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Local Correction and BPM calibration

Local Correction and BPM calibration. David Kelliher ASTEC/CCLRC/RAL 14 th May, 2007. Infer magnet misalignments from kicker strengths. Misalignment of quadrupole j can be expressed as a kick  j. Orbit position measured at ideal BPM i is the sum of these kicks.

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Local Correction and BPM calibration

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  1. Local Correction and BPM calibration David Kelliher ASTEC/CCLRC/RAL 14th May, 2007

  2. Infer magnet misalignments from kicker strengths • Misalignment of quadrupole j can be expressed as a kick j • Orbit position measured at ideal BPM i is the sum of these kicks. • MADX CORRECT module finds the set of k that best restores target orbit. • Kickers are placed in the middle of divided magnets. Assume k j.

  3. Misalignment errors (ideal BPM)

  4. Misalignment errors (ideal BPM)

  5. Misalignment errors (ideal BPM)

  6. Applying correction over momentum range (ideal BPM)

  7. Introduce BPM offset MADX allows BPM offset (or horizontal read error) via EALIGN, MREX := <offset> The offset is included in the orbit correction module CORRECT. In this study a random BPM offset following a Gaussian distribution with =50 m is applied (cut-off at 2). We assume this offset is systematic in that it doesn’t change with momentum.

  8. Misalignment errors (with uncalibrated BPM offsets)

  9. Determination of BPM offsetsLeast-Squares Minimisation method Error Orbit (BPM data) Includes magnet misalignments and BPM offset Apply a set of BPM offsets from within some range 2 > target value CORRECT Target= ideal design orbit Calculate penalty function 2 - Difference between the x positions at the BPMs and quadrupoles, between the target orbit and the result orbit. Result Orbit Find x positions at BPMs and quadrupoles 2 < target value Use offsets to calculate magnet misalignments

  10. MADX – MATCH moduleLeast-Squares Minimisation method TWISS,DELTAP=dponp,table=twisstarget; (calculate design orbit) MATCH,use_macro; //vary mrex for bpmf vary,name=mrexftry1,step=1e-4,lower=-1e-3,upper=1e-3; vary,name=mrexftry2,step=1e-4,lower=-1e-3,upper=1e-3; ….. select,FLAG=ERROR,range=bpmf[1]; mrexfin=table(bpmferror,MREX,1); ealign, mrex:=mrexfin-mrexftry1; ….. correct,RESOUT=0,flag=ring,orbit=twisserror,target=twisstarget… constraint,expr= xbpmf1=table(twissbpmf,X,1); constraint,expr= xbpmf2=table(twissbpmf,X,2); constraint,expr= xbpmf3=table(twissbpmf,X,3); lmdif,TOLERANCE = 1E-8; (Fast Gradient Minimisation algorithm)

  11. BPM calibrationLeast-Squares Minimisation method Black, sold lines is actual offset input. Red, dashed line is offset calculated by minimisation method. Monitors near F magnets Monitors near D magnets

  12. Misalignment errors Least-Squares Minimisation method

  13. Other BPM calibration methods • Beam-based alignment (BBA) of BPMs has been done in other machines by making use of nearby quadrupoles • e.g. R. Talman and N. Malitsky, “Beam-Based BPM Alignment”, Proc. PAC (2003) 2919. • The code LOCO (Linear Optic from Closed Orbit) debugs optics in storage rings by minimising the difference between the measured and model response matrix. J. Safranek, “Experimental determination of storage ring optics using orbit response measurements”, Nucl. Inst. and Meth. A388, 27 (1997)

  14. Conclusions • In the case of ideal BPMs, magnetic displacements can be calculated when the total tune is not close to integer • Calibration of BPMs is required. A least squares minimisation method is being developed using the MADX module MATCH. • Other methods of BPM calibration should be investigated

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