Angular orientation reconstruction of the Hall sensor calibration setup By Zdenko van Kesteren Supervisor: prof. dr. Frank Linde

Outline Hall sensors Calibration set up Determining internal parameters Angular orientation analysis

ATLAS muonspectrometer

3D magnetic field sensor 3D sensor with precision Prototype designed & built by NIKHEF Need to be calibrated Felix Bergsma (CERN)

Hall effect (semi)conductor in magnetic field

Hall effect V H = IB/nqd q = charge carrier n = carrier density

Hall sensor calibration Rotate sensors over two orthogonal axes in accurately known homogeneous magnetic field Repeat for several field strengths and temperatures Angular orientation should be measured very precisely, order of rad

Hall sensor calibration Calibration set up CERN (F. Bergsma) (magnet with  B about 3 x T) Calibration set up #2 Jaap Kuijt, Henk Boterenbrood, Fred Schimmel NIKHEF

Calibration setup

Coil measurements

Noise levels

Angular orientation Need to know  and  < both Calibration setup offers several ways to measure  and  : –Absolute encoder readout –3 orthogonal coils integrated on probe –Reference Hall board (will not be covered here)

Determining internal parameters Constructing a model to describe coils Imperfections in set up -> parameters in model –Rotation axes parameters –Coil geometry parameters –Coil electronics parameters Fitting model to coil data

Rotation axes geometry

Coil geometry Plus 3 angles to fix coils in space:  1,  2,  1

Coil electronics Pedestal voltage Electronical gain RC-times Shell

internal parameters Rotation geometry –  1  2  1  2  2 Coils geometry –  12  13  23  1  2  1 Coil electronics –G i P i   i (i = 1, 2, 3) 20 parameters!

Coil voltage vs. time

Modeled coil data

Internal parameters Values and errors of the parameters are not reliable Wrong assumption to fix  i in fit Normalized  2 on noise RMS Parameters are used to analyse the angular orientation

Obtaining orientation Set up offers two ways to obtain angular information: –Direct from the absolute encoders relies on  1  2  1  2  2 –By using the coil measurements relies on all parameters

Coil measurement method Values of C1, C2 and C3 gives rise to a reconstructed t rec (found by fitting)  1 t rec and  2 t rec give rotation angles  x,  y Rotation angles relate to angular orientation , 

Absolute Encoder method Encoder readout give AX and AY AX and AY relate to rotation angels  x,  y Rotation angles relate to angular orientation , 

Angular orientation

Trajectory x →

Results ,  reconstruction <10 -4 rad precision not met Internal parameters not reliable

Conclusions Data not reliable –ADCs coils do not behave properly Bergsma reconstructed B;  B of T Fit not reliable –The  i should be floating parameters in fit –Including  i in fit yields correlations between parameters