1. Solenoid Magnetic Field Mapping Paul S Miyagawa University of Manchester Introduction Mapper machine Mapper software - Simulation - Corrections - Fitting Future work

2. 27 July 2005ATLAS ID alignment meeting2/12 The Principals Martin Aleksa (project coordinator) Marcello Losasso (engineering design) Felix Bergsma (Hall probes + motors) Heidi Sandaker (DAQ) Steve Snow (NMR probes + software) John Hart + Paul S Miyagawa (software)

3. 27 July 2005ATLAS ID alignment meeting3/12 Magnetic Field Shape z-component dominant near centre of solenoid r-component more important near ends of coil Field from magnetised iron only 4.5% of total Bending power defined as B z – B r z / r

4. 27 July 2005ATLAS ID alignment meeting4/12 Objectives Momentum scale will be dominant uncertainty in W mass measurement Momentum accuracy depends on ∫ r(r max - r)B z dr, so field at intermediate radii is most important Need to measure bending power integral of magnetic field to 0.05% accuracy Field B may be described by a scalar potential  satisfying Laplace’s equation,  2  = 0 Sufficient to measure B on the surface of a cylinder (including the ends) surrounding the tracker

5. 27 July 2005ATLAS ID alignment meeting5/12 Field Mapper Machine Two propeller arms which rotate in phi Carriage slides in z along rails Up to 25 Hall probes on each arm on both sides Cross-checks between probes on opposite sides of same arm Also have cross-checks between arms Machine measures field inside solenoid before ID installed Also have 4 NMR probes permanently fixed to solenoid to set overall scale

6. 27 July 2005ATLAS ID alignment meeting6/12 Field Mapper Software Convert raw data to physical units Correct for time drifts in solenoid current Correct for time drifts in individual Hall probes Convert to a regular grid Fit data with two methods: geometrical fit and Fourier-Bessel parametrisation Use fits to correct normalization and alignment of Hall probes

7. 27 July 2005ATLAS ID alignment meeting7/12 Simulation of Raw Data Field calculated from solenoid of expected dimensions Magnetisation due to magnetic material from outside Inner Detector Random walk with time for solenoid current and Hall probe measurements Random errors for each measurement

8. 27 July 2005ATLAS ID alignment meeting8/12 Correction for Current Drift Average B-field of 4 NMR probes used to calculate “actual” solenoid current Scale all measurements to a reference current (7600 A) Effect of drift in current removed Calibration capable of coping with any sort of drift

9. 27 July 2005ATLAS ID alignment meeting9/12 Correction for Hall Probe Drift Mapping machine regularly returns to fixed calibration positions –Near coil centre to calibrate B z –Near coil end for B r –No calibration of B  Each channel is calibrated to a reference time (beginning of run) Scaling factors from calibration points used to determine scalings for measurements between calibrations

10. 27 July 2005ATLAS ID alignment meeting10/12 Geometrical Fit Sum of simple fields known to obey Maxwell’s equations –Long-thin coil (5 mm longer, 5 mm thinner than nominal) –Short-fat coil (5 mm shorter, 5 mm fatter) –Four terms of Fourier-Bessel series (for magnetisation) Use Minuit for  2 fit to data Fit gives information about position, shape, etc of coil

11. 27 July 2005ATLAS ID alignment meeting11/12 Fourier-Bessel Fit General fit able to describe any field obeying Maxwell’s equations Uses large number of parameters obtained by direct calculation –Calculate Fourier terms from B z on outer cylinder –Fit cosh(λz) terms to ends of cylinder –Fit B r to find z-independent component of field Poor fit indicates measurement errors rather than incorrect model

12. 27 July 2005ATLAS ID alignment meeting12/12 Future Plans Simulate other effects –Geometrical misalignments –Mechanical deformations –Systematic measurement errors –Readout errors, e.g., missing measurements Mapper machine scheduled to take data in late February 2006 Add magnetisation due to magnetic materials in Inner Detector Deliver final field map on a cylindrical lookup grid Need to link ID field map to other B-field maps