1. Design of a Dipole with Longitudinally Variable Field using Permanent Magnets for CLIC DRs
M. A. Domínguez, F. Toral (CIEMAT), H. Ghasem, P. S. Papadopoulou, Y. Papaphilippou (CERN)

2. Index Introduction Technical specifications Preliminary design
2D Magnetic Design
3D Magnetic Design
Field trimming
Conclusions

3. Introduction
CLIC: electron positron linear accelerator collider. Particle physics research in the multi-TeV energy scale
Two beams of 3 TeV. Expected luminosity of 2× Inversely proportional to the transverse beam emittance
Damping rings (DRs) to reduce the emittance of the injector chain incoming beams. Lattice: theoretical minimum emittance (TME) cell and simple FODO lattice filled with high field superconducting damping wigglers
The horizontal emittance is further reduced below the TME limit for a given magnetic structure by considering dipole magnets with longitudinal variable bending field. Trapezium field profile dipoles are preferred in the CLIC DR lattice
CLIC is an electron positron linear accelerator collider. It is in its design phase and its main purpose will be the particle physics research in the multi-TeV energy scale
At the interaction point, two beams of 3 TeV will collide with an expected luminosity of 2× This luminosity is inversely proportional to the transverse beam emittance.
The target of its damping rings (DR) is to reduce the emittance of the injector chain incoming beams. Their lattice is based on the combined effect of theoretical minimum emittance (TME) cell and simple FODO lattice filled with high field superconducting damping wigglers.
The horizontal emittance is further reduced below the TME limit for a given magnetic structure by considering dipole magnets with longitudinal variable bending field. Regarding the analytic evaluation, the trapezium field profile dipoles are preferred in the CLIC DR lattice design to provide the minimum horizontal emittance

4. Technical specifications
The magnetic field of a longitudinal variable field dipole varies along its length. This can provide a reduction of the horizontal beam emittance in comparison with a fixed field dipole of the same bending angle. The maximum field should be at the center of the magnet and it should decrease towards both sides.
two main field profiles have been selected: step and trapezoidal shape. The desired fields and dimensions of each case, including three different subcases for the trapezium profile, as well as the common specifications, are described in Table I. Theoretically, the case 1 of the trapezium profile would yield the best results with respect to the lowest beam emittance. The trapezium profile has not been achieved before in an accelerator magnet. If the field profile is like this, The bending radius would change linearly along the magnet length. At the same time, it is the most complicated design due to the shortest high field region length: only 6 mm. Throughout the magnet design phase all the cases are analyzed, starting with the simpler and less effective -Step profile- and pointing towards the best design in terms of beam emittance -Trapezium case 1-.

5. Preliminary design C-shaped magnets: efficient use of space
Gap is pointing outwards to ease synchrotron radiation evacuation
Yoke made of pure iron (Armco). Average field below 1T
High saturation in the high field region pole => Fe-Co (Vacoflux) preferred
Straight magnet: higher quality machining, eases assembly
Sagitta: 5mm. GFR centered with the pole and 2 additional regions with the same radius and displaced ± 2.5mm
Fixed field provided with permanent magnets
Max Temp variation ±0.1ºC => No specific temperature compensation
Taking into account radiation tolerance, volume and weight, maximum remanent magnetization, cost,…:
SmCo in the low field region
NdFeB in the high field region

6. Magnetic design: 2D
Poles cross section is smaller in the tip than in the base: flux concentration, higher field peak in the gap
Combined function magnet (dipolar and quadrupolar fields): hyperbolic profile in the pole tips
2D simulations in Quickfield
Low field region: SmCo blocks in a flat configuration over the pole
High field region: NdFeB in three blocks working in parallel to preserve the pole dimensions within reasonable limits. Highly saturated: much more difficult to reach the desired specifications

7. Magnetic design: 3D
Short magnet length (0.58 m) makes 2D simulations diverge from 3D, particularly in the high field section, where the pole tip is approximately 7 mm wide
Result comparison/validation: Ansys Maxwell, ROXIE, COMSOL and Opera
Crosstalk between high and low field regions. To minimize it, the low field region pole tip has been extruded and the high field region pole tip chamfered
Step profile: easily obtained
Trapezium profile: tough challenges. Achieved introducing a variable gap along Z axis
Ansys Maxwell showed limitations when calculating the field multipoles in the order of 1E-4 units. ROXIE was used whenever the cross-section of the magnet was constant due to its limitation of performing only straight 3D extrusions. COMSOL was used to perform a final verification of the full model simulation results. Once fully validated, Opera is our preferred data source due to the lower computational times and better integration with the CAD suite used to model the magnet.

8. Magnetic design: 3D
High field region: flat profile due to the high iron saturation
Low field region gap: not constant. Different hyperbolas for each different gap height
By contrast, to be mechanized with EDM, the pole tips must be ruled surfaces
On account on these restraints: “averaged hyperbola”. Very good results in the simulations
Regarding the pole tip shapes, as the magnets are combined function dipoles, the low field region has a hyperbolic profile . Conversely, the high field region has a flat profile due to the high iron saturation. It was firstly simulated with the corresponding hyperbolic profile, but it was observed that this profile combined with the high saturation was increasing considerably the multipole values. Therefore, it was decided to introduce a flat pole profile to maintain the field harmonics within the expected values. The low field section hyperbolic profile is then improved -higher transverse gradient- to compensate the high field region gradient loss.
The low field region gap is not constant. This implies that the hyperbola should not be the same at each different gap height. By contrast, to obtain a higher quality finishing, the mechanizing will be performed with electrical discharge machining, which implies the pole tips’ faces to be ruled surfaces. On account on these restrains, it is decided to use an “averaged hyperbola”. It is calculated based on the average gap height and field and then swept all along the low field region. This compromise solution shows very good results in the simulations.

9. Upgrade to 2.3 T
Magnet originally limited to 1.77 T peak field as a reasonable value for a non-superconducting magnet
3D simulations: peak could be increased above 2 T, increasing emittance reduction factor while keeping the field quality
A new 2.3 T optimized trapezium profile is finally proposed
The magnet was originally limited to 1.77 T peak field as a reasonable value for a non-superconducting magnet. During the 3D simulations it was verified that this peak could be increased above 2 T, increasing in this way the emittance reduction factor while keeping the demanded field quality. A new 2.3 T optimized trapezium profile is finally proposed

10. Upgrade to 2.3 T
At this point the magnet is close to meet the desired specifications.
The obtained decay –“Old profile”- at both sides of the peak does not match the ideal one (hyperbolic)
Impossible to get closer to the ideal decay –“Optimized 2.3 T profile”: a new layout is introduced
To follow the ideal hyperbolic decay, the low field region is split in two parts: low and mid field region
The peak field, integrated field (dipolar and quadrupolar), magnetic length, ... specified values are met
However, the obtained decay –“Old profile”- at both sides of the peak does not match the expected one, which ideally must be a hyperbolic decay. It is extremely difficult to make a less steep decay at both peak sides while preserving the maximum field as a reason of the high and low field crosstalk.
Due to the impossibility of getting closer to the ideal decay –“Optimized 2.3 T profile”- with the present design, a new layout is introduced

11. Upgrade to 2.3 T
Three differentiated sections: low, mid and high field. This allows a higher FTME 7, higher than the one originally proposed
New hyperbolic profiles in the low and medium field regions, while the high field one maintains the flat pole tip
Same configuration for the high and medium field regions PM: three NdFeB blocks working in parallel
Low field region maintains the SmCO in one flat block over the pole
With this upgrade the maximum field is increased up to 2.3 T and at the same time the field decay matches more precisely the ideal hyperbolic desired profile. Multipole values within the limits.
New hyperbolic profiles are calculated in the low and medium field regions, while the high field one maintains the flat pole tip, as can be observed in Fig. 5. Even though the latter remains flat, the sides have been optimized with curved su
The permanent magnet blocks in the high field region remain with the same dimensions and layout whereas the low field part has to be redesigned to be split in the new two sections, introducing a new medium field section. The low field block is, as before, made of SmCo magnets. The medium field uses the same configuration as the high field section: three blocks working in parallel. NdFeB blocks are used in this case. This layout is forced by the limited available space between the two adjacent regions.

12. Field trimming
Two main possibilities to study the feasibility of varying the magnetic field ±5% :
Active: adding coils and their corresponding power supply
Passive: splitting the yoke in two parts and therefore making it possible to adjust the magnetic circuit reluctance
Pros:
Fast field trimming
Can be adjusted during operation
Cons:
Higher cost
More complex design
Active trimming: it would rely on the installation of coils and its corresponding power supply. The main advantages of this solution would be the fast field trimming and the tuning during operation. On the other hand, this option would imply a higher cost and a more complex design.
2. Passive trimming: it can be done splitting the yoke in two parts and therefore making it possible to adjust the magnetic circuit reluctance. The smaller part can be moved closer or away to adjust the flux as needed. This option would be less expensive and entail a simpler design as its main advantages. As its main disadvantage one must bear in mind that the field cannot be adjusted during operation. However, if needed, this can be overridden installing remote actuators.
Several simulations are made to study both options as shown in Fig. 6. Regarding the active solution, the simulation shows that due to the high iron saturation –mainly in the high field region- the coils should be too large and water cooled. This approach gets away from the main ideas behind using permanent magnets: compactness and no need of power supply. Passive trimming is feasible according to simulations. It will preserve the magnet dimensions and the multipole values. This is the preferred solution and it will be probably implemented with actuators to allow remote trimming.
Pros:
Less expensive
Simpler design
Cons:
In principle the field cannot be adjusted during operation

13. Field trimming Simulations
Active: due to the high iron saturation, the coils should be too large and water cooled. This approach gets away from the main ideas behind using permanent magnets: compactness and no need of power supply
Passive: feasible according to simulations. This is the preferred solution and it will be probably implemented with actuators to allow remote trimming.

14. Conclusions
PM based design. High requested peak field implies dealing with iron saturation. Partially overcome using Fe-Co and suppressing the hyperbolic profile in the most saturated section.
Important challenge: longitudinal gradient with trapezoidal decay. Solved splitting the magnet in three differentiated field regions combined with an innovative variable gap solution
The mentioned solutions finally lead to a validated proposal that meets –and even exceeds in terms of beam emittance reduction- the specifications. This achievement is due to the trapezoidal field profile, which has been implemented for first time in an accelerator magnet
The probable need of a field trim is also evaluated and implemented creating a variable reluctance return path for the magnetic flux using movable parts

15. Thank you for your attention!

16. Multipoles

17. Multipoles