Magnetic Field Calculation in Cross Calibration Cryogenics Science Center, KEK Hiroshi Yamaguchi September 18, 2017 Magnetic Field Calculation in Cross Calibration 1
Items • Calculation magnetic field in the latest cross calibration test • Comparison material effect between measurement and calculation • Preparations for next cross calibration test September 18, 2017 Magnetic Field Calculation in Cross Calibration 2
Cross Calibration The latest cross calibration test was done in March 2017 • Thin and long glass tube (fill water in) • Using Al pipe and Teflon pipe to support the glass tube and modulation coils as well as to cancel the error magnetic field • Improve electrical circuit Motivations • Reconstruct the cross calibration results • Reduce the material effects for next cross calibration test September 18, 2017 Magnetic Field Calculation in Cross Calibration 3
Geometry (Al pipe and Teflon pipe) Standard probe is consist of an Al pipe (1 mm thickness) and a Teflon pipe (2 mm thickness) holes Center holes (to fix a glass tube) Al pipe：φ2.2 Al pipe：φ8.2 Teflon pipe：φ2.4 Teflon pipe：φ10 Slits (only Teflon pipe) Width 1 mm, depth 1 mm Modulation coil Winding modulation coils in this slits 0.24 mm Copper wire : φ0.1 mm, 30 turns Cross section of coils : 0.24 mm 2 It corresponds to 0.24 mm depth September 18, 2017 Magnetic Field Calculation in Cross Calibration 4
Stopper for Glass Tube Glass tube filled with water is fixed by using stopper made of Teflon Holes with φ4 mm to insert glass tube Teflon Shape with φ8.2 and φ10 are inserted in Al pipe hole and Teflon pipe hole, respectively Teflon pipe September 18, 2017 Magnetic Field Calculation in Cross Calibration 5
Geometry (Opera) Teflon Al Mesh size Standard probe and near atmosphere Slits for region : 0.5 mm Modulation coils Outer atmosphere region : 10 mm September 18, 2017 Magnetic Field Calculation in Cross Calibration 6
My program Write a program for magnetic field calculation by using C++ language Pro : It is easy for changing the geometry Con : The calculation can not be included a self-consist effect • At first, the magnetic fields are calculated by using my program to improve the error field • Finally, it is confirmed by using Opera � ・ P 1. Generate meshes in pipes � 2. Calculate magnetic flux between an observed point (point P) and meshes � 3. Sum contributions from all meshes Mesh profile Cylindrical Mesh：dr = 0.1 mm, dθ= 2π/256, dz = 1 mm 0.1 mm Magnetic field : 1.0 Tesla 360ﾟ/256 September 18, 2017 Magnetic Field Calculation in Cross Calibration 7
Field Calculation � � : Magnetic Field generated by MRI Coil � � �Wb · m �� � � � �A · m �� � � 0, 0, � � � 0, 0, � � �Wb · A �� · m �� � � � : Magnetic Field generated by material with magnetic susceptibility χ � in � � Magnetization : ��Wb · m �� � ( ��Wb · m� : magnetic moment in unit volume � ) � Wb · m �� � ��Wb · m� � � � �Wb · A �� · m �� �χ � ��A · m �� � ��m � � Magnetic field generated by Magnetizations � Wb · m �� � � �A · m �� · m �� � � 2�� � �Wb · A �� · m �� �� � �m � � cos � � Wb · m �� � � �A · m �� · m �� � � 4�� � �Wb · A �� · m �� �� � �m � � sin � Covert Spherical coordinates to rectangular coordinate � � sin � cos � � � � cos � cos � � � sin � sin � � � � cos � sin � � � � � � cos � � � � sin � Magnetic field (magnetic flux density) generated by material � � Wb · m �� � ��Wb · A �� · m �� � � � � A · m �� · m �� �� September 18, 2017 Magnetic Field Calculation in Cross Calibration 8
Field Calculation 6 10 Bz [ T ] 20 Compare the magnetic field between my My Calculation 10 program and Opera by using Al cylinder Opera (Height 10 mm, Diameter 10 mm) 0 10 My program is not consistent with Opera in materials Al cylinder 20 1 Difference [ T ] 0.5 0 -6 10 0.5 3 10 1 0 5 10 15 20 Z [ m ] Approximation (r >>ℓ) is applied in my calculation � � � � 1 � 1 ~ � � 1 ℓ cos � � Observe point � 4�� � � � cos � 4�� � � � 4�� � � � � � � � � � �� � �� � 2�� � � � cos � � � � � 1 �� � �� � 4�� � � � sin � � magnetic charge In the material, mesh size (ℓ) is not large than r September 18, 2017 Magnetic Field Calculation in Cross Calibration 9
Dataset Stopper for Pipe Holes at center Modulation Coil glass tube of pipes Stopper No slits Stopper in Al pipe The same holes to Standard Probe Al : φ8.2 mm Teflon : φ10 mm Winding coil in slit Stopper in Teflon pipe (W1 mm×t0.25 mm) φ10 mm Al : φ10 mm Teflon : φ10 mm φ5 mm Al : φ5 mm Teflon : φ5 mm Al pipe Teflon pipe φ3 mm Al : φ3 mm Teflon : φ3 mm φ2 mm Comparing in this Al : φ2 mm Only slits presentation Teflon : φ2 mm Opera/My program Winding coil in slit No holes (W1 mm× t 1 mm) Only my program Winding coil in slit Not generate (W1 mm×t0.25 mm) September 18, 2017 Magnetic Field Calculation in Cross Calibration 10
Comparison with Opera Al and Teflon pipes without holes and slits 9 6 10 10 Bz [ T ] Bz [ T ] 20 50 10 0 0 10 My Calculation My Calculation 50 Opera Opera 20 1 1 Difference Difference [ T ] [ T ] 0.5 0.5 0 0 -8 -8 10 10 0.5 0.5 3 10 1 1 0 0.05 0.1 0.15 0.2 0 5 10 15 20 Z [ m ] R [ m ] September 18, 2017 Magnetic Field Calculation in Cross Calibration 11
Comparison with Opera Al and Teflon pipes with holes and slits 9 6 10 10 Bz [ T ] Bz [ T ] 20 50 10 0 0 10 My Calculation My Calculation 50 Opera Opera 20 1 1 Difference Difference [ T ] [ T ] 0.5 0.5 0 0 -8 -8 10 10 0.5 0.5 3 10 1 1 0 0.05 0.1 0.15 0.2 0 5 10 15 20 Z [ m ] R [ m ] September 18, 2017 Magnetic Field Calculation in Cross Calibration 12
Comparison with Opera Al and Teflon pipes with holes and slits and the modulation coils are winded 9 6 10 10 Bz [ T ] Bz [ T ] 20 50 10 0 0 10 My Calculation My Calculation 50 Opera Opera 20 1 1 Difference Difference [ T ] [ T ] 0.5 0.5 0 0 -8 -8 10 10 0.5 0.5 3 10 1 1 0 0.05 0.1 0.15 0.2 0 5 10 15 20 Z [ m ] R [ m ] The agreement is less than 5 ppb (except the regions in materials) September 18, 2017 Magnetic Field Calculation in Cross Calibration 13
Diameters of Holes Comparison Magnetic fields in different hole size 9 9 10 10 Bz [ T ] Bz [ T ] 20 20 0 0 20 20 Standard Probe Standard Probe + Center holes + Center holes + Center holes 2 mm + Center holes 2 mm 40 40 + Center holes 3 mm + Center holes 3 mm + Center holes 5 mm + Center holes 5 mm + Center holes 10 mm + Center holes 10 mm 1 1 Difference Difference [ T ] [ T ] 0.5 0.5 0 0 -8 -8 10 10 0.5 0.5 3 10 1 1 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 Z [ m ] R [ m ] Bottom plots show difference of error field from Al and Teflon pipe without holes and slits The smaller hole size become smaller error field September 18, 2017 Magnetic Field Calculation in Cross Calibration 14
Slits for Modulation Coil Effect derived from slits for modulation coils (The center holes are not made in this calculation) 9 9 10 10 60 Bz [ T ] Br [ T ] 50 Standard Probe 40 + Slits + Modulation coils (t1.00mm) + Modulation coils (t0.25mm) 20 0 0 20 Standard Probe + Slits 40 + Modulation coils (t1.00mm) 50 + Modulation coils (t0.25mm) 60 2 1 Difference Difference [ T ] [ T ] 0.5 1 0 0 -8 -8 10 10 0.5 1 3 10 2 1 0 0.02 0.04 0.06 0.08 0.1 0 5 10 15 20 Z [ m ] R [ m ] The susceptibility of Teflon is approximate to that of copper The error field is negligible when the slit Teflon : χ = -1.025×10 -5 for modulation coil is filled with copper Cu : χ = -9.80×10 -6 wires September 18, 2017 Magnetic Field Calculation in Cross Calibration 15
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