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Canted Cosine Theta MCXB – Design Option J. Van Nugteren, G. de Rijk and G. Kirb 28-01-2013

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C anted C osine T heta. MCXB – Design Option. 28-01-2013. J. Van Nugteren, G. d e Rijk and G. Kirby. MCXB. Corrector dipole with steerable field direction 2 nested dipoles generate enormous Torque CCT should take forces from windings effectively Requirements - PowerPoint PPT Presentation

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Page 1: C anted  C osine  T heta

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)