1. Re-mapping the Residual B-Field in NA62
John Fry
Ferdi Hahn
Mike Nelson

2. Outline of Talk Reasons for residual B-field measurements
Support structures required
Programme of measurements
Consideration of systematic errors
Measurements taken to date
New Sensor programming
Revised measurement programme
B_Fields M Nelson

3. 1. Reasons for Residual B-Field Measurements
Two main reasons:
Sensitivity of the physics. The physics is very sensitive to transverse magnetic fields of the order of 10μT in the 70m decay volume.
Difference in NA62 (preliminary) measurements compared with NA48. Preliminary B-field measurements in vacuum tanks 5, 6 and 7 differ significantly from the NA48 measurements.
B_Fields M Nelson

4. Totality of the Measurements
We will remeasure:
MNP33 Field Map (specially-designed, purpose-built array of Hall probes)
MNP33 Fringe Field (use a sensor fitted with x,y,z Hall-probes)
Vacuum Tube Residual Field (same sensor)
MNP33 measurements are expected to begin in September. This
presentation will focus on the vacuum tube measurements.
Uncertainty in kinematic variables is key. Systematics on kinematic variables must be much smaller than systematics on measurement uncertainties.
Hence: systematic error on the angular deflection of the particles, Δφ, must be much smaller than the measurement uncertainty.
B_Fields M Nelson

5. Sensitivity of the Physics
From NA48 data (Evgueni): a 25 GeV/c track has an angular deflection of 35μrad. This corresponds to:
Transverse momentum kick, PT= 2.5 MeV/c (related to invariant mass.)
0.4 MeV in reconstructed mass of K → 3π (azimuthal variation)
(1.5 x 10-3 ) GeV in (missing mass)2 (π0 ) for K+ →π+ π0 (azimuthal variation)
∫B.dl = (8 x 10-3 )T m over the K+ decay length (vacuum tubes)
NA62 is a higher sensitivity and requires a higher precision than NA48.
B_Fields M Nelson

6. Requirements on Δ(∫B.dl)
Maximum systematic error tolerated: Δ (∫B dl) ~ T m
MNP33: To achieve Δ (∫B dl) ~ T m, require ΔB ~ (4 x 10-4)T. The original measurements achieved ΔB ~ (2.5 x 10-4)T
Fringe field: For Δ (∫B dl) ~ T m for 6 > |Z| > 2.7, ΔB ~ (2 x 10-4) T
Vacuum tubes: ∫B.dl = (8 x 10-3 )T m over the K+ decay length. So for Δ (∫B.dl) ~ T m, ΔB ~ (2 x )T
Crucial physics requirements for making these precise measurements along the beam axis of the vacuum tube. For the vacuum field measurements, need to consider the necessary support structures.
B_Fields M Nelson

7. 2. Support Structures Required
Key Physics requirement:
Measure the B-field on and around the beam axis, then give
preference to measurements at a large radius.
Defining a region of ‘large radius’:
Measurement of the B-field within a cone of half-angle 20mrad from GTK_3 to STRAW_4.
B_Fields M Nelson

8. Inner Tube Diameters
Require the design of a suitable choice of grids to minimise the number of measurements.
The choice of grids depends on the inner tube diameter at a given Z- position along the tube. From the BEATCH file (Niels Doble)
I D (mm) Range in Z (m) Comments
– LAVs 1-5 between (approx) 122 and 153 m
– LAVs 6-8 between (approx) 165 and 181 m
– LAV 9 ~193 m; STRAWS 1&2 ~183, ~194 m
– Magnet MNP33
– LAVs 10&11 ~203, ~218m; STRAW 3 ~205 m
2100 > STRAW 4 ~ 219 m, then transition to RICH
B_Fields M Nelson

9. Grid Structures Inner diameter < 2000mm Inner diameter > 2000mm
B_Fields M Nelson

10. 3. Programme of Measurements
Sensor developed (Felix Bergsma) to measure B-field.
Sensor contains 3 Hall probes, each measuring one of the x,y,z-components of the B-field.
Need to determine sensor offsets which are self-consistent and agree on the value of the true field.
B_Fields M Nelson

11. Measuring Offsets To measure offsets, must limit
- Electronic noise (require sufficient shielding)
- Piezoelectric and galvanic effects (no applied stresses)
- Thermal effects (reduce flow of thermal currents)
Procedure for measuring x,y,z-offsets:
- First make repeated recordings of Bx, By, Bz with the sensor in a fixed position and a standard configuration (x, y, z-Hall probes pointing in the x,y,z-Sensor directions)
B_Fields M Nelson

12. - Make enough readings so that data points are consistent (i. e
- Make enough readings so that data points are consistent (i.e. 95% lie within 2σ of the mean.)
- Rotate the sensor such that the x-Hall probe points in the ‘-x’-direction and the y-Hall probe points in the ‘-y’-direction. Make Bx and By measurements.
- Finally, rotate sensor such that the z-Hall probe points in the ‘-z’ direction and make Bz measurements.
Now average x, -x; y, -y; z, -z – readings to get Bx, By, Bz averages. Errors are given by the standard deviation in the mean of each of the three sets.
Offset = (Bi + B-i)/2
True Field = (Bi – B-i)/2
B_Fields M Nelson

13. 4. Consideration of Systematic Errors
Three main sources of error contribute to ∫B.dl:
1) Measurement error – statistical error on individual measurements contributes ~100 µT.m
2) Sampling error – systematic error due to length sampling at ~ every 3m, rather than sampling continuously: 150 – 250 µT.m
3) Offset error – systematic error due to a single offset calibration of the sensor. ~700 µT.m for an uncertainty in offset of 10 µT
Since the total error contribution must be < 1000μTm this cautions against the use of a single offset calibration for all data.
B_Fields M Nelson

14. 5 Measurements Taken to Date
May (T2K 59): measured along Vac. Tubes 5, 6, 7 (Inner Grid); Vac. Tubes 2, 4, 8, 10, 11 (Inner and Middle Grids); Vac. Tubes 12 and 15 (Inner and Outer Grids). Have also measured along LAVs 1-7 (Centre position only for LAVs.)
July: Vac. Tube 15 two measurements at two different Z-positions.
Inconsistencies on remeasurement of B_Fields at the same Z position were traced to random jumps in the offset calibration of magnitude >20 µT.
These resulted from the electronic correction automatically applied when the instrument was switched on. This offset was randomly chosen from a distribution of values with RMS ~50µT.
B_Fields M Nelson

15. 6 New Sensor Programming
Modification (Felix Bergsma): the revised software calculates the mean of the offset distribution as the new electronic correction to the Hall probes.
When switched on, the device samples the offsets 25 times and takes an average. This average was found to be stable to ~5 µT.
Despite the stability of the offset being improved, there remained problems with stability due to temperature changes in the local environment. The offsets measured at different times and places were markedly different. It was therefore crucial to check that the measured offsets were stable during the measurement of B_Fields.
This was done by measuring the offsets before and after B-field readings in situ and checking for consistency between the two sets. Care was taken not to switch the instrument off/on during the measurement cycle.
B_Fields M Nelson

16. 7 Revised Measurement Procedure
At each Z, the sensor offsets are measured for the x, y, z-Hall probes
B_fields are then measured at the different positions on the chosen grid, with sufficient sets of readings to check for consistency and enable a sensible uncertainty to be calculated.
The sensor offsets for the x, y, z Hall probes are then remeasured and if consistent with the first set of offsets, the data taken at each point on the grid are validated.
This procedure gives independent values of offsets, with good estimates of the systematic error that applies to the measurements at any particular value of Z.
B_Fields M Nelson

17. Reduced Systematic Errors
The systematic error on the offset at a particular Z can be combined linearly with the measurement uncertainty on the B_field to give an overall uncertainty on the B_Field
The overall uncertainty on ∫B.dl is then obtained by adding in quadrature the individual contributions of B.dl from each Z position.
Measurements made on 6th August showed good reproducibility. They gave contributions of ~5 µT from each of the offset and B_field measurements, or 10 µT in total for each point. This suggests that the overall uncertainty in ∫B.dl arising from measurements of offsets and B_fields will be ~150 µT.m, which in combination with the sampling error of ~200 µT.m is perfectly acceptable.
B_Fields M Nelson

18. Key Points
Measuring residual magnetic fields with the required accuracy and precision is non trivial and requires a good understanding of the instrumentation and the environment in which it is used.
Much data has been taken in May and July and inconsistencies found, which render it useless.
Improvements to the use and function of the instrument now give stable, reproducible data of high quality and precision.
In a revised procedure the systematic error in the offset is added linearly to the B_field measurement uncertainties at each Z. The uncertainty in ∫B.dl is then obtained by combining in quadrature the contributions at each Z.
The overall uncertainty in ∫B.dl is will be well within specification.
B_Fields M Nelson

19. Looking Forwards
Need to follow through the new measurement programme. There is a plan to remap the B-field along the vacuum tubes, using the new improved sensor (John Fry and Mike Nelson, September.)
Separate task: need to map the field of the MNP33 also. This will be carried out during September.
For MNP33, we will measure the field map and the fringe field.
B_Fields M Nelson