Simona Bettoni and Remo Maccaferri, CERN Wiggler modeling
Double-helix like option Slide 2 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 Slide 3
Wigglers/undulators model Large gap & long period Small gap
& short period mid-plane Slide 4 2D design (proposed by R.
Maccaferri) BEAM Advantages: Save quantity of conductor Small
forces on the heads (curved part) Slide 5 The 3D model Slide 6 The
3D model (base plane) Slide 7 The 3D model (extrusions) Slide 8 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 Slide 9 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 Slide 10 Prototype analysis
Period (mm)Gap (mm)Number of periodsTotal length (cm)
402029.4+flanges length x z y Slide 11 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) Slide
12 The 2D/3D comparison 1.9448 T -2.1258 T 1.9260 T -2.1080 T 2D
(Poisson) 3D (Tosca) Slide 13 Field uniformity (x range = 2 cm) z
(cm) Slide 14 Multipolar analysis (x range = 2 cm) Slide 15 Slide
16 Slide 17 Tracking studies Trajectory x-shift at the entrance = 3
cm z x y Slide 18 Tracking studies: the exit position Subtracting
the linear part Slide 19 Tracking studies: the exit angle Slide 20
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 Slide 21
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) Slide
22 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. Slide 23 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 Slide 24
Lowering the 2 nd integral: option 1 Slide 25 The multipoles of the
option 1 Starting configuration (CLICWiggler_7) Modified (option 1)
(CLICWiggler_8) Slide 26 Lowering the 2 nd integral: option 2 (2D)
Slide 27 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 Slide 28 Lowering the 2 nd integral: option
2 (3D) If only one IN and one OUT discrete tuning in the prototype
model Slide 29 Tracking studies (optimized configuration) Not
optimizedOptimized Slide 30 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.,
EPAC08 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 Slide 31 Possible configurations Possible to
increase the peak field of 0.5 T using holmium Nb 3 Sn2.1 T40 mm20
mm Slide 32 Working point: comparison Slide 33 Short prototype
status & scheduling Slide 34 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 Slide 35
Extra slides Slide 36 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
Slide 37 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 Slide 38
Controlling the y-shift: cancel the residuals W1W2W3W4 W1W2W3W4 2 m
in 10 cm -> 20*2 = 40 m in 2 m Slide 39 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 Slide 40 The fit accuracy: an
example Slide 41 Field uniformity (x-range = 3 cm) Slide 42
Multipolar analysis (x-range = 3 cm) Slide 43 Tracking at x-range =
3 cm: exit position Subctracting the linear part Slide 44 Tracking
at x-range = 3 cm: exit angle Slide 45 Tracking optimized (x-range
= 3 cm) Slide 46 Holmium option Slide 47 BINP wire Slide 48 2nd
integral optimization (long model) Slide 49 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 Slide 50
Damping ring layout Slide 51
