Post on 16-Jan-2016
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Canted Cosine ThetaMCXB – Design Option
J. Van Nugteren, G. de Rijk and G. Kirby28-01-2013
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
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]
4Terminology• Repeating pattern (slice)• Coil consists of three basic
parts– Spar– Ribs– Cable
• Definition of parameters
Former
5Terminology• Pitch length
• Packing factor
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%
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
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
9MCXB - V2H2 – 0.9 m• 4 layer design Horizontal and Vertical on same
formerTop
Front
Side
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°)
11MCXB - V4H4 – 0.9 mTop
Front
Side
12Skew Angle Influence• Ratio Bpeak/Bcen depends on skew angle and # of
layers
V2
V4
α
Without Iron
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
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
15Loadlines• Loadlines depend on the angle of the field in the
aperture
V2H2
100%90%
80%
70%60%
50%Without Iron
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
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
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
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)
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
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
!
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
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!
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
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
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
Thank You for Your Kind Attention
29MCXB – V2H2 – 4.0 Tm
30MCXB – V2H2 – 4.0 Tm
Front
Top
Side
31MCXB – V4H4 – 4.0 Tm
Front
Top
Side
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.
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.
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)
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
36BlueWhale Its in the name
37BlueWhale Former• Print in clear plastic to see the winding process
38BlueWhale Former• Already 3D printed some test slices for cable fit
testing
39Field Integral Optimization• and a little on radius (plotted V2 only for 0.9 m)
Without Iron
x10-2
x10-2
40Directionality - Current• The current at 50% Ic as function of angle.• During testing / training the magnet needs to see all directions
Without Iron
412D Pseudo Harmonics• Coil harmonics as function of axial coordinate• Higher harmonics should integrate to zero
V2Dipole
Quadrupole
Hexapole
...
42Quench – With Heaters• With quench heaters hitting 70% of coil in 16 ms
Peak Temperature [K]
Bulk Temperature [K]
Current [A]
Voltage [V]
Acceptable
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
……
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)