CLIC damping rings wiggler

Simona Bettoni, Remo MaccaferriAnalysis of a proposal for the design of the CLIC damping rings wigglers

Tracking at x-range = 3 cm: exit position

Subctracting the linear part

Damping ring layout

Wigglers/undulators model

Large gap & long period

Small gap & short period2D design (R. Maccaferri)

BEAMAdvantages:Short periodSmall forces on the heads (curved)The 3D model

The 3D model (base plane)

The 3D model (extrusions)

The 3D model (conductors)

Parameters the script: wire geometry (l_h, l_v, l_trasv) winding shape (n_layers, crossing positions)Conductors generated using a Matlab script.

Grouping of the conductors.

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: ready

x and x at the exit of the wiggler

Prototype analysis (CLIC_Wiggler_7.op3)

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

xzy

Field distribution on the conductors

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

BMod (Gauss)The 2D/3D comparison

1.9448 T-2.1258 T

1.9260 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 cm

zxyTracking studies: the exit position

Subtracting the linear part

Tracking studies: the exit angle

Integrals of motion

1st integral2nd integral

CLIC case (even number of poles anti-symmetric)No offset of the oscillation axisOffset of the oscillation axis= 0 for anti-symmetryIntegrals of motion: the starting point

1st integral2nd integral

First integral Bz * dySecond integral Bz * dy5e-5 Gauss*cm-1.94e5 Gauss*cm25e-11 T*m-1.94e-3 T*m2= 0 for anti-symmetry(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?

What we can use:End of the yoke length/heightHeight of the yokeTerminal pole height (|B| > 5 T)Effectiveness of the conductorsHighly saturatedLowering the 2nd integral: option 1

The multipoles of the option 1

CLICWiggler7.op3CLICWiggler8.op3Lowering 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:Easy to be doneThe disadvantage of the option 1:No perfect cancellation of the 2nd integralField not completely confined in the yokeMultipoles get worse1st layers (~1/3 A*spire equivalent)All the rest

startendLowering the 2nd integral: option 2 (3D)

If only one IN and one OUT discrete tuning in the prototype modelFine regulation would be possible in the long model and in the DR (modular)

Tracking studies (optimized configuration)

Not optimizedOptimizedWorking point: Nb3Sn & NbTiI (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., EPAC08 Proceedings.

*Wire diameter (insulated) = 1 mmWire diameter (bare) = 0.8 mm

I (A)Max|B| (T)By peak (T)12006.02.111005.51.99204.61.6Nb3SnNbTiNb3SnNbTiCu/SC ratio = 1Non-Cu fraction = 0.53

Possible configurationsPossible to increase the peak field of 0.5 T using holmium (Remo), BUT $Nb3Sn2.1 T40 mm20 mmWorking point: comparison

Short prototype status & scheduling

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, PAC07 Proceedings.

Even multipoles Odd multipoles

In a displaced system of reference: bAk defined in the reference centered in OA (wiggler axis)bTk defined in the reference centered in OT (beam trajectory)xyxyOAO TxTLeft-right symmetry of the magnet Multipoles change sign from a pole to the next one Sum from a pole to the next one

The integrated multipoles in periodic magnets36The displacement of the magnetic field axisWITHOUT THE POLE MODIFICATIONIn each semiperiod the particle trajectory is always on one side with respect the magnetic axisIn each semiperiod the particle travels on both sides with respect to the magnetic axisOpportunely choosing the B axis is in principle possible to make zero the integrated octupole in each semiperiodWITH THE POLE MODIFICATION

Octupole37

Number of poles5 fulls+2 halvesPeriod (cm)64Magnetic field in the gap (T)~2Gap (cm)3.7Particles beamse+ e-Beam energy (MeV)511Excursion of 1.3 cm with respect to the axis of the wigglerThe application to the DAFNE main rings wigglers

38Integrated b3T (T/m2)Aligned poles279.61Shifted poles0.07The results

39ConclusionsA 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 forceMultipolar analysisTracking studiesZeroing the integrals of motionA method to compensate the integrated multipoles has been presentedEven multipoles cancel from a pole to the next one and odd multipoles canceled by the opportune magnetic axis displacementHow to proceedOptimization of the complete wiggler model (work in progress):Best working point definition, if not already (margin)Modeling 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 multipolesExtra slidesLongitudinal 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 cmControlling the y-shift: cancel the residualsW1W2W3W4W1W2W3W42 mm in 10 cm -> 20*2 = 40 mm in 2 mControlling 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)

W1W2Quadrupoles very close to the beginning of the wiggler or at half distance?

The fit accuracy: an exampleMultipolar analysis (x-range = 3 cm)

Tracking at x-range = 3 cm: exit angle

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