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## PowerPoint Slideshow about 'C anted C osine T heta' - rupali

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MCXB

- 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
- Approx1 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

A bit of Background

- Idea originates from 1969 [1]
- Two nested canted solenoids
- Axial field components cancel
- Dipolar field components add up
- Visit ShlomoCaspi LBNL before Christmas
- Sparked renewed interest in CCT design
- Why now?
- Advancements in Rapid Prototyping
- Advancements in Computing

Cos-Theta

[1]

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.

Terminology

- Repeating pattern (slice)
- Coil consists of three basic parts
- Spar
- Ribs
- Cable

- Definition of parameters

Former

Terminology

- Pitch length
- Packing factor

Pre-Existing Cable

For the designs a pre-existing (MCXB) NbTi cable is available

Used Bottura scaling relation for LHC grade conductor

Comparing fits:

100%

90%

80%

70%

60%

50%

*taken from presentation Mikko 2010

What 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

…

H-A

Former

V-B

In reality cables under angle

H-B

Former

V-A

…

MCXB - 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

MCXB - 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°)

Field 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

V4

V2

All Without Iron

Field Integral Optimization

Optimized skew angle depends on coil length

V4

V2

0.9 m

1.9 m

V4

V2

1.9 m

0.9 m

Without Iron

Loadlines

Loadlines depend on the angle of the field in the aperture

V2H2

100%

90%

80%

70%

60%

50%

Without Iron

Directionality – 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

Directionality – 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

Directionality - 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

Torsion

,

- 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 centerwould be ~0.25 deg
- Unacceptably high
- Conclusion: V-H must be mechanically connected using same or somehow interconnected former(s)

Iron 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

Comparison

Compare specifications per layer with original cos-theta design (note original design has only vertical component)

!

Integrated Harmonics

ROXIE (high b3?):

Without Iron

at 2/3r = 50mm

?

- Field Code (only noise):

at 2/3r = 50mm

- Need measurement and perhaps review of codes …

Quench – No Heaters

Quench estimation usingcode Glyn

Voltage limited to 1 kV

Conclusion: need heaters

Peak Temperature [K]

Too High!

Bulk Temperature [K]

Current [A]

Voltage [V]

Quench – 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 msafter firing the heaters

Tube for heater can be ‘printed’ under ribs inside former

Proposed 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

Conclusion

- 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

Mathematical 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.

Field Calculation

- Multi Level Fast MultipoleMethod (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.

BlueWhale demonstrator Coil

First study object

Testwinding on inside

Measure field quality

MCBX Cable, 150 mm Bore

45 degree skew angle

Low packing factor (0.22)

What is the MLFMM?

Grouping the field of many elements in Multipolesand 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

BlueWhaleIts in the name

BlueWhaleFormer

Print in clear plastic to see the winding process

BlueWhale Former

Already 3D printed some test slices for cable fit testing

Field Integral Optimization

and a little on radius (plotted V2 only for 0.9 m)

Without Iron

x10-2

x10-2

Directionality - Current

The current at 50% Ic as function of angle.

During testing / training the magnet needs to see all directions

Without Iron

2D Pseudo Harmonics

Coil harmonics as function of axial coordinate

Higher harmonics should integrate to zero

V2

Dipole

Quadrupole

Hexapole

...

Quench – With Heaters

With quench heaters hitting 70% of coil in 16 ms

Peak Temperature [K]

Acceptable

Bulk Temperature [K]

Current [A]

Voltage [V]

Quench – 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

…

V-B

Former

V-A

H-B

Former

H-A

…

Quench - Inductances

- 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)

Layer 1,3 - 8.65 mH

Layer 2,4 - 9.95 mH

All layers – 17.6 mH

Layer 2,4,6,8 – 44.4 mH

All layers – 79.8 mH

Layer 1,3,5,7 – 39.1 mH

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