Download - C anted C osine T heta
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Canted Cosine ThetaMCXB – Design Option
J. Van Nugteren, G. de Rijk and G. Kirby28-01-2013
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2MCXB• Corrector dipole with steerable field direction
– 2 nested dipoles generate enormous Torque– CCT should take forces from windings effectively
• Requirements– 150 mm bore, pre-existing cable– Operating at 50% Ic– Need designs for 1.5 Tm and 4 Tm– Approx 1 and 2 m long respectively
• Look at Vertical and Horizontal field– V2H2 1.5 Tm / 4.0 Tm– V4H4 1.5 Tm / 4.0 Tm– Decided to focus mainly on 1.5 Tm
V2H2
V4H4
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3A bit of Background• Idea originates from 1969 [1]• Two nested canted solenoids
• Axial field components cancel• Dipolar field components add up
• Visit Shlomo Caspi LBNL before Christmas
• Sparked renewed interest in CCT design
• Why now?– Advancements in Rapid
Prototyping– Advancements in Computing
Cos-Theta
Block
CCT
[1] D. Meyer and R. Flasck, A new configuration for a dipole magnet for use in high energy physics applications,Nuclear Instruments and Methods, no. 80, pp. 339-341, 1970.
[1]
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4Terminology• Repeating pattern (slice)• Coil consists of three basic
parts– Spar– Ribs– Cable
• Definition of parameters
Former
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5Terminology• Pitch length
• Packing factor
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6Pre-Existing Cable• For the designs a pre-existing
(MCXB) NbTi cable is available• Used Bottura scaling relation for
LHC grade conductor• Comparing fits:
Strand parameters value unit
fcu2sc 1.75
Strand diameter 0.48 mm
Metal section 0.181 mm2
No of filaments 2300
Filament diam. 6.0 µm
I(5T,4.2K) 203* A
jc 3085* A/mm2
Cable Parameters value unit
No of strands 18
Metal area 3.257 mm2
Cable thickness 0.845 mm
Cable width 4.370 mm
Cable area 3.692 mm2
Metal fraction 0.882
Key-stone angle 0.67 degrees
Inner Thickness 0.819 mm
Outer Thickness 0.870 mm
*taken from presentation Mikko 2010
100%90%
80%70%
60%50%
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7What layer on Which Former?
• To optimally transfer Torque one Vertical and one Horizontal layer on each former
• A and B represents the direction of the spiral
• For insulation between the layers this is not ideal
• Right now assumed VA-HB-VB-HA layout
• Pattern can be repeated from here
V-A
V-B
H-B
H-A
Former
Former
……
In reality cables under angle
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8MCXB - V2H2 – 0.9 m• 4 layer design• Field integral 1.3 Tm without Iron• Packing factor = 0.55• 2530 A (45°) - 3072 A (0°) at 50% Ic
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9MCXB - V2H2 – 0.9 m• 4 layer design Horizontal and Vertical on same
formerTop
Front
Side
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10MCXB - V4H4 – 0.9 m• 8 layer design• Field integral 1.9 Tm without Iron• Packing factor = 0.55• 2530 A (45°) - 3072 A (0°) at 50% Ic• 2002 A (45°) – 2438 A (0°)
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11MCXB - V4H4 – 0.9 mTop
Front
Side
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12Skew Angle Influence• Ratio Bpeak/Bcen depends on skew angle and # of
layers
V2
V4
α
Without Iron
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13Field Integral Optimization• Two counteracting processes
– Higher skew angle increases Bpeak/Bcen– Lower skew angle increases length of coil ends
• Leads to a field integral optimized value for the skew angle
All Without Iron
V2
V4
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14Field Integral Optimization• Optimized skew angle depends on coil length
V4
V2
Without Iron
V4
V2
0.9 m 1.9 m
0.9 m 1.9 m
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15Loadlines• Loadlines depend on the angle of the field in the
aperture
V2H2
100%90%
80%
70%60%
50%Without Iron
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16Directionality – Field Integral• System is
coupled• Angular Plot– Angle gives
field direction– Amplitude
gives field integral
– X-coordinate gives horizontal field integral
– Y-coordinate gives vertical field integral
Without Iron
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17Directionality – Normal Forces
• Normal Forces are also angle dependent
• Maximum force is 7800 N/m
• For titanium former 3% only of the shear stress
V2H2
Without Iron
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18Directionality - Torque• Torque is angle
dependent• Peak value is 25000
Nm Torque• To compare: Glyn’s
Mercedes ML has only 616.9 Nm Torque
• 40.5 X Mercedes ML
Without Iron
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19Torsion
• , • If the horizontal and vertical layers are not on the same former
• Assuming a 10 mm thick solid titanium tube
• With only the ends fixed• The stress is then 32.9
MPa• The torsion in the center
would be ~0.25 deg• Unacceptably high• Conclusion: V-H must be
mechanically connected using same or somehow interconnected former(s)
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20Iron Yoke Field Enhancement• Calculated Iron yoke influence using ROXIE– Long computation times– Non-standard coil for ROXIE
• With iron can gain approximately 0.3-0.5 Tm
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21Comparison• Compare specifications per layer with original cos-
theta design (note original design has only vertical component)Unit Cos - theta*
V onlyMikko
CCT-V2H20 deg – no
iron
CCT-V2H245 deg – no
iron
CCT-V4H40 deg – no
iron
CCT-V4H445 deg – no
iron
Integrated field Tm 1.5 1.3 1.8 1.8 2.6
Nominal field T 2.3 2.0 2.4 2.9 3.4
Mag. length m 0.65 0.9 0.9 0.9 0.9
Nominal current A 2400 3083 2530 2452 2002
Stored energy kJ 28 41 56.4 131 159
Self inductance mH 10 8.6 17.6 39.1 79.8
Working point 50% 50% 50% 50% 50%
Cable width/mid-height
mm 4.37 / 0.845 4.37 / 0.845 4.37 / 0.845 4.37 / 0.845 4.37 / 0.845
Total length m ~1 ~1 ~1 ~1 ~1
Aperture mm Ø140 Ø150 Ø150 Ø150 Ø150
Total mass kg ~2000
Cable Length m ~270 V2 - 341 V2H2 – 709.1 V4 - 940 V4H4 - 1940
Nturns per layer 240 240
!
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22Integrated Harmonics• ROXIE (high b3?):
• Field Code (only noise):
• Need measurement and perhaps review of codes …
Without Iron
?at 2/3r = 50mm
at 2/3r = 50mm
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23Quench – No Heaters• Quench estimation using code Glyn• Voltage limited to 1 kV• Conclusion: need heaters
Peak Temperature [K]
Bulk Temperature [K]
Current [A]
Voltage [V]
Too High!
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24Quench – With Heaters• Placement for the quench heaters to hit all turns at once in high field
area (idea G. de Rijk)• Would be able to get entire coil normal in ~8 ms after firing the heaters• Tube for heater can be ‘printed’ under ribs inside former
𝑡=2𝜋 𝑅
4 sin (𝛼 )𝑉=
2𝜋 0.0754sin (45 ° )20
≈ 8 ms
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25Proposed Steps• First – 0.5 m long 2 layer version (BlueWhale)– Winding test– Field quality measurement
• Second – 0.9 meter titanium former, insulated cable, V2 coil which comprises 5/6 components– 1/2 x Former– 2 x Cable– 2 x Outer compression ring
• Afterwards – re-optimize the design
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26Conclusion• Numerical tooling for the design of CCT coils has been
developed• Optimized field integrals as function of length for 150
mm free bore coil• Proposed a design for MCXB corrector coils
– Can be applied to horizontal and vertical
• Needs work– Improved (ROXIE) model with Iron– Assembly technique and Pre-stress on cable– Better stress analysis in tube for the 25000 Nm Torque– Protection– Redesign ground insulation (H-V separation?)– Improve CAD interface for former
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Thank You for Your Kind Attention
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29MCXB – V2H2 – 4.0 Tm
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30MCXB – V2H2 – 4.0 Tm
Front
Top
Side
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31MCXB – V4H4 – 4.0 Tm
Front
Top
Side
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32Mathematical Model• Central Spiral [2]
• Cable Orientation (at each coordinate)– Direction Vector– Radial vector– Normal vector
• Use to create– Strand coordinates– Cable Surface– Cutout Surface
[2] S. Russenschuck, Field Computation for Accelerator Magnets. Wiley, 2010.
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33Field Calculation
• Multi Level Fast Multipole Method (MLFMM) – Based on algorithm by
Greengard and Leslie [3]– Code developed at the
University of Twente by E.P.A. van Lanen and J. van Nugteren
– Used for the full scale modeling of CICC cables for ITER
– Uses GPU using NVIDIA CUDA (or CPU if preferred)
– Later adapted for magnetic field calculations (Field)
– No Iron :(
[3] L. Greengard, The rapid evaluation of potential fields in particle systems, tech. rep., Cambridge, 1988.
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34BlueWhale demonstrator Coil• First study object• Test winding on inside • Measure field quality
• MCBX Cable, 150 mm Bore• 45 degree skew angle• Low packing factor (0.22)
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35What is the MLFMM?
• Grouping the field of many elements in Multipoles and Localpoles
• Magnetic field of distant elements is approximated using their Multipole
• Computation times reduced to O(N) instead of O(N2)
Note: This is a highly simplified schematic
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36BlueWhale Its in the name
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37BlueWhale Former• Print in clear plastic to see the winding process
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38BlueWhale Former• Already 3D printed some test slices for cable fit
testing
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39Field Integral Optimization• and a little on radius (plotted V2 only for 0.9 m)
Without Iron
x10-2
x10-2
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40Directionality - Current• The current at 50% Ic as function of angle.• During testing / training the magnet needs to see all directions
Without Iron
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412D Pseudo Harmonics• Coil harmonics as function of axial coordinate• Higher harmonics should integrate to zero
V2Dipole
Quadrupole
Hexapole
...
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42Quench – With Heaters• With quench heaters hitting 70% of coil in 16 ms
Peak Temperature [K]
Bulk Temperature [K]
Current [A]
Voltage [V]
Acceptable
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43Quench – No Heaters
• 1 kV cable insulation is limiting dump voltage increasing peak temperature
• Can improve with:– Cable-ground insulation
for ~5 kV– Horizontal Vertical
Separation (problem with Torque)
– Quench Heater
H-A
V-A
H-B
V-B
Former
Former
……
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44Quench - Inductances
Layer 1,3 - 8.65 mH Layer 2,4 - 9.95 mH All layers – 17.6 mH
Layer 1,3,5,7 – 39.1 mHLayer 2,4,6,8 – 44.4 mH All layers – 79.8 mH
• Need to consider several scenarios– 0, 45 and 90 degrees field angle using inductances and dump resistances for
relevant layers only • Inductance matrices (Field Code)