Ⅱ-9. Instrumentation

RIKEN Accel. Prog. Rep. 52 (2019)

Precise magnetic field measurement of WiSES

WiSES1) (Window-frame Spectrometer for ElectronScattering) is an electron spectrometer for the SCRIT(Self-Conﬁning RI Ion Target) experiment.2,3) The
dipole magnet4) of WISES has a large aperture for themeasurement of scattered electrons in a wide scattering
angle at once. The gap volume of the magnet is 140 cm(width), 29 cm (height), 170 cm (depth). In elastic electron scattering experiments, a typical momentum resolution of δp/p ∼ 10−3 for 150–300 MeV electron energy
is required to separate elastic and inelastic scattering
events. The momentum resolution measured by elastic
scattering for 12 C and 208 Pb is found to not reach thedesign value. To improve further momentum resolution,
we will measure the precise 3D magnetic ﬁelds of theWiSES magnet with a precision of δB/B ∼ 10−3 .
We will use three Hole probes to measure Bx , By ,and Bz at the same time. The Hall probe has a Hallsensor inside and reacts to the component of the magnetic ﬁeld with respect to the normal direction of thesensor surface. However, the Hall probe also detects themagnetic ﬁeld with respect to the tangent of the sensor,
namely the Planar Hall eﬀect.5) Bprobe detected by theHall probe is expressed as follows:
Bprobe = B cos θ + pH (B sin θ)2 sin 2ϕ,(1)

where θ is the angle between the normal direction of thesensor and the magnetic ﬁeld, and ϕ is the rotation angleof the sensor. The ﬁrst term in Eq. (1) is the Hall eﬀect.
The second term in Eq. (1) corresponds to the Planar
Hall eﬀect. To determine the value of the Planar Hall
coeﬃcient pH of the second term, we measured the 2ϕdependence of each probe in a uniform magnetic ﬁeld.

spacerBiaxial rotary table∗30.0020-0.002-0.004
0100

200

300

400

500

600

[deg]

Fig. 2. Result of 2ϕ dependent magnetic ﬁeld by the Planar
Hall eﬀect. Each color corresponds to the ﬁtting for eachprobe.

The setup is shown in Fig. 1. The probe was mounted
on a rotating stage in the homogeneous ﬁeld region ofthe WiSES magnet. The absolute value of the ﬁeld wasmeasured by NMR, which was also located in the homogeneous region. The stage could rotate around twoaxes corresponding to θ and ϕ of Eq. (1), with resolutions of 0.3 mrad. In this measurement, θ was set to be90◦ to suppress the inﬂuence of the ﬁrst term of Eq. (1).
The results for the three probes are shown in Fig. 2.
By adding some mis-alignment angles of our system asﬁtting parameters into Eq. (1), our data are well reproduced. In the present ﬁtting, the followings points areincluded:(a) the contribution from the ﬁrst term of Eq. (1) owing to a small deviation from the 90◦ ,(b) the angle between the probe and the rotary axisof the stage, etc.

ReferencesFig. 1. Setup of Planar Hall eﬀect measurement in WiSES.
RIKEN Nishina Center
ELPH, Tohoku University
Department of Rikkyo University

0.004

Consequently, the pH s are evaluated to be 0.008, 0.01,
and 0.015. These values are consistent with a previous
study (pH = 0.0148).6) NMR values for each probe areshown in Fig. 2. Although, the evaluation of systematicerrors are ongoing. We will mount three probes on asystem to make a triaxial probe, and create a precise
map of the magnetic ﬁeld of the WiSES magnet at thenext stage.

Hall sensor∗2

NMR value = 0.411 [ T ]NMR value = 0.408 [ T ]NMR value = 0.408 [ T ]0.006

BHall probe

∗1

B[T]

H. Wauke,∗1,∗2 A. Enokizono,∗1 Y. Honda,∗1,∗2 K. Kasama,∗1,∗2 T. Ohnishi,∗1 T. Suda,∗1,∗2 S. Takayama,∗1,∗2T. Tamae,∗1,∗2 K. Tsukada,∗1,∗2 M. Wakasugi,∗1 and M. Watanabe∗11) T. Adachi et al., RIKEN Accel. Prog. Rep. 45, 144 (2012).
2) M. Wakasugi et al., Phys. Rev. Lett. 100, 164801 (2008).
3) T. Suda et al., RIKEN Accel. Prog. Rep. 45, 184 (2013).
4) T. Tamae et al., RIKEN Accel. Prog. Rep. 47, 196 (2014).
5) C. Goldberg, R. E. Davis, Phys. Rev. 94, 1121 (1954).
6) S. Tomita, Master Thesis, Tohoku Univ., (2017).

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