MAGNET MAPPING SSU FC SSD Four superconducting magnet

MAGNET MAPPING SSU FC SSD • Four superconducting magnet modules: – 2 Spectrometer Solenoids • 5 coils in each module – 2 Focus Coil modules • 2 ‘split field’ coils in each module 20 February 2021 1/17

INTERNALLY Tracker Focus Coil 2 coils on one bobbin • • Spectrometer Solenoid 5 coils on one bobbin Currents ~ 200 Amps; Fields up to 4 Tesla axially Rigid cold – warm supports support forces up to 25 tons Dimensions of coils known to ~ 0. 1 mm Physics says align axes to 0. 5 mm wrt to beam axis. . . 20 February 2021 2/17

TOLERANCES Offsets • • • Tilts MC study of trajectory of initially on-axis muons for sets of coils with – Randomly offset axes – Randomly tilted axes • within fixed radius circle at each end of each bobbin Tilts more important than offsets Study was for STEP VI Align bobbin axes to 0. 5 mm wrt beam axis – Step IV less critical; DMIC not studied 20 February 2021 3/17

MAPPING GOALS • Find magnetic axes of the magnets – with respect to fiducials • Align modules so that magnetic axes on beam axis – Ideally to better than 0. 5 mm • Check alignment in Hall • Check fields agree with calculated fields – and / or • Find effective conductor dimensions 20 February 2021 4/17

THE CERN MAPPER Seven 3 -axis Hall probes r = 0, 30 … 180 mm Disc moves longitudinally Disc can be rotated 20 February 2021 5/17

PROCEDURE • Mapping: – Mapper placed (approximately) on module axis • Survey wrt module fiducials – Longitudinal (z) scan at fixed angle of disc (f ) • Change f and repeat – Repeat at different currents • Analysis: – Transform field components to Cartesians in Mapper system – Apply survey corrections – Apply Maxwell: • Corrections (probe rotations) to ensure curl B = 0 • Use div B = 0 to obtain axis – Transform axis to module fiducial system Sounds easy. . . but • 20 February 2021 6/17

• Huge amount of data – Subtly different between modules • Several surveys – Subtly different between modules • Several transformations – Easy to get wrong • Mechanics of mapper • Enough material for several D. Phil theses. . . 20 February 2021 7

CURL CORRECTION Field vectors in plane of mapper disc Before • Probes measure Bz , ‘ Br ’ and ‘ Bf ’ in system of mapper disc • Small rotations of probes apparent curl – Determine rotations & correct 20 February 2021 After 8/17

AXIS FINDING • Magnetic axis Bperp = 0 • Maxwell-Gauss: • Expect Bx to be linear in x close to axis: Bx = k(x –x 0) + a Bz at each z x 0 is axis angle between mapper and magnetic axes • Fit to find axis: x 0 = p + a z • Model independent 20 February 2021 9/17

SURVEY CORRECTIONS FC 2 d. Y versus X SSD • Mapper disc doesn’t move in straight line – Transverse movement surveyed for each module • < 0. 6 mm for FCs • ~ 2 – 3 mm for SSU & SSD – Survey corrections applied to x and y coordinates 20 February 2021 10/17

SOME FIELDS SSD FC 2 • Same scale for Bx and Bz – 8 (x, y) points at each z • Information about axis from where Bz changing fastest 20 February 2021 11/17

FIT RESIDUALS & ERRORS Horizontal FC 1 Flip Mode Vertical • • Fit residuals ~ a few Gauss – Clear systematic effects • Attributable to mechanics of mapper Comparison of different runs – Axis positions known to 0. 1 – 0. 3 mm • Good enough 20 February 2021 12/17

RESULTS SSD upstream SSD downstream • Magnetic axes of modules – Determined to < 0. 3 mm – Found to be within ~1 mm centres of module flanges – except for SSD • 4 mm discrepancy at one end • 11 mm at other end • Checked with simple vector plots – unambiguous – Manufacturing error (SSD has a chequered history. . . ) • Can it be accommodated? 20 February 2021 13/17

IN PRACTICE • Modules coupled by bellows – Little transverse compliance – Some manufacturing errors • Determine installed positions of modules – SSD magnetic axis 8 – 9 mm off beam axis – Do the data concur? 20 February 2021 14/17

TRACKER – FIELD ALIGNMENT • Data taken with each SS independently – Fit to obtain angle of Tracker axis – SS magnetic axis • Field lines are axis of helical trajectory – Results not inconsistent with known (mis)alignments • But complicated by slowing of muons in tracker planes – Work in progress 20 February 2021 15/17

CONSEQUENCES • MC studies of real misalignment – Not a big effect for Step IV measurements • but not desirable (obviously) • Data taken to – Confirm/check alignment of Trackers in SSU & SSD • Not inconsistent – Alignment of FC • Analyses ongoing • Use current hiatus to fix problem: – – Metrology of module flanges Manufacture new bellows to allow for offset axes Refine installation procedures Re-position modules 20 February 2021 16/17

THE END 20 February 2021 17/17

SSD SURVEY 20 February 2021 18/17