1. SNS Injection Fields and Coils
Christopher Crawford
University of Kentucky
The theme is magnets, how important they are for studying nuclear physics,
and how interesting they are in their own right.
And the other unifying element is symmetries,
both used as a tool for the discovery of new particles and interactions
but also just to organize the natural world around us – that’s what I see as the main role of a physicist.
nEDM2014, Ascona, CH

2. Problem to solve:
Spin transport of CN & 3He more delicate than for UCN
In the doldrums between “adiabatic” and “sudden” regime
Ballistic transport: controlled velocity of CN and 3He Strategy: ROTATE first and then TAPER down
Diffusive transport: 3He atoms K Strategy: ROTATE/TAPER during ballistic injection (before diffusion)
Additional requirements
Must NOT distort field in measurement region
Avoid use of magnetic materials
Tight geometric constraints in many cases
Design sequence
Transport
Requirements
Calculation of Ideal Field
Calculation of
Coil Windings/ Optimizations
Validation
Surface Current Coil Construction
Geometric constraints
nEDM2014 Workshop

3. Outline
Use scalar potential to calculate 3d-printed circuit surface current coils, unique to desired field & geom.
Physical interpretation of the magnetic scalar potential
Boundary value problem (BVP) to calculate winding geometry
Application to a finite-double-cos-theta coil: first prototype
Cos-theta / solenoid “elbow” interface
Calculation of constant adiabaticity magnetic profile for polarized cold neutrons and 3He atoms
Parametrization of field along central axis
Longitudinal / transverse field taper / rotation profiles
Coil designs for tapered neutron / 3He injection
Construction with 6-axis industrial robotic arm
nEDM2014 Workshop

4. Electric & Magnetic: Flux & Flow
A-sheets
B.C.’s: Flux lines bounded by charge Flux lines continuous
Flow sheets continuous (equipotentials) Flow sheets bounded by current
Solenoid:
Cos-theta coil:
Geometrical Gauss -> Ampere’s law
U interpretation as boundary currents
Statement in terms of boundary conditions
Technique for calculating coils
nEDM2014 Workshop

5. Magnetic Scalar Potential
FLUX FLOW
Field Equations field potential
Boundary conditions field potential
Surface Current
Magnetic flow sheets
(scalar equipotential)
Magnetic flux lines
nEDM2014 Workshop

6. Calculation of optimal design
Based on physical interpretation of magnetic scalar potential U.
1. Solve Laplace equation Wind the coil along equipotential for U imposing desired contours along the boundary of flux boundary conditions each region (flow boundary cond.)
nEDM2014 Workshop

7. Double-cos-theta-coil
Inside windings
nEDM2014 Workshop

8. Double-cos-theta-coil
Outside windings
nEDM2014 Workshop

9. Double-cos-theta-coil
Combined
nEDM2014 Workshop

10. Prototype Double Cos-Theta Coil
nEDM2014 Workshop

11. `Clamshell Coil’ for 3He transport
Solenoid with field cancellation coil
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

12. `Clamshell Coil’ for 3He transport
Split for assembly
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

13. `Clamshell Coil’ for 3He transport
Continuous transition to cos-theta coil
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

14. `Clamshell Coil’ for 3He transport
Inside windings
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

15. `Clamshell Coil’ for 3He transport
Inside windings (rerouted)
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

16. `Clamshell Coil’ for 3He transport
Outside windings
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

17. `Clamshell Coil’ for 3He transport
Combined winding (50 wires)
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
nEDM2014 Workshop

18. `Clamshell Coil’ for 3He transport
Field map
C4 ‘clamshell coil’ problem
Steps in calculation of solenoid to cos-theta transition
Calculation of field and comparison of uniformity
Biot-Savart calculation
based on computed winding geometry
nEDM2014 Workshop

19. Guide taper and spin precession
Centerline parametrization
Adiabaticity parameter
nEDM2014 Workshop

20. Neutron Spin Transport Coil
71 ‘mG
Field tapers from 5 G to 40 mG in 2m
Segmented, 6x current between coil
Merges into field of B0 coil
Inner/outer coils combined into single winding 50
(center)
total taper 25
guide taper (edge)
B0 taper cm
Guide field windings shown with 25 turns
nEDM2014 Workshop

21. Taper and Rotate from 5 G to 50 mG
generalize approximation to include transverse component for rotation
Resulting field profile
tapered flux
50mG flux
U = 0
tapered flux
nEDM2014 Workshop

22. 3He Injection field from nEDM ABS
T1a/b coil @ 4K
T2a/b coil @ vacuum
preferably outside vacuum
(smaller diameter stub)
nEDM2014 Workshop

23. Construction of Surface Current Coils
Calculate 3d traces from equipotential contours of solution to Laplace eq. using Finite Element Analysis
Electroplate copper on a G10 form to create blank 3-D printed circuit board
Use Staubli RX130 industrial arm, displacement sensor, and high-speed drill to etch traces along the extracted contours
nEDM2014 Workshop

24. Conclusion
One can separate the problem of spin transport into two independent analytic problems:
Calculation of IDEAL FIELD by parametrization along centre-line
Calculation of IDEAL surface-current COILS by means of a physical interpretation of the magnetic scalar potential
THANKS FROM KENTUCKY!
nEDM2014 Workshop