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Magnetic Multipoles, Magnet Design

Magnetic Multipoles, Magnet Design. Alex Bogacz, Geoff Krafft and Timofey Zolkin. Maxwell’s Equations for Magnets - Outline. Solutions to Maxwell’s equations for magnetostatic fields: in two dimensions ( multipole fields)

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Magnetic Multipoles, Magnet Design

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  1. Magnetic Multipoles, Magnet Design Alex Bogacz, Geoff Krafft and Timofey Zolkin USPAS, Fort Collins, CO, June 10-21, 2013

  2. Maxwell’s Equations for Magnets - Outline • Solutions to Maxwell’s equations for magnetostatic fields: • in two dimensions (multipole fields) • in three dimensions (fringe fields, end effects, insertion devices...) • How to construct multipole fields in two dimensions, using electric currents and magnetic materials, considering idealized situations. • A. Wolski, University of Liverpool and the Cockcroft Institute,CAS Specialised Course on Magnets, 2009, http://cas.web.cern.ch/cas/Belgium-2009/Lectures/PDFs/Wolski-1.pdf USPAS, Hampton, VA, Jan. 17-28, 2011

  3. Basis • Vector calculus in Cartesian and polar coordinate systems; • Stokes’ and Gauss’ theorems • Maxwell’s equations and their physical significance • Types of magnets commonly used in accelerators. • following notation used in: A. Chao and M. Tigner, “Handbook of Accelerator Physics and Engineering,” World Scientific (1999). USPAS, Hampton, VA, Jan. 17-28, 2011

  4. Maxwell’s equations USPAS, Fort Collins, CO, June 10-21, 2013

  5. Maxwell’s equations USPAS, Fort Collins, CO, June 10-21, 2013

  6. Physical interpretation of USPAS, Fort Collins, CO, June 10-21, 2013

  7. Physical interpretation of USPAS, Fort Collins, CO, June 10-21, 2013

  8. Linearity and superposition USPAS, Fort Collins, CO, June 10-21, 2013

  9. Multipole fields USPAS, Fort Collins, CO, June 10-21, 2013

  10. Multipole fields USPAS, Fort Collins, CO, June 10-21, 2013

  11. Multipole fields USPAS, Fort Collins, CO, June 10-21, 2013

  12. Multipole fields USPAS, Fort Collins, CO, June 10-21, 2013

  13. Multipole fields USPAS, Fort Collins, CO, June 10-21, 2013

  14. Multipole fields USPAS, Fort Collins, CO, June 10-21, 2013

  15. Generating multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  16. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  17. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  18. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  19. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  20. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  21. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  22. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  23. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  24. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  25. Multipole fields from a current distribution USPAS, Fort Collins, CO, June 10-21, 2013

  26. Superconducting quadrupole - collider final focus USPAS, Fort Collins, CO, June 10-21, 2013

  27. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  28. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  29. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  30. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  31. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  32. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  33. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  34. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  35. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  36. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  37. Multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  38. Generating multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  39. Generating multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  40. Generating multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  41. Generating multipole fields in an iron-core magnet USPAS, Fort Collins, CO, June 10-21, 2013

  42. Maxwell’s Equations for Magnets - Summary USPAS, Fort Collins, CO, June 10-21, 2013

  43. Multipoles in Magnets - Outline Deduce that the symmetry of a magnet imposes constraints on the possible multipole field components, even if we relax the constraints on the material properties and other geometrical properties; Consider different techniques for deriving the multipole field components from measurements of the fields within a magnet; Discuss the solutions to Maxwell’s equations that may be used for describing fields in three dimensions. USPAS, Fort Collins, CO, June 10-21, 2013

  44. Previous lecture re-cap USPAS, Fort Collins, CO, June 10-21, 2013

  45. Previous lecture re-cap USPAS, Fort Collins, CO, June 10-21, 2013

  46. Allowed and forbidden harmonics USPAS, Fort Collins, CO, June 10-21, 2013

  47. Allowed and forbidden harmonics USPAS, Fort Collins, CO, June 10-21, 2013

  48. Allowed and forbidden harmonics USPAS, Fort Collins, CO, June 10-21, 2013

  49. Allowed and forbidden harmonics USPAS, Fort Collins, CO, June 10-21, 2013

  50. Allowed and forbidden harmonics USPAS, Fort Collins, CO, June 10-21, 2013

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