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 2014-11-05

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 180 m/s @ 4K 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 2014-11-05

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 2014-11-05

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 2014-11-05

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 2014-11-05

Calculation of optimal design Based on physical interpretation of magnetic scalar potential U. 1. Solve Laplace equation 2. Wind the coil along equipotential for U imposing desired contours along the boundary of flux boundary conditions each region (flow boundary cond.) nEDM2014 Workshop 2014-11-05

Double-cos-theta-coil Inside windings nEDM2014 Workshop 2014-11-05

Double-cos-theta-coil Outside windings nEDM2014 Workshop 2014-11-05

Double-cos-theta-coil Combined nEDM2014 Workshop 2014-11-05

Prototype Double Cos-Theta Coil nEDM2014 Workshop 2014-11-05

`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 2014-11-05

`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 2014-11-05

`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 2014-11-05

`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 2014-11-05

`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 2014-11-05

`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 2014-11-05

`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 2014-11-05

`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 2014-11-05

Guide taper and spin precession Centerline parametrization Adiabaticity parameter nEDM2014 Workshop 2014-11-05

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 0 25 50 75 100 cm Guide field windings shown with 25 turns nEDM2014 Workshop 2014-11-05

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 2014-11-05

3He Injection field from nEDM ABS T1a/b coil @ 4K T2a/b coil @ vacuum preferably outside vacuum (smaller diameter stub) nEDM2014 Workshop 2014-11-05

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 2014-11-05

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 2014-11-05