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Analysis of a proposal for the design of the CLIC damping rings wigglers

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## Analysis of a proposal for the design of the CLIC damping rings wigglers

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**Analysis of a proposal for the design of the CLIC damping**rings wigglers Simona Bettoni, Remo Maccaferri**Outline**• Introduction • The model • 2D (Poisson) • 3D (Opera Vector Fields-Tosca) • The analysis tools • Field uniformity • Multipoles (axis and trajectory) • Tracking studies • The integrals of motion cancellation • Possible options • The final proposal • The prototype analysis • Method to reduce the integrated multipoles • Conclusions**Wigglers/undulators model**Large gap & long period Small gap & short period**2D design (R. Maccaferri)**• Advantages: • Short period • Small forces on the heads (curved) BEAM**The 3D model (conductors)**Conductors generated using a Matlab script. Grouping of the conductors. • Parameters the script: • wire geometry (l_h, l_v, l_trasv) • winding “shape” (n_layers, crossing positions)**The analysis tools**• Tracking analysis: • Single passage: ready/done • Multipassage: to be implemented • Field uniformity: ready/done • Multipolar analysis: • Around the axis: ready /done • Around the reference trajectory: ready x and x’ at the exit of the wiggler**Field distribution on the conductors**BMod (Gauss) • Maximum 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**The 2D/3D comparison**1.9260 T 2D (Poisson) -2.1080 T 1.9448 T 3D (Tosca) -2.1258 T**Tracking studies**Trajectory x-shift at the entrance = ± 3 cm z x y**Tracking studies: the exit position**Subtracting the linear part**Integrals of motion**= 0 for anti-symmetry 1st integral 2nd integral Offset of the oscillation axis CLIC case (even number of poles anti-symmetric) No offset of the oscillation axis**Integrals of motion: the starting point**= 0 for anti-symmetry 1st integral 2nd integral (cm)**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?**→ Highly saturated → → • What we can use: • End of the yoke length/height • Height of the yoke • Terminal pole height (|B| > 5 T) • Effectiveness of the conductors**The multipoles of the option 1**CLICWiggler7.op3 CLICWiggler8.op3**Option 1 vs option 2**• The “advantage” of the option 2: • Perfect cancellation of the 2nd 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: • Easy to be done • The “disadvantage” of the option 1: • No perfect cancellation of the 2nd integral • Field not completely confined in the yoke • Multipoles get worse → start → → → end → 1st layers (~1/3 A*spire equivalent) All the rest**Lowering the 2nd integral: option 2 (3D)**If only one IN and one OUT → discrete tuning in the prototype model Fine regulation would be possible in the long model and in the DR (modular)**Tracking studies (optimized configuration)**Not optimized Optimized**Working point: Nb3Sn & NbTi**Wire diameter (insulated) = 1 mm Wire diameter (bare) = 0.8 mm Non-Cu fraction = 0.53 Cu/SC ratio = 1 * Nb3Sn NbTi Nb3Sn NbTi *MANUFACTURE AND TEST OF A SMALL CERAMIC-INSULATED Nb3Sn SPLIT SOLENOID, B. Bordini et al., EPAC’08 Proceedings.**Possible configurations**Possible to increase the peak field of 0.5 T using holmium (Remo), BUT $**Reduction of the integrated multipoles**S. Bettoni, Reduction of the integrated odd multipoles in periodic magnets, PRST-AB, 10, 042401 (2007), S. Bettoni et al., Reduction of the Non-Linearities in the DAPHNE Main Rings Wigglers, PAC’07 Proceedings.**The integrated multipoles in periodic magnets**In a displaced system of reference: y y’ xT bAk → defined in the reference centered in OA (wiggler axis) bTk → defined in the reference centered inOT (beam trajectory) O T OA x x’ Even multipoles → Left-right symmetry of the magnet Multipoles change sign from a pole to the next one Sum from a pole to the next one Odd multipoles →**The displacement of the magnetic field axis**WITHOUT THE POLE MODIFICATION In each semiperiod the particle trajectory is always on one side with respect the magnetic axis Octupole ↑ WITH THE POLE MODIFICATION Opportunely choosing the B axis is in principle possible to make zero the integrated octupole in each semiperiod In each semiperiod the particle travels on both sides with respect to the magnetic axis**The application to the DAFNE main rings wigglers**Excursion of ±1.3 cm with respect to the axis of the wiggler**Conclusions**• A novel design for the CLIC damping ring has been analyzed (2D & 3D) • Advantages: • Possibility to have a very small period wiggler • Small forces on the heads • Analysis on the prototype: • Maximum force • Multipolar analysis • Tracking studies • Zeroing the integrals of motion • A method to compensate the integrated multipoles has been presented • Even multipoles cancel from a pole to the next one and odd multipoles canceled by the opportune magnetic axis displacement • How to proceed • Optimization of the complete wiggler model (work in progress): • Best working point definition, if not already (margin) • Modeling of the long wiggler • 2nd integral optimization for the long model • Same analysis tools applied to the prototype model (forces, multipoles axis/trajectory, tracking) • Minimization of the integrated multipoles**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 residuals**W1 W2 W3 W4 W1 W2 W3 W4 2 mm in 10 cm -> 20*2 = 40 mm in 2 m**Controlling the x-shift: cancel the residuals (during the**operation) Quadrupoles very close to the beginning of the wiggler or at half distance? W1 W2 … Entering at x = 0 cm Entering at x = -DxMAX/2 • Entering at x = +DxMAX/2 (opposite I wiggler … positron used for trick)**Tracking at x-range = ±3 cm: exit position**Subctracting the linear part