1. The design schemes of the low field dipole magnets

2. 1、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.
Field non-linearity: 5%?
Integral field difference from magnet to magnet.
Field deviation: 5E-4

3. 1、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.

4. 1、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.

5. 1、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

6. 1、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.)

7. 1、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 (Hc), 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.

8. 2、Design scheme of the LEP’s low field magnet
1) Main parameters of the LEP’s dipole magnet

9. 2、Design scheme of the LEP’s low field magnet
2) Design scheme of the magnet
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.

10. 2、Design scheme of the LEP’s low field magnet
2) Design scheme of the magnet
LEP’s six-core prototype dipole magnet.

11. 3、Design scheme of the LHeC’s low field magnet
1) Main parameters of the magnet

12. 3、Design scheme of the LHeC’s low field dipole magnet
2) Design scheme of the magnet
Because of the very low magnetic field, the yoke is composed of silicon steel laminations interleaved with plastic spacers, with a thickness ratio between plastic and iron of 2:1.
The coils of each pole had only one turn, which were welded by solid aluminium conductors.

13. 3、Design scheme of the LHeC’s low field dipole magnet
2) Design scheme of the magnet
A short prototype dipole magnet of LHeC. The laminations and plastic plates were glued together to form the core of the magnet.

14. 4、CEPCB’s low field dipole magnet
1) 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.

15. 4、CEPCB’s low field dipole magnet
1) 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.

16. 4、CEPCB’s low field dipole magnet
2) 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

17. 4、CEPCB’s low field dipole magnet
2) 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.

18. 4、CEPCB’s low field dipole magnet
3) Designed parameters of the prototype magnet

19. 5、Comparison of the low field dipole magnets