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 15 th December 2017
Content 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 1 of 23
Ryan Kaldari, 2006, NASA Wikipedia Baryogenesis: Why does the universe contains more matter than antimatter? Big Bang Symmetry between matter and antimatter Antimatter Matter Early Universe Sakharov* conditions: 1. Baryon number violating interactions 2. Thermal non-equilibrium 3. Violation of C, CP symmetry *Andrej Sakharov 21 May 1921 14 December 1989 Possible sources: Strong CP violation (SM) Electroweak CP violation (SM) Today Measurement (WMAP) Cosmological SM Expectation (η B η B ) η γ 6.14 ± 0.25 10 10 10 18 2 of 23
Electric Dipole Moments (EDMs) as a new source of CP violation s d E B E B s d P H = μ B d E P: H = μ B + d E T: H = μ B + d E : MDM d: EDM μ = g T A. Knecht, 2008, Wikimedia d s e s d = η e s 2m 2mc E B Permanent EDMs of light hadrons are T-violating CPT theorem CP violation Standard Model expectation: d 10 31 e cm (Estimated by the neutron EDM limit) 3 of 23
EDM measurement at the accelerator facility COSY (COoler SYnchrotron) COSY facts Electron Cooler Provides polarized protons and deuterons Circumference 184 m Polarimeter Stochastic Cooling Momentum 3.7 GeV/c Intensity 10 9 to 10 10 particles Four experimental areas Beam diagnostic systems Spin manipulators Polarised Source RF Wien Filter (Stripline design) 4 of 23
Spin dynamics in storage rings Thomas-BMT-Equation: ds = S Ω dt MDM + S Ω EDM μ = 2 G + 1 d = qη 2mc S q 2m S s d Ω MDM = q mγ γgb + G 1 γ 2 1 Ω EDM = qη 2m E c + β B β E c β E = 0 β B = 0 G Proton 1.792847357 Deuteron -0.142561769 5 of 23
EDM measurement principle in a pure magnetic storage ring (COSY) EDMs introduce vertical polarization component of a horizontal polarized beam Measure vertical polarization Ω MDM = q mγ Ω EDM = qη 2m γgb β B Perfect accelerator and an EDM Realistic accelerator without an EDM B B y Ω = Ω EDM + Ω MDM y Ω = Ω MDM s s Scenario d (e cm) Orbit RMS (mm) ΔS y /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] 6 of 23
Particle orbit Dipole magnet Quadrupole magnet X (mm) Ideal Orbit 0 Ideal Orbit Orbit: mean displacement at all positions in the accelerator 7 of 23
Common Beam Position Monitor (BPM) system at COSY Electrode right Electrode up Vertical BPM Horizontal BPM Electrode down 40 cm Beam position determination Electrode left σ Pos (μm) 0.2 10.0 100.0 Source Thermal noise Resolution Accuracy 8 of 23
Development of a Rogowski coil Beam Position Monitor y Segment 4 z Segment 1 Non-equally distributed windings x Free area Segment 3 Segment 2 Parameters R (mm) 40.0 a (mm) 5.0 Geometrical centre R Copper winding 2a N 366 s (μm) 150 9 of 23
Voltage measurement principle with a lock-in amplifier Signal V sig (t) Mixer Low-pass filter Amplitude, Phase Zurich Instruments HF2LI Lock-in amplifier Reference V ref (t) 10 of 23
Development of a Rogowski coil BPM Development process Theoretical calculations & simulation Test measurements at the accelerator COSY Construction, manufacturing & test measurements with a testbench in the laboratory https://imgur.com/gallery/glxgy3l 11 of 23
Induced voltage calculation Model: Pencil-current with constant velocity at position (x 0, y 0 ) Current: Particle Beam Position: r 0 = I = I 0 e z Coil x 0 y 0 0 r = x y z Segment 4 2a R r o (x 0, y 0 ) y r φ Segment 1 x Magnetic field: B = μ 0 2π I r r 0 r r 0 2 Induced voltage for N windings: Segment 3 Segment 2 12 of 23
Voltage ratio calculation Definition of the horizontal and vertical voltage ratio: Calculation of the horizontal and vertical voltage ratio: Calculation of the sensitivities: (R = 40.000 mm and a = 5.075 mm) 13 of 23
Development of a calibration method Offset and rotation of the coil: Different signal strength: y x x x x x Geometrical centre Electrical centre Calculation of single voltage ratio: Definition of a minimization function (6 free parameters): 14 of 23
Laboratory measurements with the Rogowski coil BPM Preamp Measurement setup 4 1 Preamp Measurement procedure y 0 Preamp 3 2 Preamp x 0 Slave Sine wave Master TTL pulse TTL pulse Data Acquisition (PC) Test of the calibration algorithm Measurement parameters Frequency 750 khz Particles 10 10 Number of measurements Range 10 5 5 mm to 5 mm 15 of 23
Laboratory measurements with the Rogowski coil BPM x off (mm) y off (mm) φ ( ) 1 Σg i (%) g 2 Σg i (%) g 3 Σg i (%) g 4 Σg i (%) 3.4 3.3 0.40 20.9 28.3 28.7 22.1 Reconstruction of the wire positions (0 mm, 0 mm) Accuracy: 150 μm Caused by the asymmetry of the coil (5 mm, 5 mm) This effect is not considered in the calibration algorithm Resolution: 1.25 μm (-5 mm, -5 mm) The theoretical resolution limit is reached 16 of 23
Beam position measurements with a Rogowski coil BPM at COSY Horizontal orbit bumps: Values: 2% to 2% Step size: 0.2% Frequency: 750 khz Number of particles: 10 10 17 of 23
Beam position measurements with a Rogowski coil BPM in COSY Horizontal ratio: Horizontal model ratio expectation: Vertical ratio: Vertical model ratio expectation: 18 of 23
Beam position measurements with a Rogowski coil BPM in COSY 19 of 23
Beam position measurements with a Rogowski coil BPM in COSY 20 of 23
Deuteron EDM limits for the precursor experiments at COSY Measurement method Common BPM (μm) Rogowski coil BPM (μm) Orbit RMS ( μm) σ EDM,sys,orbit (e cm) Absolute beam positions Accuracy 100.00 150.00 100 5 10 20 First deuteron EDM limit measured with COSY A relative beam position measurement would reduce the σ EDM,sys,orbit in magnitudes 21 of 23
Summary CP-violating process (EDMs) for matter over antimatter dominance Antimatter Matter Hardware development to supress systematic effects (orbit control) Development of a Rogowski coil-based BPM Theoretical calculations & simulation Test measurements in the accelerator COSY Construction, manufacturing & test measurements with a testbench in the laboratory 22 of 23
Future Rogowski coil developments Coil design and flange improvements Investigation as a non-invasive beam profile monitor SQUID development 23 of 23
Backup Backup 1
Systematic Effects I Misaligned magnets lead to polarization build up orbit distortion Quadropole shifts σ < 1 mm & no EDM Correct orbit to minimize polarization build up Courtesy: Marcel Rosenthal (m.rosenthal@fz-juelich.de) Backup 2
Systematic Effects II Quadropole shifts σ < 1 mm Courtesy: Marcel Rosenthal (m.rosenthal@fz-juelich.de) Backup 3
Probability density Probability density Probability density Probability density Definition of accuracy and resolution a) Reference value Low accuracy b) Low resolution Accuracy Reference value Accuracy Low accuracy High resolution Reference value Resolution Value c) d) High accuracy Low resolution Reference value Resolution Value High accuracy High resolution Resolution Value Resolution Value Backup 4
Voltage measurement principle with a lock-in amplifier Signal V sig (t) Mixer Low-pass filter Amplitude, Phase Zurich Instruments HF2LI Lock-in amplifier Reference V ref (t) Backup 5
A (V) Voltage measurement principle with a lock-in amplifier Low-pass filter Signal + Noise ω ω ref ω sig ω + ω (Hz) Backup 6
Theoretical calculations for the Rogowski coil BPM Magnetic field: Taylor expansion series: Induced voltage for N windings: Backup 7
Theoretical calculations for the Rogowski coil BPM Induced voltage for segment 1: Backup 8
Theoretical calculations for the Rogowski coil BPM x = 10 mm y = 10 mm x = -10 mm y = -10 mm Backup 9
Calculation of the voltage ratios for the orbit bump measurements Horizontal: Theoretical: Takes the first order of x 0 for the horizontal voltage ratio into account Vertical: Takes the first x 0 for the vertical voltage ratio into account Backup 10
Orbit bump Horizontal orbit bumps with steerer value of 0% Backup 11
Orbit bump: Comparison of initial and final orbit Initial position Initial position after bump Backup 12
Voltage noise calculations Thermal noise: Calculation of the thermal noise for the different devices with a bandwidth of Δf = 6.81 Hz Device T (K) σ U (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 Backup 13
Voltage noise calculations Two different signal chains: 1. quartered segment 2. quartered segment + low-noise preamplifier Readout of the signal chain is an uncooled lock-in amplifier Signal chain T (K) for quartered segment σ U,total (nv) σ x (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 Cooling only the signal chain lead not to a major increase of resolution because the dominant noise source is the lock-in amplifier itself Backup 14