1. Some Design Considerations and R &D of CEPCB Dipole Magnet
Kang Wen
2016-4

2. Contents Physical requirements Cost consideration
Earth field consideration
Field quality consideration
R & D of prototype dipole magnet
Summary

3. 1、Physical Requirements
1) Quantity: 5120
Magnetic length: 8m
Bending radius: 6519m
Gap: 40mm
The field: from 31Gs to 614Gs
Repetitive frequency: 0.1Hz
GFR: 52mm
Field uniformity: 3E-4
9) Field difference from magnet to magnet: 5E-4

4. 2、Cost consideration
Since CEPCB has 5120 dipole magnets, each long 8m, the total length of the magnets is 41km, covering 76% of the booster ring (54km), the cost of the magnet becomes an important issue for the magnet design.
To save the money, we can take the LEP’s dipole magnet design as a reference design.
Since the field was very low, LEP used the steel- concrete cores with the filling factor of 20% and hollow aluminium conductor coils to produce the main dipole magnets for its collider in 1980s.
For safety consideration (production, lift and delivery), the length of each steel-concrete core was controlled within 5.75m, which was used as unit to assemble the magnets with required length in the tunnel.
The coils of each pole had only one turn, which were welded by hollow aluminium conductors as long as the cores in the tunnel.

5. 2、Cost consideration
Because the cross section of the cores for CEPCB dipole magnets is only half of LEP dipole magnets, the length of each core should be controlled within 4m. So a 8m long magnet will consist of two cores in longitudinal direction.
Since the Joule loss in the coils of CEPCB dipole magnets is very low, the coils will be made by solid aluminium conductor without water cooling. The coils of each pole will have one turn, which will be formed by aluminium conductors with the same length as the cores in the tunnel.
The ratio of mass density and price of concrete to steel lamination, aluminium conductor to copper conductor are shown in right table. The money of material can be saved dramatically.
LEP’s design

6. 2、Cost consideration
2) To save the money, we can also propose a new CEPCB magnet design
Since the field is very low, LEP’s design could use concrete to replace most of steel laminations in longitudinal direction in the cores.
With the same reason, we can cut the steel of cores in transversal direction and propose a CEPCB’s magnet design with thin return yoke.
The coils are also made by solid aluminium instead of copper conductors.
As LEP’s design, the CEPCB dipole magnet will consist of two cores with 4m length and the final assembly will be finished in the tunnel.
CEPCB’s design

7. 2、Cost consideration
3) An improved CEPCB magnet design with thinner return yoke.
In the previous design, the thickness of the magnet return yoke is mainly determined by the mechanical strength since it must be strong enough to compensate its weight and the magnetic force between two poles.
If we use some kind of supporters in the magnet gap to compensate its weight and the magnetic force, we can reduce the thickness of the return yoke further and get another design of CEPCB dipole magnet.
CEPCB’s design-1
CEPCB’s design-2

8. 2、Cost consideration
4) Cost comparison of the different magnet designs.
The cost of either LEP’s design or CEPC’s design is only about 35% of conventional design.
The cost of CEPC’s design-1 is a little higher than LEP’s design, but that of CEPC’s design-2 is similar to LEP’s design.

9. 2、Cost consideration Advantages of the CEPCB’s design
To produce a pure steel core is easier than to produce a steel-concrete core, so the production cost of the magnet will be reduced.
The field quality of magnet with the pure steel core is easier to be controlled.
The total weight of the magnet becomes lighter without concrete.
Disadvantages of the new design
The CEPCB’s design magnet has no successful experiences.

10. 3、Earth field consideration
When CEPCB dipole magnet works at the minimum field of 30Gs, the earth field( 0.5Gs) will be its 1.7%. So we have to consider the effect of earth field.
Earth field will influence the field quality of the magnet, such as field uniformity and excitation properties.
The strength and direction of earth field are different in different places. For the CEPC’s booster with circumference of 54km, different earth field will make the field of the dipole magnet different.
In the parts of the accelerator without magnets, earth field will also affect the particle beam like a corrector magnet at low energy.
A good design of the CEPCB dipole magnet should be a design that can shield earth field as much as possible.

11. 3、Earth field consideration
The effects of earth field on the magnets with C-type and H-type cores have been simulated. It can be seen that the magnet with H-type core has better field shielding than the magnet with C-type core.
By component of Earth field
C-type core
H-type core

12. 3、Earth field consideration
Bx component of Earth field
C-type core
H-type core
For the H-type core magnet, the closed structure of the core can shield earth field very well and reduce it from 0.5 Gs to 0.03Gs. So H-type core will be selected for CEPCB’ dipole magnet.
Effect of earth field is not a problem for the magnet with H-type core. But outside the magnets, earth field will still affect particle beam at low energy.

13. 4、Field quality of the CEPCB low field magnet
For particle accelerator physics, three main specifications of dipole magnets are very important.
Good field region and field uniformity.
GFR: 52mm. Field uniformity: +/- 3E-4
Excitation curve and field reproducibility.
Field reproducibility: 2E-4
Integral field difference from magnet to magnet.
Field deviation: 5E-4

14. 4、Field quality of the CEPCB low field magnet
Because we don’t have BH curves of solid iron or steel laminations at very low field, we can’t simulate accurately the field quality of the CEPCB dipole magnet at low field. Fortunately, we were measuring the field of CSNS/RCS extraction Lambertson magnet by using the Hall probe field measurement system, so we have directly studied the field properties when it worked from 32Gs to 640Gs.

15. 4、Field quality of the CEPCB low field magnet
1) Good field region and field uniformity
The distributions of the field at 30Gs, 60Gs, 90Gs, 120Gs and 640Gs in the center of the Lambertson magnet have been measured. It can be seen that the lower the field, the worse the field uniformity. The field uniformity of 32Gs is 10 times worse than that of 640Gs.

16. 4、Field quality of the CEPCB low field magnet
2) Excitation curve and field reproducibility
Compared to the high field of 640Gs, non-linearity is serious at the low field of 32Gs, which reaches 23%. For conventional dipole magnets like for BEPCII storage ring, the non-linearity of the field was required to be less than 5%.
The non-linearity of field means that the field can not change with excited current linearly. The waveform of the field will be deformed compared to that of the current.
In order to decrease the non-linearity of the field down to 5%, the lowest field should be increased to 120Gs

17. 4、Field quality of the CEPCB low field magnet
2) Excitation curve and field reproducibility
Except the first cycle, the curves of the second and the third cycles seem overlapped very well. But when we check the difference point to point between the second and third cycle, the field difference or reproducibility is 0.5% at the low field of 30Gs. And in order to get the field reproducibility of 0.02%, the lowest field of the magnet should be higher than 120Gs. (The lowest field of dipole magnet for LHeC is 127Gs at injection energy of 10GeV.)

18. 4、Field quality of the CEPCB low field magnet
3) Integral field difference from magnet to magnet
Field difference from magnet to magnet is determined by properties deviation of core material, difference of core stacking factor and physical length.
If the cores of magnets are made by steel laminations, the properties deviation of materials can be smoothened by lamination shuffling.
The difference of core stacking factor and physical length could be controlled by the optimized procedures of core fabrication.
However, if the field reproducibility can not reach 2E-4, the field difference between magnets can not reach 5E-4.

19. 5、R & D of CEPCB low field dipole magnet
1) Fund supported from IHEP’s workshop
The workshop promised to support the development of a 4m long prototype dipole magnet for CEPCB. So we can start R & D of CEPCB low field dipole magnet at present.
The total cost is about 20w RMB.
Cost of the magnet material and fabrication: 5w RMB
Cost of dies and toolings: 15w RMB
2) Purpose of R & D
To verify the production procedures of CEPCB dipole magnet.
To study the low field properties of CEPCB dipole magnet.

20. 5、R & D of CEPCB low field dipole magnet
3) Design of the prototype magnet
The 4m long core has a H-type frame for better shielding of earth field.
The core is made by silicon steel laminations. The coil (one turn per pole) is made by solid alumimium bars without water cooling.
By using the supporters in the magnet gap to compensate the core weight and magnetic force, the return yoke of the core can be made as thin as possible.
In the upper and lower pole areas of laminations, 8 rectangle holes and 2 round holes will be stamped to reduce the weight of the cores as well as to increase the field in the laminations.

21. 5、R & D of CEPCB low field dipole magnet
3) Design of the prototype magnet
In order to install the vacuum chamber, the core can be divided into upper and lower parts.
Around the outside of each part, four long bars are used to wield the laminations of the half core together. In the round hole of each pole, there is another long bar to pressure pole part of the laminations together.

22. 5、R & D of CEPCB low field dipole magnet
4) Field simulation of the prototype magnet
The field simulations show that the magnetic fluxes are flowing in the laminations as expected. The holes in the pole areas can adjust and optimize the flux flowing very well.
The field distribution curve along x direction shows that the field uniformity in the good field region is better than 3E-4

23. 5、R & D of CEPCB low field dipole magnet
4) Field simulation of the prototype magnet
The magnetic flux density in the most areas of the laminations is high than 3000Gs while field in the gap is 620Gs.
The magnetic flux density in the most areas of the laminations is high than 150Gs while field in the gap is 30Gs.
So the design of CEPCB dipole magnet with the holes in the pole areas as well as the thin return yokes can not only increase the magnetic flux density by 5 times and improve the field reproducibility, but also decrease the weight of the core and reduce cost of the magnet.

24. 5、R & D of CEPCB low field dipole magnet
5) Designed parameters of the prototype magnet

25. 5、R & D of CEPCB low field dipole magnet
6) R & D plan of the prototype magnet
To finish the magnet physical and mechanical design.
To complete the production of the magnet.
To test the magnet.

26. 6、Summary
For low field magnets, weight and cost of the magnets can be reduced obviously by reducing the steel longitudinal direction like LEP’s design or by reducing the steel in transversal direction.
The effect of earth field can be neglected for the H-type magnet since its closed frame core can shield earth field very well.
In order to meet the physical requirements of field uniformity and field reproducibility, the lowest field of dipole magnet should be 120Gs.
The design of CEPCB dipole magnet with the holes in the pole areas as well as the thin return yokes can increase the magnetic flux density in the core and improve the field reproducibility in the gap.
With fund support from IHEP workshop, a prototype dipole magnet for CEPCB will be developed.

27. Thank you for your attention!