1. 7 th March 2008 Magnet Modelling N. Sammut On behalf of the FIDEL Working Group

2. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 2/33

3. N. Sammut 7 th March 2008Magnet Modelling FIDEL Overview Aim Describe the magnetic state of the LHC on a circuit by circuit basis Provide the current settings of the main magnets Provide current settings for correctors Consists of: 1) Set of equations to describe the functional dependence of the field and field errors 2) Set of Parameters to fit the equations with the measured behaviour of the magnets Specification Tolerances on the harmonics are calculated from beam requirements The commissioning requirements are taken as the desired feed-forward prediction to be reached by FIDEL Courtesy S. Fartoukh LHC FIDEL data fusion beam instrumentation and actuators beam parameters beam 3/33

4. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 4/33

5. N. Sammut 7 th March 2008Magnet Modelling FIDEL Deliverables Provide models for determining magnet main field and field quality in the static domain (i.e. current dependent) and in the dynamic domain (i.e. current and time e.g.: MB, MQ..) Provide list of model parameter values for all circuits in LHC for setting magnet field and for calculation of higher order harmonics. Define pre-cycles and recommend best setup practices for magnets during operation. (Provide list of pre-cycles required for all circuits) Perform additional magnetic measurements for operation support. What exactly to provide for MAD-X remains to be defined. 5/33

6. N. Sammut 7 th March 2008Magnet Modelling FIDEL Status – The Model 1) The Static Field Model 2) The Dynamic Field Model Geometric d.c. magnetization Saturation Residual Magnetization Decay Snapback 3) The Scaling Laws Decay Scaling Powering History Snapback Correlation Ramp Rate Dependence - Dependent on current - Are reproducible from cycle to cycle - Loadline cycle - Dependent on current and time - To a certain extent may not be reproducible from cycle to cycle - LHC Cycle - model relies on the decomposition of the field into the different contributions Model has been defined and published as an LHC Specification combining all effects based on warm and cold magnetic measurements: (Phys Revs ST-AB: 2006, 2007) 6/33

7. N. Sammut 7 th March 2008Magnet Modelling The Static Field Model geometric ComponentRangeDescription Important at all field levels absolute field is linear in current, normalized field is constant use warm measurements conditions and warm cold correlation due to persistent currents mostly important at low fields (but present throughout) d.c. magnetisation only important at high field associated with details of iron yoke geometry (shape of inner contour, slits, holes, …) modelling is empirical and based on a saturation curve (smooth step function) saturation residual magnetisation important at low currents magnet components may remain permanently magnetised modelling is empirical providing a good fit to the experimental data 7/33

8. N. Sammut 7 th March 2008Magnet Modelling Computing Parameters of Static Field Model geometricsaturation d.c. magnetisation residual magnetisation result 8/33

9. N. Sammut 7 th March 2008Magnet Modelling Dynamic Field Model – Decay and scaling 9/33

10. N. Sammut 7 th March 2008Magnet Modelling Dynamic Field Model – Powering History 10/33

11. N. Sammut 7 th March 2008Magnet Modelling Dynamic Field Model – Snapback b 3 decay amplitude (units) Median error b 3 – 0.14 units 11/33

12. N. Sammut 7 th March 2008Magnet Modelling Skeleton Table of FIDEL parameters (data structure) has been generated for all circuits. Detailed conventions for interface with LSA are currently being finalised. Most of the data has already been collected and validated in the FIDEL repository. We aim to have all data collected by the end of March. 3 Tracking Test Campaigns (July 2007, October 2007, December 2007) performed to test the FIDEL concept and the LSA implementation. Demonstrated the tracking of B1-B2, B1-B1 and correction of b3 and b5 with very good results. (EPAC 2008, drafted departmental report) FIDEL Status 2 12/33

13. N. Sammut 7 th March 2008Magnet Modelling Schedule for Providing FIDEL data Details, see http://cern.ch/fidel/#workplanhttp://cern.ch/fidel/#workplan Magnetic data collection & consolidation completed. First complete set of Model parameters for all circuits, including pre-cycles. Not fit for beam yet. First complete set of Model parameters for all circuits, including pre-cycles. Fit for use with beam. First week of April First week of May First week of June 13/33

14. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 14/33

15. N. Sammut 7 th March 2008Magnet Modelling How is FIDEL linked to LSA? The set of equations that describe the functional dependence of the field and the harmonics is defined in an LHC specification and are embedded into LSA specific functions The set of parameters that fit all the equations to the measured behaviour of the magnets are placed in a file – the FIDEL data structure. This is uploaded into the LSA database. - file contains all the parameters of all the magnet types, arranged in a logical structure. 15/33

16. N. Sammut 7 th March 2008Magnet Modelling How does LSA implement FIDEL? 1)Generate current settings (I ref ) of main optic elements -K (magnet strength) is obtained from the optics -B (main field) is obtained by using K and the momentum -I ref is obtained by using B and Fidel TF (calibration curve) 2) Generate current settings of spool pieces (I spoolpiece ) - B n is obtained by using I ref and Fidel (harmonic curve) - K spoolpiece is obtained by using B n and the ratio of magnetic lengths between the two magnets (dipole and corrector) - I spoolpiece obtained by using Fidel TF (corrector calibration curve) NB We still need an LSA mechanism to handle compensation using combinations of circuits instead of only one LSA plan to implement a mechanism to determine powering history parameters from current measurements 16/33

17. N. Sammut 7 th March 2008Magnet Modelling Courtesy M. Strzelczyk FiDeL Fit/Analysis/ Model FiDeL CALIBRATION CURVES Calibration Curves 17/33

18. N. Sammut 7 th March 2008Magnet Modelling Fidel Implementation – Static Errors Courtesy M. Strzelczyk 18/33

19. N. Sammut 7 th March 2008Magnet Modelling Fidel Implementation – Dynamic Errors Courtesy M. Strzelczyk 19/33

20. N. Sammut 7 th March 2008Magnet Modelling start injection plateau decide to ramp start to ramp I MB b3 dipole  bn applied as trim Corrections applied as a function of time during the injection plateau After time tinj snapback is predicted How does LSA correct decay and snapback using FIDEL? Decay prediction calculated before arriving to injection plateau 20/33

21. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 21/33

22. N. Sammut 7 th March 2008Magnet Modelling How do we feed errors back into FIDEL? ‘Feedback’ from beam measurements will be used to correct for limitations in FIDEL prediction over the whole cycle. FIDEL updates will help to maintain the knowledge of the magnetic machine Equations or parameters are changed if: 1) Errors are considered to be reproducible 2) Source of the error is known and understood 3) Source of error is decoupled from other effects FIDEL changes can occur in: 1)Fidel model equations 2)Fidel equation parameters (data structure) The time frame of a typical FIDEL change is in the order of months 22/33

23. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 23/33

24. N. Sammut 7 th March 2008Magnet Modelling Circuit vs Magnet Modelling For Control: Geometric - One W/C correlation - One Geometric value per circuit Saturation Residual magnetisation dc magnetisation Snapback correlation Decay Powering History } Weighted average according to magnet families } Average of entire magnet population For the Online Model: The geometric component will be calculated on a magnet by magnet basis. The same values as used for control will be used for other parameters 24/33

25. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 25/33

26. N. Sammut 7 th March 2008Magnet Modelling Tracking Test - Two main dipoles and one main quadrupole equipped with rotating coils - A detailed characterisation of the magnets was performed, the FIDEL parameters were computed and entered into the data structure - By using FIDEL, LSA powered the main magnets, forecasted the harmonics and powered the b 3 and b 5 correctors for compensation 26/33

27. N. Sammut 7 th March 2008Magnet Modelling Recent Results – Tracking of B2/B1 Bounds for nominal performance Bounds for tune-loop lock-in limit Bounds for commissioning performance Magnets tested B 2 /B 1 or B 1 /B 1 average range (units) MB2624 – SSS0640.358 ± 0.014 MB2598 – SSS0640.286 ± 0.013 MB2598 – MB26241.238 ± 0.068 27/33 Tolerances Commissioning = ± 0.09 Nominal ± 0.003

28. N. Sammut 7 th March 2008Magnet Modelling Recent Results - Harmonic Compensation Reproducibility to 0.1units MB 2598 Ap1 decay snapback b5 corrector reaches full strength 28/33

29. N. Sammut 7 th March 2008Magnet Modelling Recent Results - Harmonic Compensation The best results are obtained if the corrector TF is changed by 2%. This is comparable with the measurement uncertainty These effects will be studied in more detail in the tracking test of Spring 2008 29/33

30. N. Sammut 7 th March 2008Magnet Modelling Plan 1)What is FIDEL? – Overview 2)FIDEL status 3)How is FIDEL Linked to LSA? 4)How are errors fed back into FIDEL? 5)Circuit vs Magnet Modelling 6)Recent FIDEL results 7)Further FIDEL Improvements 30/33

31. N. Sammut 7 th March 2008Magnet Modelling Further FIDEL Improvements Model hysteresis dependence of MQM, MQY, MQTs on powering history Correction of loadline measurements to compensate for decay on loadline plateaus. Study of impact of differences between series measurements and detailed characterisation measurements used in Tracking Test Measurements: - Statistical measurements for ramp rate dependence - Detailed loadline measurements - 4 th tracking measurement campaign - Powering History - Improve the understanding of b3 compensation - Simulations to test effects of different cycles and measurements if impact on field is considered to be large Model improvements at low fields where filaments are not fully penetrated 31/33

32. N. Sammut 7 th March 2008Magnet Modelling Conclusion - The FIDEL model is well established - The data structure and the interface with LSA have been defined and implemented - The FIDEL parameters are currently being calculated and will be ready for beam by 1st week of June. - The FIDEL concept and its implementation in LSA have been tested and proved to work in the tracking test. - Some effects are not fully understood but the indications are that these are within tolerances - There is still a significant amount of work to be done to have the parameters ready for all the circuits and even more if the parameters are needed on a magnet by magnet basis. 32/33

33. N. Sammut 7 th March 2008Magnet Modelling Questions ? 33/33

34. N. Sammut 7 th March 2008Magnet Modelling What limits FIDEL prediction accuracy? In the Tracking Test we obtained  0.1 units for b3 but (ie :  5 units of chromaticity) BUT - These are results obtained after a much more detailed characterisation before the tracking test - These are results obtained with correction of 1 magnet - FIDEL relies on measurements of a small population of magnets that are not evenly distributed amongst the sectors - Some magnets were measured 5 years ago: limited data on changes over the magnet lifetime - Systematic calibration errors in measurement instrumentation - Decay measured in series measurements has to be scaled due to ramp rate effect based on a few measurements. (EPAC 2008) - A small number of ‘fluke’ effects seen in measurements (e.g. large a2) - Operation outside the parametric space investigated during series tests

35. N. Sammut 7 th March 2008Magnet Modelling Dynamic Model Error b1b1 b3b3 b5b5 decay model 0.320.130.04 decay scaling 0.50.060.02 powering history model I FT 0.01 0.0007 0.007 t FT -- t preparation -- powering history scaling I FT 0.840.030.016 t FT -0.02- t preparation -0.07- total decay error 1.020.160.05 snapback model -0.03 snapback correlation -0.14- total snapback error -0.14- values in units