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Correction magnets

Correction magnets. Half-integer resonance correction 2Q x =45 , 2Q z =41. Resonance sources: Random error of MR_QM (216 magnets) Random error of the quadrupole field component of MR_BM (96 magnets) Random misalignment error of MR_SX (72 magnets) HCOD at the SX locations.

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Correction magnets

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  1. Correction magnets

  2. Half-integer resonance correction 2Qx=45 , 2Qz=41 • Resonance sources: • Random error of MR_QM (216 magnets) • Random error of the quadrupole field component of MR_BM (96 magnets) • Random misalignment error of MR_SX (72 magnets) • HCOD at the SX locations • Main assumptions (at the injection energy): • QM: 1=|(GL)/(GL)0| 510-4, max=2 • BM: … Systematic - based on measured data ... • … Random (relative): 1=0.5, max=2 • SX: H = 510-4 [m] , max=2H

  3. Harmonic analysis of beta-beating Qx = 22.28 Qz = 20.78 Harmonic correction: H … 44 & 45 V … 41 & 42

  4. Harmonic correction of normal quadrupole The correction scheme is based on the quadrupole trim coils which are placed at the dispersion-free straight sections. Minimum required ‘knobs’ to correct two harmonics in the horizontal and vertical planes is 10 (blue bars) If the required strength of the quadrupole trim coils is more than 5% of the main strength of the quadrupole coils, additional quadrupole correctors can be used (red bars)

  5. Normal Sextupole Resonances:observation and correction 3Qx = 67 -Qx +2Qz= 19 Qx + 2Qz = 64

  6. Resonance sources: • Injection Dog-Leg … vertical beta-beating <  3% • LINEAR chromaticity correction … amplitude dependent tune-shift … …  = 54 mmmrad   ~ + 0.02 • Sextupole component (systematic) of BM at the injection energy … based on the measured data: (B//L/B)~3.910-3 [m-2] Main assumptions (at the injection energy): • Assumption: RANDOM error of the sextupole field component in BM … around the systematic value: =0.5 (relative), cut=2

  7. ON-momentum particle motion 3Qx=67 -Qx+2Qz=19 Qx+2Qz=64

  8. –Qx+2Qz=19 observation Qx = 22.2575 Qz = 20.6200 p/p = 0.0 xz = 54 mmmrad H Scraper Acceptance V COSY Infinity: 1000 turns, Symplectic tracking, OV 7 3 0

  9. Correction of Normal Sextupole Resonance • Two independent sextupole correctors are placed at the dispersion-free straight section: RF+FAST_Extraction_Straight_Section. • The required strength of the sextupole correctors has been defined to make zero the resonance norm (the resonance stop-band-width). • The required strength of the sextupole correctors for each resonance has been determined for different error-seeds of the random sextupole field component of the MR bending magnets.

  10. –Qx+2Qz=19 correction Qx = 22.2575 Qz = 20.6200 p/p = 0.0 xz = 54 mmmrad H V COSY Infinity: 1000 turns, Symplectic tracking, OV 7 3 0

  11. –Qx+2Qz=19 : OFF-momentum particle AFTER correction Qx = 22.2575 Qz = 20.6200 H p/p = 0.0095 VRF = 280 kV h=9 xz = 54 mmmrad Scraper=81  V COSY Infinity: 5000 turns, Symplectic tracking, OV 7 3 0

  12. 3Qx=67: OFF-momentum particle Qx =22.315 Qz = 20.70 dp/p = 0.007 xz = 54 mmmrad VRF = 280 kV h=9 Before correction After correction H H Scraper COSY Infinity: 5000 turns, Symplectic tracking, OV 7 3 0

  13. Qx+2Qz=64: OFF-momentum particle Qx =22.34 Qz = 20.80 dp/p = 0.007 xz = 54 mmmrad VRF = 280 kV h=9 Before correction After correction Scraper

  14. Harmonic correction of normal sextupole Normal sextupole resonances can be corrected by an appropriate set of the sextupole correctors placed at the dispersion-free straight section of Main Ring. The required strength of the sextupole correctors has been defined for each normal sextupole resonance in vicinity of the ‘bare’ working point for different seeds of the random sextupole error. Maximum integrated strength of the sextupole correctors at the injection energy is (kCSL)~0.06 m-2. The momentum acceptance at the injection energy after the correction of the normal sextupole resonance is determined by the maximum height of the RF bucket for both cases h=9 and h=18.

  15. Summary • With frozen space charge model, long term particle behavior is studied. Loss of a percent level is sensitive to lattice conditions. • Harmonic correction scheme of lattice is studied and location of correction elements and its strength is calculated.

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