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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