particles
Four experimental areas
Beam diagnostic systems
Spin manipulators
Spin dynamics in storage rings
5 of 23
Thomas-BMT-Equation:
•𝑑𝑆
𝑑𝑡= 𝑆 × ΩMDM + 𝑆 × ΩEDM
• ΩMDM =𝑞
𝑚𝛾𝛾𝐺𝐵 + 𝐺 −
1
𝛾2−1
𝛽×𝐸
𝑐
• ΩEDM =𝑞𝜂
2𝑚
𝐸
𝑐+ 𝛽 × B
G
Proton 1.792847357
Deuteron -0.142561769
𝜇 = 2 𝐺 + 1𝑞
2𝑚𝑆
𝑑 =𝑞𝜂
2𝑚𝑐𝑆
𝛽 ⋅ 𝐸 = 0
𝛽 ⋅ 𝐵 = 0
𝒅
𝒔
Fabian Trinkel | III Physikalisches Institut B
EDM measurement principle in a pure magnetic storage ring (COSY)
6 of 23 Fabian Trinkel | III Physikalisches Institut B
ΩMDM =𝑞
𝑚𝛾𝛾𝐺𝐵
ΩEDM =𝑞𝜂
2𝑚𝛽 × B
Ω = ΩEDM + ΩMDM
𝑠
𝑦
𝐵
Perfect accelerator and an EDM Realistic accelerator without an EDM
Scenario 𝒅 (e⋅cm) Orbit RMS (mm) 𝚫𝐒𝐲/𝐧
Perfect accelerator with an EDM 5 ⋅ 10−19 0 1.7 ⋅ 10−9
Realistic accelerator without an EDM 0 1.3 1.7 ⋅ 10−9
Source: Simulation M. Rosenthal, 2016, PhD thesis [3], Phys. Rev. ST Accel. Beams 16, 114001 2013 [6]
Ω = ΩMDM
𝑠
𝑦
𝐵
• EDMs introduce vertical polarization component
of a horizontal polarized beam
• Measure vertical polarization
Particle orbit
7 of 23 Fabian Trinkel | III Physikalisches Institut B
Ideal
Orbit 0
Orbit: mean displacement at all positions in the accelerator
Ideal
Orbit
Dipole magnet Quadrupole magnet
Ideal
Orbit
Dipole magnet Quadrupole magnet
X (mm)
Common Beam Position Monitor (BPM) system at COSY
8 of 23
Electrode right
Electrode left
Electrode down
Electrode up
Beam position determination
≈40 cm
Horizontal BPM Vertical BPM
𝝈𝑷𝒐𝒔 (μm) Source
≈ 0.2 Thermal noise
≈ 10.0 Resolution
≈ 100.0 Accuracy
Fabian Trinkel | III Physikalisches Institut B
Development of a Rogowski coil Beam Position Monitor
9 of 23 Fabian Trinkel | III Physikalisches Institut B
Free
area
Non-equally
distributed
windings
Parameters
𝑅 (mm) 40.0
𝑎 (mm) 5.0
𝑁 366
𝑠 (μm) 150
𝑅 2𝑎
Copper
winding
×
Geometrical
centre
𝑥
𝑧 𝑦
Segment 1
Segment 2 Segment 3
Segment 4
Voltage measurement principle with a lock-in amplifier
10 of 23
Zurich Instruments HF2LI
Lock-in amplifier
Fabian Trinkel | III Physikalisches Institut B
Signal 𝑉sig(𝑡)
Reference 𝑉ref(𝑡)
Mixer Low-pass filter
Amplitude,
Phase
Development of a Rogowski coil BPM
11 of 23
Development process
Theoretical calculations &
simulation
Construction, manufacturing
& test measurements with
a testbench in the laboratory
Test measurements at the
accelerator COSY
https://imgur.com/gallery/glxgY3L
Fabian Trinkel | III Physikalisches Institut B
Induced voltage calculation
12 of 23
Model:
Pencil-current with constant
velocity at position (𝑥0, 𝑦0)
Particle Beam Coil
Current: 𝐼 = 𝐼0 ⋅ 𝑒𝑧
Position: 𝑟0 = 𝑥0
𝑦0
0 𝑟 =
𝑥𝑦𝑧
Magnetic field: 𝐵 = 𝜇02𝜋𝐼
× 𝑟 −𝑟0𝑟 −𝑟0
2
x
y Segment 1
Segment 2 Segment 3
Segment 4
(𝑥0, 𝑦0) 𝑟𝑜
𝜑
2𝑎 𝑟 𝑅
Induced voltage for N windings:
Fabian Trinkel | III Physikalisches Institut B
Voltage ratio calculation
13 of 23
• Definition of the horizontal and vertical voltage ratio:
Fabian Trinkel | III Physikalisches Institut B
• Calculation of the horizontal and vertical voltage ratio:
• Calculation of the sensitivities: (𝑅 = 40.000 mm and 𝑎 = 5.075 mm)
Development of a calibration method
14 of 23
• Offset and rotation of the coil:
• Different signal strength:
• Calculation of single voltage ratio:
• Definition of a minimization function (6 free parameters):
Fabian Trinkel | III Physikalisches Institut B
x
y
x x
Geometrical
centre
Electrical
centre
x
x
Laboratory measurements with the Rogowski coil BPM
15 of 23
𝑥0
𝑦0
Data Acquisition (PC)
Master Slave
TTL
pulse
Preamp
Preamp
Preamp
Preamp
TTL
pulse
Sine
wave
4
3
1
2
Measurement setup Measurement procedure
• Test of the calibration algorithm
Fabian Trinkel | III Physikalisches Institut B
Measurement parameters
Frequency 750 kHz
Particles 1010
Number of
measurements
105
Range −5 mm to 5 mm
Laboratory measurements with the Rogowski coil BPM
16 of 23
𝒙𝒐𝒇𝒇 (mm) 𝒚𝒐𝒇𝒇 (mm) 𝝋 (°)
𝟏
𝚺𝐠𝐢 (%)
𝒈𝟐
𝚺𝐠𝐢 (%)
𝒈𝟑
𝚺𝐠𝐢 (%)
𝒈𝟒
𝚺𝐠𝐢 (%)
3.4 3.3 −0.40 20.9 28.3 28.7 22.1
(0 mm, 0 mm)
(5 mm, 5 mm)
(-5 mm, -5 mm)
• Reconstruction of the wire positions • Accuracy: ≈ 150 μm
• Caused by the
asymmetry of the coil
• This effect is not
considered in the
calibration algorithm
• Resolution: ≈ 1.25 μm
• The theoretical resolution
limit is reached
Fabian Trinkel | III Physikalisches Institut B
Beam position measurements with a Rogowski coil BPM at COSY
17 of 23
Horizontal orbit bumps:
• Values: −2% to 2%
• Step size: 0.2%
• Frequency: 750 kHz
• Number of particles: 1010
Fabian Trinkel | III Physikalisches Institut B
Beam position measurements with a Rogowski coil BPM in COSY
18 of 23
Cycle 1
Vert
ical dis
pla
cem
ent
Time (s)
Initial beam position
Local orbit bump
Initial beam position
Vertical ratio:
Vertical model ratio expectation:
Horizontal ratio:
Horizontal model ratio expectation:
Fabian Trinkel | III Physikalisches Institut B
Time (s)
Initial beam position
Local orbit bump
Cycle 1
Horizonta
l dis
pla
cem
ent
Initial beam position
𝑥2
𝑥1
Beam position measurements with a Rogowski coil BPM in COSY
19 of 23 Fabian Trinkel | III Physikalisches Institut B
Beam position measurements with a Rogowski coil BPM in COSY
20 of 23 Fabian Trinkel | III Physikalisches Institut B
21 of 23
Deuteron EDM limits for the precursor experiments at COSY
Measurement
method
Common
BPM (μm)
Rogowski coil
BPM (μm)
Orbit RMS
( 𝛍m)
𝝈𝐄𝐃𝐌,𝐬𝐲𝐬,𝐨𝐫𝐛𝐢𝐭
(𝑒 ⋅ 𝑐𝑚)
Absolute beam
positions
Accuracy 100.00 150.00 ≈ 100 ≈ 5 ⋅ 10−20
First deuteron
EDM limit measured
with COSY
Fabian Trinkel | III Physikalisches Institut B
Relative
beam
positions
Resolutio
n
10.00 1.25 ≈ 1 ≈ 5 ⋅ 10−22
• A relative beam position measurement would reduce the 𝝈𝐄𝐃𝐌,𝐬𝐲𝐬,𝐨𝐫𝐛𝐢𝐭 in magnitudes
Summary
22 of 23
CP-violating process (EDMs) for
matter over antimatter dominance
Anti-
matter Matter
Hardware development to supress
systematic effects (orbit control)
Fabian Trinkel | III Physikalisches Institut B
Development of a Rogowski coil-based BPM
Theoretical calculations &
simulation
Construction, manufacturing
& test measurements with
a testbench in the laboratory
Test measurements in the
accelerator COSY
Future Rogowski coil developments
23 of 23
Investigation as a non-invasive beam profile monitor
Fabian Trinkel | III Physikalisches Institut B
Rogowski coil
Cryocooler
Radiation shields
Electrical feedthrough
75 mm 430 mm
SQUID development
Coil design and flange improvements
Backup
Backup 1 Fabian Trinkel | III Physikalisches Institut B
Systematic Effects I
Fabian Trinkel | III Physikalisches Institut B
• Misaligned magnets
lead to
• polarization build up
• orbit distortion
Correct orbit to
minimize polarization
build up
Courtesy: Marcel Rosenthal (m.rosenthal@fz-juelich.de)
Quadropole shifts 𝜎 < 1 mm & no EDM
Backup 2
Systematic Effects II
Fabian Trinkel | III Physikalisches Institut B
Courtesy: Marcel Rosenthal (m.rosenthal@fz-juelich.de)
Quadropole shifts 𝜎 < 1 mm
Backup 3
Definition of accuracy and resolution
Value
Pro
babili
ty d
ensity
Reference value
Accuracy
Resolution
Value
Pro
babili
ty d
ensity
Accuracy
Resolution
Reference value
Value
Pro
babili
ty d
ensity
Resolution
Reference value
Value
Pro
babili
ty d
ensity
Resolution
Reference value High accuracy
High resolution High accuracy
Low resolution
Low accuracy
Low resolution Low accuracy
High resolution a) b)
c) d)
Fabian Trinkel | III Physikalisches Institut B Backup 4
Voltage measurement principle with a lock-in amplifier
Zurich Instruments HF2LI
Lock-in amplifier
Fabian Trinkel | III Physikalisches Institut B
Signal 𝑉sig(𝑡)
Reference 𝑉ref(𝑡)
Mixer Low-pass filter
Amplitude,
Phase
Backup 5
Voltage measurement principle with a lock-in amplifier
𝜔 (Hz)
𝐴 (V
)
𝜔ref 𝜔sig 𝜔− 𝜔+
Low-pass filter Signal + Noise
Fabian Trinkel | III Physikalisches Institut B Backup 6
Theoretical calculations for the Rogowski coil BPM
Induced voltage for N windings:
Magnetic field:
Taylor expansion series:
Fabian Trinkel | III Physikalisches Institut B Backup 7
Theoretical calculations for the Rogowski coil BPM
Induced voltage for segment 1:
Fabian Trinkel | III Physikalisches Institut B Backup 8
Theoretical calculations for the Rogowski coil BPM
x = -10 mm
y = -10 mm
x = 10 mm
y = 10 mm
Fabian Trinkel | III Physikalisches Institut B Backup 9
Calculation of the voltage ratios for the orbit bump measurements
Backup 10
Horizontal:
Vertical:
Theoretical:
Takes the first 𝑥0 for the
vertical voltage ratio into account
Takes the first order of 𝑥0 for the
horizontal voltage ratio into account
Orbit bump
Fabian Trinkel | III Physikalisches Institut B
Horizontal orbit bumps with steerer value of 0%
Backup 11
Orbit bump: Comparison of initial and final orbit
Backup 12
Initial position Initial position
after bump
Voltage noise calculations
Backup 13
Thermal noise:
Device T (K) 𝝈𝑼 (nV)
Lock-in amplifier 293.15 13.05
Low-noise preamplifier 293.15 2.00
Quartered segment 293.15 1.14
Cooled quartered segment 77.15 0.22
Quartered segment amplified 293.15 10.34
Cooled quartered segment amplified 77.15 2.07
Calculation of the thermal noise for the different devices
with a bandwidth of Δ𝑓 = 6.81 Hz
Voltage noise calculations
Backup 14
Signal chain T (K) for quartered segment 𝝈𝐔,𝐭𝐨𝐭𝐚𝐥 (nV) 𝝈𝒙 (𝝁m)
1 293.15 13.10 1.07
2 293.15 16.77 1.35
1 77.15 13.05 1.05
2 77.15 13.36 1.08
Two different signal chains:
1. quartered segment
2. quartered segment + low-noise preamplifier
Readout of the signal chain is an uncooled lock-in amplifier
• Cooling only the signal chain lead not to a major increase of resolution because
the dominant noise source is the lock-in amplifier itself
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