CLIC Damping Rings Gradient Dipoles Manuel Domínguez Fernando Toral

Summary Technical specifications Permanent magnets 2-D Simulations Field profiles Field quality FEM suites Overview

Technical specifications 96 dipoles with fixed longitudinal and transverse gradient Possibility to include a small correction of the field amplitude (5%) Good field region radius: 5 mm Field quality  1*10-4 Transverse gradient: 11 T/m, vertical focusing Longitudinal gradient: two possibilities, step or trapezoidal

Permanent Magnets Permanent magnets are the best choice to provide a fixed field: no power consumption and very compact. Taking into account: Temperature variation in the tunnel will be as low as ±0,1ºC Sm-Co radiation tolerance is higher than Ne-Fe-B Low radiation expected, but higher in the low field sections (magnet ends) The permanent magnet volume and weight reduction using Ne instead of Sm goes up to 45%. The cost of Neodymium magnets is lower than SmCo. We are pointing towards the use of: Ne-Fe-B magnets in the high field region Sm-Co magnets in the low field region NO specific temperature compensation

2-D Simulations C-shaped magnets is the best layout for efficient use of space. Gap is pointing outwards to ease synchrotron radiation evacuation. Low field region. Achieved: 1.01T, ΔB/B = 1*10-4, rGFR = 5mm High field region. Different configuration: Three magnets working in parallel to preserve the pole dimensions within reasonable limits Achieved: 1.77T, ΔB/B = 1*10-4, rGFR = 5mm The above conditions were much more difficult to reach as the pole tip iron is saturated. The field quality is more sensitive to any minor change in the dimensions.

3-D: Field profiles Step profile Easily achievable - Crosstalk Tech specs met

3-D: Field profiles Trapezium profile: Preferred option to reduce beam emittance Different trials to achieve the desired trapezium profile: 1st option: Trying to keep the gap constant along Z axis Low field region with pole cuts. Each part with different PM grades Variable pole width 2nd Option: Variable gap along Z axis. Preferred option Vas a decir algo sobre cambio de intensidad de imanes y tamaño? También gap constante, pero ancho de polo variable

3-D Simulations Trapezoidal profile. Case 1 preferred (Optics simulations) No major problems with case 1 & 2 L1 lower than 14 mm strongly increases the saturation in the high field pole and leakage flux Three different options. #1 is preferred Ejemplo similar en psi (6T)

3-D: Field profiles Case 1 With such a thin pole tip is extremely difficult to reach the theoretical trapezoidal profile (achieved in cases 1& 2) 1.77T pole longitudinal reduction and 1T pole extrusion to improve the field in the gap between the two magnet parts We will send the step and the three trapezoidal field profiles data to CERN to run the corresponding optics simulations and select one to proceed to the next steps

3-D: Field Quality Short magnet length (0.58m) makes 2D simulations diverge from 3D, specially in the case of the 1.77 T section (pole tip ≈ 0.007m!) High saturation in the 1.77 T pole leads to undesired multipole values and higher flux leakage. These effects are reduced using Iron-Cobalt (Vacoflux) in the pole The saturation in this pole lead as well to a different pole tip design. It does not match the theoretical calculations and had to be adjusted and optimised based on simulations (lower field in the gap GFR).

3D: Field Quality First simulations were made with Ansys-Maxwell. Very difficult to achieve numerical accuracy to evaluate the field harmonics, even with dense meshes: good quality field region is very close to curved surface of pole.

3D: Field Quality ROXIE: magnetic field computation software specially developed at CERN to overcome problems of FEM codes to compute accurate field harmonics. Widely used for electromagnets, first time used with permanent magnets! Limitations: First results showed oscillations on the field profile without physical meaning. The pole is too close to the GFR. They were solved decreasing the element size Execution time was decreased using M(B) algorithm Difficult to simulate the crosstalk between magnets Can only make iron extrusions parallel to the beam path (Z) Can’t simulate the trapezium field profile with variable gap!

3D: Field Quality 1T: 1.7 T: Good correlation with analytical models Good field quality 1.7 T: Field achieved higher than required to compensate the flux leakage in 3-D Non-linear behaviour due to iron saturation: no good correlation with analytical models Large b3 to be compensated by iron shaping.

3D: FEM suites Ansys Maxwell: ROXIE: Comsol and Opera: Poor accuracy of field harmonics. ROXIE: Reference for fields and multipoles Impossible to extrude a variable gap (ruled out for step profiles) Comsol and Opera: Models already done and simulated Currently been fully validated: main challenges are the high order field harmonics and the pole surface modelling.

Overview Achieved: 2-D simulations satisfying the desired field quality within the GFR, for both low and high field magnet sections. Tool for automatic calculation of the optimal PM dimensions: The optimal PM working point (BHmax) is obtained and therefore the PM volume needed is at minimum 3D Gradient field profiles: both step and trapezoidal profiles are possible. Beam optics calculation is necessary to choose the final magnet geometry. Field quality calculation is challenging.

Overview Next milestones: Interact with CERN colleagues to select the best field profile Final optimization of pole profile to achieve the required field quality Mechanical calculations: magnetic forces Engineering design: 3D model and fabrication drawings

Thank you for your attention!

Technical specifications 96 dipoles with fixed longitudinal and transverse gradient Possibility to include a small correction of the field amplitude (5%) Good field region radius: 5 mm Field quality  1*10-4 Transverse gradient: 11 T/m, vertical focusing Longitudinal gradient: two possibilities, step and trapezoidal. Firstly, we will concentrate our efforts on the step, because the modelling is easier.

Permanent Magnets Permanent magnets are the best choice to provide a fixed field: no power consumption and very compact. Taking into account: Temperature variation in the tunnel will be as low as ±0,1ºC Sm-Co radiation tolerance is higher than Ne-Fe-B Low radiation expected, but higher in the low field sections (magnet ends) The magnet volume and weight reduction using Ne instead of Sm goes up to 45%. The cost of Neodymium magnets is lower than SmCo. We are pointing towards the use of: Ne-Fe-B magnets in the high field region Sm-Co magnets in the low field region NO specific temperature compensation

2-D Simulations: high field section Different configuration: Three magnets working in parallel to preserve the pole dimensions within reasonable limits Achieved: 1.77T, ΔB/B = 1*10-4, rGFR = 5mm The above conditions were much more difficult to reach as the pole tip iron is saturated. The field quality is more sensitive to any minor change in the dimensions.

First 3-D magnetic simulations Short magnet length (0.58m) makes 2-D simulations diverge from 3-D, specially in the case of the high field section (0.052 m long). First simulations were made with Ansys-Maxwell. Very difficult to achieve numerical accuracy to evaluate the field harmonics, even with dense meshes: good quality field region is very close to curved surface of pole.

3-D magnetic: Roxie (I) Roxie is a magnetic field computation software specially developed at CERN to overcome problems of FEM codes to compute accurate field harmonics. First results showed oscillations on the field profile without physical meaning. It was solved decreasing the element size. Execution time was decreased using M(B) algorithm.

3-D magnetic: Roxie (II) Good correlation with analytical models Good field quality 1.7 T: Field achieved higher than required to compensate the flux leakage in 3-D Non-linear behaviour due to iron saturation: no good correlation with analytical models Large b3 to be compensated by iron shaping.

3-D magnetic simulations In summary: Ansys-Maxwell is not accurate enough to compute the field harmonics. 3-D modelling of magnets iron geometries extruded from several 2-D sections is very time consuming in Roxie. We are following this strategy: First model iterations will be made with Ansys, to achieve the required field profile. The field quality will be evaluated with Roxie. Alternatives to be studied: Opera has not been considered by now, but likely the same problems than Ansys, because it is based on FEM. Radia (ESRF) could be an alternative, it is based on boundary elements as Roxie.

Cross-talk (I) Interaction between 1T and 1.77T regions 1.77T pole longitudinal reduction and 1T pole extrusion to improve the field in the gap between the two magnet parts

Cross-talk (II) Lower d (d=11mm) Intermediate d (d=16mm) Higher d (d=21mm) Smooth transition from high to low field Lowers the field in the central section Base simulation, compromise solution regarding the flux exchange between the 1.77T and 1T regions Higher field in the central section Higher gap between different field regions

Summary 2-D simulations have been done achieving the requirements: longitudinal and transverse field gradient, field quality. Tool for automatic calculation of the optimal magnet dimensions in 2-D based on analytical methods: The optimal magnet working point (BHmax) is obtained and therefore the magnet volume needed is at minimum We are confident now on results of 3-D simulations. It is necessary to agree the longitudinal field profile to finish the calculations and go on with the fabrication design.

Schedule Agreement New schedule (May 2016) WP2 - Technical specifications - Magnetic and mechanical design - Fabrication drawings of parts and tooling - Fabrication of parts and tooling - Assembly - Characterization tests - Final reporting   March 2015 September 2015 March 2016 September 2016 January 2017 May 2017 July 2017 July 2016 October 2016 February 2017 September 2017 A lot of problems to start activity, mainly to hire a new engineer. He started in November 2015.