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BPM Resolution Studies at PETRA III

DEELS 2019. ESRF, 3. -5. June 2019. BPM Resolution Studies at PETRA III. Gero Kube DESY (MDI). Introduction Comments on BPM Resolution „ Three BPM“ Correlation & Prinicipal Components Analysis Resolution Studies at PETRA III Conclusion. PETRA III @ DESY. PETRA history.

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BPM Resolution Studies at PETRA III

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  1. DEELS 2019 ESRF, 3. -5. June 2019 BPM Resolution Studies at PETRA III Gero Kube DESY (MDI) • Introduction • Comments on BPM Resolution • „Three BPM“ Correlation & Prinicipal Components Analysis • Resolution Studies at PETRA III • Conclusion

  2. PETRA III @ DESY • PETRA history • 1978 – 1986: e+e-collider(upto 23.3 GeV / beam) • 1988 – 2007: pre-acceleratorfor HERA (p @ 40 GeV, e @12 GeV) • since 2007: dedicated 3rdgeneration light source, commissionedin 2009 TDR: DESY 2004-035 • → 14 beamlines(15 experimental stations) operating in parallel • from 2014: staged extension project W. Drube et al., 2016 https://doi.org/10.1063/1.4952814 • → upto 12 additional beamlines(presently not all ofthem in operation) Extension Hall East Ada Yonath Max von Laue Hall Extension Hall North Paul P. Ewald DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  3. PETRA IV: Overview PETRA IV storage ring and pre-accelerators • useofexistingacceleratortunnel • → asymmetric ring structure • additional experimental hall • → 29 straight ID sections time line • presently • → preparation of Conceptual • Design Report DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  4. PETRA IV: Diffraction Limited Light Source DLS design BPM resolution requirements • singlebunch / single turn< 20 μm (assuming 0.5 mA in singlebunch → 2.5×1010particlesbunch ) • closedorbit< 100 nm (rms, 200 mA in 1600 bunches) at 300 Hz BW courtesy: I. Agapov (DESY) DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  5. BPM Resolution position determination in circular accelerator y position resolution (small displacements from center) x beam : monitor constant : signal-to-noise ratio • geometry (buttonsize) → signalstrength • infrastructure→ cablelength & attenuation • read-out electronics depends on goal • performancetest→ existing Libera Brilliance readout electronics @ PETRA III • pickupgeometry→ beam pipediameter • buttonsize → smallcorrection (P1+P2) – (P3+P4) (P1+P4) – (P2+P3) main focus: read-out electronics y = Ky x = Kx P1+P2+P3+P4 P1+P2+P3+P4 DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  6. BPM Resolution Measurements modern ADCs optimized for cw signals • signalfrom BPM button→ farawayfromcwsignal BPM signal measurement with beam → 2 kindsofjitter • beam jitter • → realchangeof beam angle andpositioncausedbyfluctuations in accelerator • (groundmotion, energyfluctuation, kicks, …) • → seenbyseveral / all BPMs simultaneously • (correlation via beam optics) • noiseof BPM electronics • → quantitiytobemeasured • → nocorrelationbetweenadjacent BPM readings common methods for correlation analysis • „three BPM“ correlationmethod • Principal Components Analysis(PCA) correlation analysis in order to disentangle both jitter sources BPM resolution with beam generated signals brief review DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  7. „Three BPM“ CorrelationMethod principle setup: 3 adjacent BPMs connection via transport matrices • no non-linear elementsbetween BPMs BPM1 BPM2 BPM3 beam BPM reads position information difference: measured position vs. expectation calculate variance (error propagation) all BPM readings with same error σΔ → N consecutivepositionmeasurements DEELS 2019 Workshop @ ESRF, 3.- 5.6.2019 Gero Kube, DESY / MDI

  8. „Three BPM“ CorrelationMethod (2) procedure • N consecutivepositionmeasurementswith 3 adjacent BPMs • determinationoftransfermatrixelementsX21, X23 • → straightforward:calculationaccordingto beam optics • → modelindependent:Moore-Penrose pseudo inverse • (least-squareestimateforX) • BPM resolution • → evaluateformula constant offset ≈ 0 • successiveapplicationto all BPMs • → groupingthreeadjacent BPMs • example: KEK-BM. Arinaga et al., NIM A499 (2003) 100 restrictions • no non-linear elements→ difficult at DLS • same errorof BPM readings→ not possible at PETRA III • sometimesweakcorrelationswithneighbour BPMs • → large uncertainty in BPM resolution (especiallywith Moore-Penrose) phase advance ≠ n/2 π n = ±1, 3, 5, … DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  9. Principal Components Analysis (PCA) method of multivariate statistics • conversion of set of correlated variables into set of linearly uncorrelated ones • → principalcomponents (PC) • cleansingofcorrelations in datasets • → structuringof large datasets, compression, … prinicipal axis determination • orientation of firstprincipalaxis • → axisrotation such thatoveralldatavarianceismaximized (requirescenteringofdata) → alternative: minimizeprojections (hint: χ2) • orientation of second (third, …) principalaxis • → remove contribution of 1st PC from data • → repeat rotation and variance maximization • condition: uncorrelated with (i.e., perpendicular to) first principal component mathematics behind • eigen vectors → principalcomponents • eigen values (Λ)→ amountofvariancefor PC • form covariance matrix C→ real & symmetricmatrix • diagonalization of C→ C = V Λ VT • V :formedbyorthonormal eigen vectors • sort eigenvectors according to eigenvalues DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  10. PrincipalComponents Analysis (2) alternative numerical method → Singular Value Decomposition (SVD) orbit (spacecoordinate) • instead of diagonalization of covariance matrix • → SVDofdatamatrixM • relationbetweensingularandeigen values: • → turns (timecoordinate) (M real: V* → VT) courtesy: Wikipedia • advantage • → SVD numericallymorestable (formation of MMTcan cause loss of precision → Läuchli matrix) • → benefit: SVD provides additional information (acceleratorphysics) application to BPM data • construction of BPM matrixM • → BPM datacentered • → normalization: C.X. Wang, SLAC-R-547 (2003) • exploration of SVD matrix properties • → U:columnvectorscontaininformationabouttemporalpattern (tune, …) • → V:columnvectorscontaininformationaboutspatialpattern (orbit / βfunction, …) • comment: U/Vas temporal/spatialvectors → depends on orientationofmatrixM DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  11. PCA Example test measurement @ PETRA III SVD analysis • fillpattern: 960 bunches @ 5.6 mA • singlevertical kick withexcitationkicker • 2048 turnsrecorded • dominant modes (singularvalues) → mode 1 & 2 temporal modes • informationabout tune • → FFT ofu1, u2 spatial modes • informationabout beam optics→ BPM resolution • singularvaluesσ1, σ2, …= 0 → calculatecleanedorbitdata DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  12. PETRA III BPM System 11 different pickuptypes: 3 different cable types • Max von Laue hall RFA ½̋, ⅜̋ , ⅞̋ – 50 Ω cable lengths: 10m … 200m 246 individual settings • standardoctants: normalizetoKx,y = 10 mm RMSx,y = f(signal power) I. Krouptchenkov et al., Proc. DIPAC 2009, Basel, TUPD03, p. 291 DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  13. BPM Resolution Studies resolution studies @ PETRA III • singlebunchwithQbvarying • singlevertical kick withexcitationkicker • 2048 turns Kx,y normalization PCA for beam jitter removement combinationofmeasurementsforvariousQb plotasfunction ofsignal power DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  14. TbT Single Bunch Resolution machine studies at PETRA III with existing BPM system • LiberaBrilliance (Instrumentation Technologies) min(RMSx,y) ≈ 30 μm LiberaBrillianceresolution not sufficientfor PETRA IV PETRA IV CDR: rely on successor model → Libera Brilliance+ DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  15. Test of Read-out Electronics beam test @ PETRA III: december 2018 • LiberaBrilliance • → BPM_SOL_24, in use at PETRA III • LiberaBrilliance+ • → CDR: PETRA IV system • → onesystemboughtfor DORIS / Olympus • → onesystemrecentlybought • Libera Spark • → newplatform, nolong-term stabilization • → borrowedfrom I-Tech (thanksto Peter Leban) Combiner / Splitter Combiner / Splitter Combiner / Splitter Combiner / Splitter Signal Combiner/Splitter MACOM DS-409-4 LiberaBrilliance+ (old) LiberaBrilliance LiberaBrilliance+ Libera Spark Signal Combiner/Splitter MACOM DS-409-4 ~ 1 dB Attenuation BPM TbT resolution determination • orbitdatacontaincontributions due to • → correlated beam jitter • → noiseof BPM electronics 10 dB Attenuator disentangle contributions BPM_SOL_24 • correlationanalysis→ does not workforsingle BPM • eliminatecorrelatedjitter→ sum & splitorbitdata DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  16. Resolution Comparison Libera Brilliance+ • digital down conversion (DDC) • σ < 10 μm neverachieved • σ = 19.8 μm @ IB = 1.549 mA (-29 dB) • → correctforattenuation: IB= 0.38 mA (≈ -42 dB) • time domainprocessing (TDP) • σ = 10.3 μm @ IB = 1.323 mA (-30 dB) • → correctforattenuation: IB= 0.38 mA wouldfulfilrequirements → but Libera Spark isbetter… DDC mode < 20 μm (rms) → IB ≈ 0.4 mA TDP mode≈ 10 μm (rms) → IB ≈ 0.4 mA DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  17. Closed Orbit & Stability long term stability • useroperation: 480 bunches in 100 mA, top-up • all Liberas in closedorbit (SA) mode→ driftcompensation (digital signalconditioning, DSC) on Spark: no DSC available Brilliance+ without DSC good climatization (hutches, racks) mandatory DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  18. Closed Orbit Resolution specification: < 100nm (rms) in brightnessmode(200mA in 1600 bunches) @ BW 300 Hz • horizontal orbit first 12 hours (before beam dump): σrms = 20.76 nmin SA mode (BW 4Hz, Kx,y = 10mm; BW 4Hz → seeBrilliance+ User Manual, p.34) → scalingwith band width: × sqrt(300/4) = 8.66 → σrms = 180 nm (@ BW 300Hz) DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

  19. Conclusion BPM resolution studies • require correlation analysis in order to disentangle noise and beam generated jitter • → „three BPM“ correlationmethod & PCA correlation analysis • „three BPM“ correlationmethod→ not suitablefor PETRA III BPM system • PCA → powerful tool, not onlyforresolutionstudies (e.g. BPM performanceevaluation @ SSRF, …) • → modelindependent, but limited bymodemixing Z.-C. Chen et al., Chinese Physics 38 (2014) 077004 Nucl. Sci and Tech. 25 (2014) 020102 • closedorbit→ specsnot fulfilled (< 100 nm @ 300 Hz bandwidth) σy,rms ≈ 180 nm @ 300 Hz bandwidth andKx,y= 10 mm Libera Brilliance • singlebunchresolution→ specs not fulfilledfor PETRA IV Libera Brilliance+ • singlebunchresolution→ specsfulfilled @ bunchcurent IB ≈ 0.4 mA andmonitorconstantKx,y = 10 mm DDC mode< 20 μm (rms), TDP mode≈ 10 μm (rms) Libera Spark • singlebunchresolutionmuchbetter→ closedorbit: needsstabilization next step: Independent Component Analysis (ICA) DEELS 2019 Workshop @ ESRF, 4.6.2019 Gero Kube, DESY / MDI

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