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Simona Bettoni and Remo Maccaferri, CERN Wiggler modeling Double-helix like option

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Outline Introduction The model 2D (Poisson) 3D (Opera Vector Fields-Tosca) The analysis tools Field uniformity Multipoles (on axis and trajectory) Tracking studies The integrals of motion cancellation Possible options The final proposal The prototype analysis Conclusions

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Wigglers/undulators model Large gap & long period Small gap & short period mid-plane

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2D design (proposed by R. Maccaferri) BEAM Advantages: Save quantity of conductor Small forces on the heads (curved part)

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The 3D model

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The 3D model (base plane)

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The 3D model (extrusions)

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

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

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Prototype analysis Period (mm)Gap (mm)Number of periodsTotal length (cm) 402029.4+flanges length x z y

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Field distribution on the conductors Maximum field and forces (P MAX ~32 MPa) on the straight part Manufacture: well below the limit of the maximum P for Nb 3 Sn Simulation: quick to optimize the margin (2D) B Mod (Gauss)

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The 2D/3D comparison 1.9448 T -2.1258 T 1.9260 T -2.1080 T 2D (Poisson) 3D (Tosca)

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

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Multipolar analysis (x range = ±2 cm)

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Tracking studies Trajectory x-shift at the entrance = ± 3 cm z x y

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Tracking studies: the exit position Subtracting the linear part

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Tracking studies: the exit angle

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Integrals of motion 1 st integral 2 nd integral CLIC case: even number of poles (anti-symmetric) No offset of the oscillation axis Offset of the oscillation axis = 0 for anti-symmetry

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Integrals of motion: the starting point 1 st integral 2 nd integral First integral Bz * dySecond integral Bz * dy 5e-5 Gauss*cm-1.94e5 Gauss*cm 2 5e-11 T*m-1.94e-3 T*m 2 = 0 for anti-symmetry (cm)

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Lowering the 2 nd 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 m) and only after refine in 3D.

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Lowering the 2 nd integral: how can we do? What we can use: End of the yoke length/height Height of the yoke Terminal pole height (|B| > 5 T) Effectiveness of the conductors → → → Highly saturated

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Lowering the 2 nd integral: option 1

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

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

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Option 1 vs option 2 The “advantage” of the option 2: Perfect cancellation of the 2 nd integral Field well confined in the yoke Possibility 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 done The “disadvantage” of the option 1: Not perfect cancellation of the 2 nd integral Field not completely confined in the yoke Multipoles get worse 1 st layers (~1/3 A*spire equivalent) All the rest → → → → → start end

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

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Tracking studies (optimized configuration) Not optimizedOptimized

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Working point: Nb 3 Sn & NbTi I (A)Max|B| (T)By peak (T) 12006.02.1 *MANUFACTURE AND TEST OF A SMALL CERAMIC-INSULATED Nb3Sn SPLIT SOLENOID, B. Bordini et al., EPAC’08 Proceedings. * Wire diameter (insulated) = 1 mm Wire diameter (bare) = 0.8 mm I (A)Max|B| (T)By peak (T) 12006.02.1 11005.51.9 9204.61.6 Nb 3 Sn NbTi Nb 3 Sn NbTi Cu/SC ratio = 1 Non-Cu fraction = 0.53

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Possible configurations Possible to increase the peak field of 0.5 T using holmium Nb 3 Sn2.1 T40 mm20 mm

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Working point: comparison

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Short prototype status & scheduling

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Conclusions A novel design for the CLIC damping ring has been analyzed (2D & 3D) Advantages: o Less quantity of conductor needed o Small forces on the heads Analysis on the prototype: o Maximum force o Multipolar analysis o Tracking studies o Zeroing the integrals of motion Future plans Optimization of the complete wiggler model (work in progress): o Best working point definition o Modeling of the long wiggler o 2 nd integral optimization for the long model o Same analysis tools applied to the prototype model (forces, multipoles axis/trajectory, tracking) o Minimization of the integrated multipoles

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Extra slides

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

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

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Controlling the y-shift: cancel the residuals W1W2W3W4 W1W2W3W4 2 m in 10 cm -> 20*2 = 40 m in 2 m

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Controlling the x-shift: cancel the residuals (during the operation) Entering at x = 0 cm Entering at x = - x MAX /2 Entering at x = + x MAX /2 (opposite I wiggler … positron used for trick) W1W2 … To be evaluated the effect of the kicks given by the quadrupoles

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The fit accuracy: an example

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Field uniformity (x-range = ±3 cm)

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Multipolar analysis (x-range = ±3 cm)

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Tracking at x-range = ±3 cm: exit position Subctracting the linear part

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Tracking at x-range = ±3 cm: exit angle

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Tracking optimized (x-range = ±3 cm)

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Holmium option

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BINP wire

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2nd integral optimization (long model)

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Long wiggler modeling Problem: 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 Np “Build” the magnetic map from this

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Damping ring layout

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