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Magnetic Design
S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL)
Superconducting Undulator Integrated Design Review
Jun. 6, 2014
Integrated Design Review, Jun. 6, 2014
Undulator Layout
2
Undulator period = 19.0 mm, gap = 8.0 mmPeak field requirement Beff = 1.86 T
Single wire winding– 0.6 mm diameter wire– 60 μm thick s-glass braid insulation
Wire turns around at the end of the poleNb3Sn to NbTi joints at the end of the undulator
Single Wire WindingElectron Beam
Joint Section
3Integrated Design Review, Jun. 6, 2014
Simulation ToolsOpera 2D– Coil pack optimization of periodic design– Initial end design calculations
Opera 3D– 3D verification for periodic design (load line calculation)– End design– Calculation of force and stored energy (inductance)
¼ Period Model End Design Model
4Integrated Design Review, Jun. 6, 2014
Coil OptimizationFind optimal number of turns per layer and total layers necessary to meet peak field requirement (1.86 T @ λ = 19.0 mm, g = 8.0 mm)Wire diameter = 0.6 mm, insulation thickness = 60 μmScaling relation used with Jc = 2000 A/mm2 @ 12 T5 layers is sufficient to operate below 80 %Modest gains margin can be obtained by adding more layers
Number of layers
Num
ber o
f tur
ns p
er la
yer Load Line Margin Load Line Margin
8 turns per layer
5Integrated Design Review, Jun. 6, 2014
Operating CurrentOperating current is reduced as the number of layers is increased (operate at higher conductor peak field)Need to perform short-sample tests on the candidate conductors in order to understand the stability marginCan increase length of conductor to reduce the risk of stability problemsOperating current for B0 = 1.86 T Load Lines
8 by 5
8 by 7
8 by 9
On-Axis Field
Peak Conductor Field
Design Point
Integrated Design Review, Jun. 6, 2014
End Design
6
Want zero net displacement and steering due to the endsEven or Odd number of poles– Even – zero net steering, non-zero net displacement– Odd – zero net displacement, non-zero net steering
2δ
Even number of poles
δ+K
-K
Odd number of poles
+K +K
+δ -δ
Steering + Displacement
Displacement Only
Ideal
7Integrated Design Review, Jun. 6, 2014
End pattern
Odd poles/even coilsBinomial expansion pattern– Poles: 0, +1/4, -3/4, +1, -1,…– Coils: +1/8, -4/8, +7/8, -1, +1,…
7 x 8 turns/pocket:– Turns/coil: 7, 28, 49, 56, 56,…
Requirements:I1 (end) < 40 μTm, I2 (end) < 50 μTm2
0 +1/4 -3/4 +1 -1
+1/8 -1/2 +7/8 -1
Yoke
Poles Coils
Y
Z# turns:
potential:
8Integrated Design Review, Jun. 6, 2014
Non-Ideal End Effects
Non-ideal effects due to finite permeability and differential saturation of end poles– End kick is dependent on the undulator field– Dipole field is generated by unbalanced yoke
fieldx x x
xx x
x x x
xx x
1 2
Magnetic Field (one period filter)
As field is ramped:Pole 2 saturates before 1
Second Field Integral
End Kick
Curvature due to dipole field
End Kick
Non-zero offset
9Integrated Design Review, Jun. 6, 2014
Dipole Corrector
End corrector #1 (dipole)
Wound on top of the main coil in the remaining pocket on each endAdds both a dipole and end kicks Used to correct the dipole first
Second Field Integral
10Integrated Design Review, Jun. 6, 2014
End corrector #2 (kick)
Wound in a separate yoke on each endDecoupled from the main yoke Add only end kicks
Used to cancel the exit kick once the 1st coil is tuned
Kick Corrector
Second Field Integral
11Integrated Design Review, Jun. 6, 2014
Correction Current as a Function of Undulator Current
0 200 400 600 800 1000 1200 1400 1600 18000
5
10
15
20
25
30
35
Undulator Current Density [A/mm2]
Corr
ecto
r Cur
rent
Den
sity
[A/m
m2]
0 200 400 600 800 1000 1200 1400 1600 18001.0
1.5
2.0
2.5
3.0
Undulator Current Density [A/mm2]
Corr
ecto
r Cur
rent
Den
sity
[A/m
m2]
0.56 T
0.83 T1.12 T
1.48 T1.86 T
Corrector #1 Corrector #2
Required
Max current [A] Sensitivity [A]
1st corrector 2.2 0.004
2nd corrector 13.1 0.01* Sensitivity based on dipole field < 10 μT* Sensitivity based on end kick < 1 μTm
12Integrated Design Review, Jun. 6, 2014
Conclusions
Magnetic design for the periodic and end sections is completeEnd corrector summary– Correctors of type # 1 (dipole correctors) at each end are wired
in series (1 power supply) – Correctors of type # 2 (end kick correctors) at each end are
independent to allow entrance and exit kick adjustment (2 power supplies)
One master power supply controls the undulator field and three slave power supplies provide end corrections