Analysis of the Magnetic Field Measured by a Rotating Hall Probe in a Solenoid to Locate its Magnetic Axis

We have analyzedthe motion of a Hallprobe,which is rotatedabout an axis that is arbitrarily displacedand oriented with respect to the magnetic axis of a solenoid. We outline how the magnetic field measured by the rotating Hall probe can be calculated. We show how to compare theoretical results with actual measurements, to determine the displacementand orientation of the axis of rotation of the probe ffom the magnetic axis. If the center of rotation of the probe is known by surveying,the correspondingpoint on the magnetic axis of the solenoidcan be located. This is applied to a solenoid that wasbuilt for BNLby Oxford Instruments. INTRODUCTION After a 5 T, 1 m long superconducting solenoid was delivered by Oxford Instruments, it was decided to do an independent measurement of the straightness of the magnetic axis. A common way to perform this measurement is to rotate a Hall probe at several points along the axis of the solenoid, recording measured field vs rotation angle at each axial stop. Information about the displacement of the axis of rotation from the magnetic axis is obtained by analyzing the measured data. In this paper, we derive from f~st principles the field measured by a rotating Hall probe, whose axis of rotation is arbitrarily displaced from and arbitrarily oriented to the magnetic axis of a solenoid. We use the results we obtain to analyze the measurements made for the Oxford Instmments solenoid. We are aware of the work by Stockli et. al., in which countemeights were used to straighten out the guide tube before making measurements 1]. Our analysis makes this unnecessary. THEORY /., ! r:: Assume that the magnetic axis is along the z-axis of the x-y-z rectangular coordinate system (Fig. 1), and that the axis of rotation of the probe is initially parallel to it, and displaced by some vector, dR – (a) to (b) in l?$j. 1. ,For convenience, we take