DO WE NEED TO MODEL HYSTERESIS ? EPISODE III: SPOOL PIECES

1. FiDeL meeting, 7th July 2009 DO WE NEED TO MODEL HYSTERESIS ?EPISODE III: SPOOL PIECES E. Todesco Magnets, Superconductors and Cryostats Group Technology Department, CERN Ackowledgements: W. VenturiniDelsolaro, V. Remondino, P. Hagen

2. CONTENTS • Three types of problemsrelated to hysteresis • Magnetscrossingzero (correctors+MQT) • Correctors having a decayat injection (spool pieces) and/or zerocrossing • Magnetwithdecreasingcurrent (MQY MQM) • Update on situation for MQM MQY, including IP2 • (Analysed in June 2009)

3. B3 spool pieces • During injection, b3 in the dipolesat -3 to -6 units • Correctedthrough spool pieces – neededcurrentsaround 20-40 A in the MCS • Moreover, b3decays of about 1 unit • Then, duringrampit changes sign(zerocrossing) and goes up to 1.5-4.5 units b3 to becorrected in eachsector Current in MCS for correcting b3according to linear model

4. B3 spool pieces • Expected b3duringramp b3 to becorrectedduringinection and ramp in sector 1-2

5. B3 spool pieces • Linear approximation of the transferfunction of MCS • Non linearities: • Saturation lessthan 1% up to nominal of 550 A • Residualmagnetiazion of about 2% at 20 A - to beanalysed Field versus current in MCS TF versus current in MCS

6. B3 spool pieces • Error due to linear approximation modeledwithhyperbolic fit (residualmagnetization component), i.e. err=k/I • Measurementsavailable up to 1 A Error in B due to linear approximation versus current in MCS

7. B3 spool pieces • Evaluation of uncorrected b3 (in sector 1-2) • Measurementsavailable up to 1 A • The effectissmal (<0.05 units) • Singularity on the zerocrossing: continuous but not derivable, gives 0.015 units (no divergence) Uncorrected b3 during injection and ramp due to linear approximation in MCS TF, sector 1-2

8. B4 SPOOL PIECES • For b4, thereis no decay • The only change is due to saturation (static part) • Moreover, thereis no zerocrossing in any of the octants • In some octants, smallcurrent (2 A) b4to becorrectedduringinjection and ramp in sector7-8 Current in MCO during injection and ramp in sector7-8

9. B4 SPOOL PIECES • Hysteresis in b4 correctors is 2.9×10-6 Tm • The uncorrected b4 due to ignoring the hysteresisisnegligible Uncorrected b4 due to neglectedhysteresis in 7-8

10. B5 SPOOL PIECES • For b5, thereisbothdecay and zerocrossing • In some octants, smallcurrent (2 A) Current in MCD during injection and ramp in sector5-6 b5to becorrectedduringinjection and ramp in sector5-6

11. B5 SPOOL PIECES • Hysteresis in b5 correctors is 8.6×10-5 Tm • The uncorrectedb5 due to ignoring the hysteresisis about 0.05 units itcanbeneglected • Frombeamdynamics computations, one needs to have a correction at 80% at injection, i.e., within 0.2 units Uncorrected b5 due to neglectedhysteresis in 5-6

12. SUMMARY • Neglecting MCS hysteresisthe maximal error in the correction of b3issmallerthan 0.05 units no need to model hysteresis • Neglecting MCO hysteresisthe maximal error in the correction of b4issmallerthan0.01 units no need to model hysteresis • Neglecting MCD hysteresis the maximal error in the correction of b5issmallerthan0.1 units no need to model hystere • This confirmspreviousestimatesfrom W. Venturini , Chamonix XV

13. APPENDIX • Equations to deal with the hysteresis • Transfer function: geometric plus residualmagnetization wherehis the hysteresisat 0 current (in T m) s • Weneglect the residualmagnetization: the relative error in the currentis • This induces an error in the correctedmultipole of

14. APPENDIX • Summary table