1. Yingshun Zhu Design of Small Aperture Quadrupole Magnet for HEPS-TF
On behalf of Magnet system
Institute of High Energy Physics, Chinese Academy of Sciences
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2. Contents Introduction Overall design considerations
Magnetic field calculation
Design parameters and R&D plan
Summary
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3. Introduction
A storage-ring-based high energy photon source (HEPS) with a beam energy of 6 GeV, circumference about 1300m, and emittance less than 0.1 nm•rad is proposed to be constructed in China.
A R&D project to build a test facility for HEPS has been approved. (HEPS-TF)
Small aperture quadrupole magnet is one of the important magnets in HEPS-TF.
Small aperture quadrupole magnet will be used in HEPS storage ring.
Low Emittance Rings 2015 Workshop

4. Introduction Design requirement of quadrupole magnet:
Design challenges:
High field gradient;
High field quality;
Small bore diameter;
Limited pole width.
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5. Overall design considerations
First of all, the magnet design should meet the field requirements.
Solid or laminated yoke;
Number of yoke segments;
Conductor type, air or water cooling;
Pole profile and mechanical accuracy;
Compatible with industrial fabrication technique;
Reduce operation cost;
Mechanical boundary condition;
Appropriate electrical and water circuit parameters.
Low Emittance Rings 2015 Workshop

6. Overall design considerations
For small aperture quadrupole magnet, the non-systematic field harmonics are more sensitive to pole profile errors.
Strict machining precision is required to obtain the high field quality.
Overall design:
Common solid iron (DT4) for core material, four-piece structure;
Saddle coil is selected:
Achieve the field gradient requirement using common soft iron;
Increase the magnetic efficiency;
Reduce the magnetic saturation in the yoke;
Reduce the effect of material non-uniformity on field quality ;
Enhance magnet rigidity.
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7. Overall design considerations
Hollow copper conductor for the coil.
Water cooling system.
Small current density to reduce magnet power and operation cost.
Increased magnet transverse dimension.
Sufficient magnetic optimization.
Special pole shape to meet the 11mm gap between adjacent poles.
Smooth pole profile, avoid shape corner.
Reasonable electrical and water circuit parameters.
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8. Magnetic field calculation
2D and 3D magnetic field calculations are performed by OPERA.
Field quality in several models with different pole shapes were studied. Then magnet cross section is determined.
Special pole shape is adopted so that the gap between poles is 11mm.
Optimized pole
2D flux lines
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9. Magnetic field calculation
Low field level in the yoke; Only a part of the pole is saturated.
Good 2D field quality.
2D field quality
2D Bmod distribution
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10. Field error analysis
Random pole position error of about 10 microns will introduce sextupole field, typically about 0.6×10-4.
3% deviations of iron B-H property in the pole tip region will introduce sextupole field about 0.4× (Case 1)
3% deviations of iron B-H property in the pole root region will introduce sextupole field about 0.25×10-4. (Case 2)
Case 1
Case 2
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11. Field error analysis
Sextupole field introduced by 3% deviations of iron B-H property in the iron yoke region can be neglected.
Multipole fields generated by 2mm shape error of coil can be neglected.
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12. 3D magnetic calculation
OPERA-3D model
Pole end
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13. 3D magnetic calculation
Central magnetic field gradient of 80 T/m is achieved.
Without pole end chamfer, very good integrated field quality is obtained.
3D field quality
Field distribution along longitudinal direction
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14. 3D magnetic calculation
Normalized integral transfer function:
The magnetic saturation in the iron core is not serious.
The magnet works mainly in the linear region of excitation curve.
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15. Design parameters and R&D plan
Main design parameters of the quadrupole magnet:
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16. Mechanical precision
The magnet pole will be fabricated by EDM machine.
Mechanical precision requirement:
Pole machining error <10 μm ;
Deviations of iron B-H property in the pole tip and root region < 3%;
Machining error on the interface of adjacent 1/4 cores <10 μm ;
Coil shape error < 2 mm.
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17. R&D plan
Firstly, a model quadrupole magnet is to be manufactured and measured, which is almost identical with the real quadrupole magnet except that the effective length is only 200mm.
Then the small aperture quadrupole magnet will be manufactured and measured.
Model quadrupole magnet
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18. Summary
It is challenging to meet the requirement of small aperture quadrupole magnet for HEPS-TF.
The magnetic field design of the small aperture quadrupole magnet has been finished.
The magnetic performance of the magnet meets the requirement.
Firstly, a model quadrupole magnet is to be fabricated and measured.
The actual field quality depends on the material property, fabrication tolerance and assembly error.
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19. Thanks for your attention!
Low Emittance Rings 2015 Workshop