c anted c osine t heta

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)