Magnetic Field Mapping of the Belle Solenoid

The magnetic field mapping was carried out with the accelerator magnets located inside the Belle solenoid excited to their nominal field values [78]. The two superconducting magnet complexes, QCS-R and QCS-L, are inserted in the holes along the axis of the end yokes. Each magnet complex consists of a solenoidal coil for compensation of the Belle solenoidal field, a quadrupole for focusing of the beams onto the interaction point, and several correction coils all located in a single cryostat [79]. Figure shows the side and end views of the field mapping arrangement and a conceptual illustration of the field mapping device is shown in Fig. . The volume to be mapped was reasonably isolated from the outside because of the limited gap between the pole tips and the QCS cryostat. Since the accessibility was limited, the field mapping device must be fully contained inside the Belle solenoid. Conventional magnetic motors could not be used to drive the device. We used an ultrasonic motor as a driver [80].

Figure: Side and end views of the field mapping device. Some of the rods connecting both end plates are not shown.

Figure: Conceptual illustration of the field mapping device.

A commercial field probe with three orthogonally oriented Hall sensors was used to measure the and $\phi$ field components [81]. An NMR probe installed on one of the connecting rods provided an absolute calibration of field strength with a precision better than 1 Gauss [82]. It was also used to monitor the stability of the magnet during the measurement. A field map of 100,000 points was made for a period of a month. Fig. shows a contour plot of fields measured inside the tracking volume for the nominal magnet settings. The field strength is shown in Fig. as a function of z for various radii. The tracking performance was evaluated with the reconstructed mass peak of particles from $B$ meson decays. The fitted value of the peak mass was 3.089 GeV/c$^2$ compared with the established value of 3.0969 GeV/c$^2$. Thus, the uncertainty in the absolute calibration of the present measurement is estimated to be approximately 0.25%.

Figure: Contour plot of magnetic fields measured in the Belle coordinate system with the origin at the interaction point.

Figure: Field strength as a function of $z$ for $r$ = 0, 50, and 80 cm.