Simona Bettoni and Remo Maccaferri, CERNWiggler modelingDouble-helix like option

OutlineIntroductionThe model2D (Poisson)3D (Opera Vector Fields-Tosca)The analysis toolsField uniformityMultipoles (on axis and trajectory)Tracking studiesThe integrals of motion cancellationPossible optionsThe final proposalThe prototype analysis Conclusions

Wigglers/undulators modelLarge gap & long periodSmall gap & short periodmid-plane

2D design (proposed by R. Maccaferri)BEAMAdvantages:Save quantity of conductorSmall forces on the heads (curved part)

The 3D model

The 3D model (base plane)

The 3D model (extrusions)

The 3D model (conductors)Conductors grouped to minimize the running timeParameters the script: Wire geometry (l_h, l_v, l_trasv) Winding shape (n_layers, crossing positions)Conductors generated using a Matlab script

The analysis tools Tracking analysis: Single passage: ready/done Multipassage: to be implemented Field uniformity: ready/done Multipolar analysis: Around the axis: ready /doneAround the reference trajectory: readyx and x at the exit of the wiggler

Prototype analysisxzy

Period (mm)Gap (mm)Number of periodsTotal length (cm)402029.4+flanges length

Field distribution on the conductorsMaximum field and forces (PMAX ~32 MPa) on the straight part

Manufacture: well below the limit of the maximum P for Nb3Sn Simulation: quick to optimize the margin (2D)BMod (Gauss)

The 2D/3D comparison1.9448 T-2.1258 T1.9260 T-2.1080 T2D (Poisson)3D (Tosca)

Field uniformity (x range = 2 cm)z (cm)

Multipolar analysis (x range = 2 cm)

Multipolar analysis (x range = 2 cm)

Multipolar analysis (x range = 2 cm)

Tracking studiesTrajectory x-shift at the entrance = 3 cmzxy

Tracking studies: the exit positionSubtracting the linear part

Tracking studies: the exit angle

Integrals of motion1st integral2nd integralCLIC case: even number of poles (anti-symmetric)No offset of the oscillation axisOffset of the oscillation axis= 0 for anti-symmetry

Integrals of motion: the starting point1st integral2nd integral= 0 for anti-symmetry(cm)

First integral Bz * dySecond integral Bz * dy5e-5 Gauss*cm-1.94e5 Gauss*cm25e-11 T*m-1.94e-3 T*m2

Lowering the 2nd integral: what do we have to do?To save time we can do tracking studies in 2D up to a precision of the order of the difference in the trajectory corresponding to the 2D/3D one (~25 mm) and only after refine in 3D.

Lowering the 2nd integral: how can we do?What we can use:End of the yoke length/heightHeight of the yokeTerminal pole height (|B| > 5 T)Effectiveness of the conductorsHighly saturated

Lowering the 2nd integral: option 1

The multipoles of the option 1Starting configuration(CLICWiggler_7)Modified (option 1)(CLICWiggler_8)

Lowering the 2nd integral: option 2 (2D)

Option 1 vs option 2The advantage of the option 2:Perfect cancellation of the 2nd integralField well confined in the yokePossibility to use only one IN and one OUT (prototype)The disadvantage of the option 2:Comments?The advantage of the option 1:Quick to be doneThe disadvantage of the option 1:Not perfect cancellation of the 2nd integralField not completely confined in the yokeMultipoles get worse1st layers (~1/3 A*spire equivalent)All the reststartend

Lowering the 2nd integral: option 2 (3D)If only one IN and one OUT discrete tuning in the prototype model

Tracking studies (optimized configuration)Not optimizedOptimized

Working point: Nb3Sn & NbTi*MANUFACTURE AND TEST OF A SMALL CERAMIC-INSULATED Nb3Sn SPLIT SOLENOID, B. Bordini et al., EPAC08 Proceedings.*Wire diameter (insulated) = 1 mmWire diameter (bare) = 0.8 mmNb3SnNbTiNb3SnNbTiCu/SC ratio = 1Non-Cu fraction = 0.53

I (A)Max|B| (T)By peak (T)12006.02.1

I (A)Max|B| (T)By peak (T)12006.02.111005.51.99204.61.6

Possible configurationsPossible to increase the peak field of 0.5 T using holmium

Nb3Sn2.1 T40 mm20 mm

Working point: comparison

Short prototype status & scheduling

ConclusionsA novel design for the CLIC damping ring has been analyzed (2D & 3D)Advantages:Less quantity of conductor needed Small forces on the heads

Analysis on the prototype:Maximum forceMultipolar analysisTracking studiesZeroing the integrals of motionFuture plansOptimization of the complete wiggler model (work in progress):Best working point definitionModeling of the long wiggler2nd integral optimization for the long modelSame analysis tools applied to the prototype model (forces, multipoles axis/trajectory, tracking)Minimization of the integrated multipoles

Extra slides

Longitudinal field (By = f(y), several x)Scan varying the entering position in horizontal, variation in vertical: Dz = 0.1 mm for x-range = 1 cm Dz = 2 mm for x-range = 2 cm

Horizontal transverse field (Bx = f(y), several x)Scan varying the entering position in horizontal, variation in vertical: Dz = 0.1 mm for x-range = 1 cm Dz = 2 mm for x-range = 2 cm

Controlling the y-shift: cancel the residualsW1W2W3W4W1W2W3W42 mm in 10 cm -> 20*2 = 40 mm in 2 m

Controlling the x-shift: cancel the residuals (during the operation)Entering at x = 0 cmEntering at x = -DxMAX/2Entering at x = +DxMAX/2 (opposite I wiggler positron used for trick)

W1W2To be evaluated the effect of the kicks given by the quadrupoles

The fit accuracy: an example

Field uniformity (x-range = 3 cm)

Multipolar analysis (x-range = 3 cm)

Tracking at x-range = 3 cm: exit positionSubctracting the linear part

Tracking at x-range = 3 cm: exit angle

Tracking optimized (x-range = 3 cm)

Holmium option

BINP wire

2nd integral optimization (long model)

Long wiggler modelingProblem: very long running time (3D) because of the large number of conductors in the model

Solution:Build 2D models increasing number of periods until the field distribution of the first two poles from the center give the same field distribution (Np)Build 3D model with a number of poles NpBuild the magnetic map from this

Damping ring layout