SNS Injection Fields and Coils Christopher Crawford University

SNS Injection Fields and Coils Christopher Crawford University of Kentucky n. EDM 2014, Ascona, CH 2014 -11 -05

Problem to solve: • Spin transport of CN & 3 He more delicate than for UCN – In the doldrums between “adiabatic” and “sudden” regime – Ballistic transport: controlled velocity of CN and 3 He Strategy: ROTATE first and then TAPER down – Diffusive transport: 3 He atoms 180 m/s @ 4 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 Geometric constraints n. EDM 2014 Workshop Validation Surface Current Coil Construction 2014 -11 -05 2

Outline • Use scalar potential to calculate 3 d-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 3 He atoms – – Parametrization of field along central axis Longitudinal / transverse field taper / rotation profiles Coil designs for tapered neutron / 3 He injection Construction with 6 -axis industrial robotic arm n. EDM 2014 Workshop 2014 -11 -05 3

Electric & Magnetic: Flux & Flow A-sheets B. C. ’s: Flux lines bounded by charge Flow sheets continuous (equipotentials) Solenoid: Flux lines continuous Flow sheets bounded by current Cos-theta coil: n. EDM 2014 Workshop 2014 -11 -05 4

Magnetic Scalar Potential FLUX FLOW • Field Equations field potential • Boundary conditions field potential Magnetic flux lines Magnetic flow sheets (scalar equipotential) Surface Current n. EDM 2014 Workshop 2014 -11 -05 5

Calculation of optimal design Based on physical interpretation of magnetic scalar potential U. 1. Solve Laplace equation for U imposing desired flux boundary conditions 2. Wind the coil along equipotential contours along the boundary of each region (flow boundary cond. ) n. EDM 2014 Workshop 2014 -11 -05 6

Double-cos-theta-coil Inside windings n. EDM 2014 Workshop 2014 -11 -05 7

Double-cos-theta-coil Outside windings n. EDM 2014 Workshop 2014 -11 -05 8

Double-cos-theta-coil Combined n. EDM 2014 Workshop 2014 -11 -05 9

Prototype Double Cos-Theta Coil n. EDM 2014 Workshop 2014 -11 -05 10

`Clamshell Coil’ for 3 He transport • Solenoid with field cancellation coil n. EDM 2014 Workshop 2014 -11 -05 11

`Clamshell Coil’ for 3 He transport • Split for assembly n. EDM 2014 Workshop 2014 -11 -05 12

`Clamshell Coil’ for 3 He transport • Continuous transition to cos-theta coil n. EDM 2014 Workshop 2014 -11 -05 13

`Clamshell Coil’ for 3 He transport • Inside windings n. EDM 2014 Workshop 2014 -11 -05 14

`Clamshell Coil’ for 3 He transport • Inside windings (rerouted) n. EDM 2014 Workshop 2014 -11 -05 15

`Clamshell Coil’ for 3 He transport • Outside windings n. EDM 2014 Workshop 2014 -11 -05 16

`Clamshell Coil’ for 3 He transport • Combined winding (50 wires) n. EDM 2014 Workshop 2014 -11 -05 17

`Clamshell Coil’ for 3 He transport • Field map Biot-Savart calculation based on computed n. EDM 2014 Workshop winding geometry 2014 -11 -05 18

Guide taper and spin precession • Centerline parametrization • Adiabaticity parameter n. EDM 2014 Workshop 2014 -11 -05 19

Neutron Spin Transport Coil 71 ‘m. G 50 (center) total taper 25 guide taper (edge) • • Field tapers from 5 G to 40 m. G in 2 m Segmented, 6 x current between coil Merges into field of B 0 coil Inner/outer coils combined into single winding B 0 taper 0 0 25 50 75 100 cm Guide field windings shown with 25 turns n. EDM 2014 Workshop 2014 -11 -05 20

Taper and Rotate from 5 G to 50 m. G • generalize approximation to include transverse component for rotation • Resulting field profile 50 m G U=0 flu x tapered flux n. EDM 2014 Workshop 2014 -11 -05 21

3 He Injection field from n. EDM ABS T 1 a/b coil @ 4 K T 2 a/b coil @ vacuum preferably outside vacuum (smaller diameter stub) n. EDM 2014 Workshop 2014 -11 -05 22

Construction of Surface Current Coils • Calculate 3 d traces from equipotential contours of solution to Laplace eq. using Finite Element Analysis • Electroplate copper on a G 10 form to create blank 3 -D printed circuit board • Use Staubli RX 130 industrial arm, displacement sensor, and high-speed drill to etch traces along the extracted contours n. EDM 2014 Workshop 2014 -11 -05 23

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! n. EDM 2014 Workshop 2014 -11 -05 24