1 / 15

The cos-theta coil re-re-visited

The cos-theta coil re-re-visited. Christopher Crawford, University of Kentucky DNP Fall Meeting, Newport News, VA 2013-10-26. Magnetic scalar potential. Field Equations field potential Boundary conditions field potential.

jcundiff
Download Presentation

The cos-theta coil re-re-visited

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The cos-theta coil re-re-visited Christopher Crawford, University of Kentucky DNP Fall Meeting, Newport News, VA 2013-10-26

  2. Magnetic scalar potential • Field Equationsfield potential • Boundary conditionsfield potential B.C.’s:Flux lines bounded by charge Flux lines continuous Flow sheets continuous (equipotentials) Flow sheets bounded by current

  3. What is a cos θ coil ? U = -x = - ρ cos φ CYLINDER SPHERE Symmetryz φ Wire pos. φi θi Const. surf. ρ0 r0 Moment Topology infinite bound U = -z = - r cos θ Cos θ coil U=-z Solenoid Cos φ coil

  4. Single cos θ coil

  5. Single solenoid

  6. Single cos φ coil

  7. Arbitrary angle

  8. Flux containment • Three limits of boundary conditions in the return yoke: • μ = ∞(ferromagnetic) • Magnetization currents • High static shielding factor • THIN! • Image currents: automatic self-compensation (approximate) (exact) • μ = -1(superconductor) • Super- currents • Infinite dynamic shielding factor • Need space between the coil and shield • μ = 1(wires) • Conductor currents • No external field distortion • Must calculate wire positions! • Three topologies: • sphere • Separate shells • cylinder • Common surface • Restores z-symmetry • torus • No flux return

  9. Double cos θ coil • Dipole Moments • μinner = - μouter • I = ΔA/A H0

  10. Double cos φ coil • n3He Spin Rotator • (TEM RF mode): • Reverses either longitudinal OR transverse polarizedneutrons • No fringe fieldsin the neutronbeam • Self-shielding –no eddy currentsin Aluminum enclosure

  11. Discretization of cos φ coil • Standard winding:one wire at centerof each slice • Optimization:– nominal dipole m=1– vanishing higher moments m=3,5,7,… • Nonlinear equations:– solved iteratively by Newton-Rhapson method for φi– up to m=15 (15 wires) or m=27 (30 wires)

  12. Discretization of cos φ coil • Equally spaced wiresFourier cosine series • Optimization:– nominal dipole m=1– vanishing higher moments m=3,5,7,… • Linear equations:– unitary matrix– can null N-1 odd moments using N wire pairs– can tune individual currents in situ– use as shim coils for series cos θ winding

  13. Rounded cos φ coil

  14. Rounded cos θ coil B0

  15. Conclusion • The Cos θ coil can be classified according tosymmetry, moment, and topology • Can use double layers for exact field-cancellation • Use the scalar potential, one can apply the properties ofa symmetric cos θ coil to any geometry

More Related