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Separating dipolar and quadrupolar wakes with Mafia

Separating dipolar and quadrupolar wakes with Mafia . Andreas Wagner (IT/IS) 8th SPS impedance informal meeting Wednesday 17/12/2008. Overview. Transverse Wakefield Properties Axially Symmetric Structures Non- Axially Symmetric Structures Numeric calculation of Wakefield components.

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Separating dipolar and quadrupolar wakes with Mafia

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  1. Separating dipolar and quadrupolar wakes with Mafia Andreas Wagner (IT/IS) 8th SPS impedance informal meeting Wednesday 17/12/2008

  2. Overview • Transverse Wakefield Properties • Axially Symmetric Structures • Non- Axially Symmetric Structures • Numeric calculation of Wakefield components Presentation title - 2

  3. Axial Symmetric Structures • Pillbox cavaity Presentation title - 3

  4. Axial Symmetric Structures • Energy Loss vs beam offset Presentation title - 4

  5. Axial Symmetric Structures • Magnitude of wake field depends on displacement of source charge and is independent of test charge position ! Presentation title - 5

  6. Axial Symmetric Structures • Transverse kicks vs test charge position Presentation title - 6

  7. Non-axially-symmetric structures • Elliptic Model of LEP Shielded bellows Presentation title - 7

  8. Non-axially-symmetric structures • Elliptic Model of LEP Shielded bellows Presentation title - 8

  9. Non-axially-symmetric structures • Transverse kicks vs test charge position Presentation title - 9

  10. Non-axially-symmetric structures • Generalized Impedance Presentation title - 10

  11. Non-axially-symmetric structures • Transverse kicks for on axis beam: • Ansatz: Subtract this wake for beams with finite offset ! Presentation title - 11

  12. Non-axially-symmetric structures • Transverse kicks vs test charge position minus contribution of on-axis beam Presentation title - 12

  13. Non-axially-symmetric structures • The major difference to axially symmetric structures is this offset dependent "quadrupolar“ wake potential acting on a trailing particle: Presentation title - 13

  14. Non-axially-symmetric structures • Electrostatic Separators Presentation title - 14

  15. Non-axially-symmetric structures • Electrostatic Separators Presentation title - 15

  16. Non-axially-symmetric structures • Transverse kicks vs test charge position Presentation title - 16

  17. Non-axially-symmetric structures • Transverse kicks vs test charge position minus contribution of on-axis beam Presentation title - 17

  18. Calculation of “Quadrupolar Wakes” • Separating dipolar and quadrupolar wakes with Mafia/GdfidL ... • Calculation with on-axis source charge to obtain “quadrupolar” wake component • Calculation with displaced source charge distribution; substraction of “quadrupolar” component yields the “dipol”wake Presentation title - 18

  19. Wakes in non-axially-symmetric structures •  To describe a non-axially-symmetric structure one needs typically 4 transverse wake tables Presentation title - 19

  20. Thank you for your attention ! • Questions ? Presentation title - 20

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