Solenoid Magnetic Field Mapping

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

2. Magnetic Field Shape • z-component dominant near centre of solenoid • r-component more important near ends of coil • field from magnetized iron only 4.5% of total

3. Objectives • Momentum scale will be dominant uncertainty in lepton mass measurement • Momentum accuracy depends on <equation>, so field at intermediate radii is most important • Need to measure bending power integral of magnetic field to 0.05% accuracy • Bending power defined as Bz – Br z / r

4. Field Mapper Machine • Two propellor 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

5. 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 parametrization • Use fits to correct normalization and alignment

6. Simulation of Raw Data • Field calculated from solenoid of expected dimensions • Magnetization due to magnetic material from outside Inner Detector • Random walk with time for solenoid current and Hall probe measurements • Random errors for each measurement

7. 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 random walk in current removed

8. Correction for Hall Probe Drift • Mapping machine regularly returns to fixed calibration positions • Near coil centre to calibrate Bz • Near coil end for Br • No calibration of Bphi • Each channel is calibrated to a reference time (beginning of run) • Scaling factors from calibration points used to determine scalings for measurements between calibrations

9. 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 magnetization) • Use Minuit for chi2 fit to data

10. Fourier-Bessel Fit • General fit able to describe any field obeying Maxwell’s equations • Needs large number of parameters • Poor fit indicates measurement errors rather than incorrect model • Main contribution to field found from measurements on cylinder surface, i.e., large radii • Measurements at smaller radii needed at ends of cylinder

11. Comparison of Fit Results

12. Future Plans • Simulate other effects • Geometrical misalignments • Systematic measurement errors • Readout errors, e.g., missing measurements • Mapper machine scheduled to take data in late February 2006 • Add magnetization due to magnetic materials in Inner Detector