Separating dipolar and quadrupolar wakes with mafia
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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

Separating dipolar and quadrupolar wakes with Mafia

Andreas Wagner (IT/IS) 8th SPS impedance informal meeting Wednesday 17/12/2008


Overview
Overview

  • Transverse Wakefield Properties

    • Axially Symmetric Structures

    • Non- Axially Symmetric Structures

    • Numeric calculation of Wakefield components

Presentation title - 2


Axial symmetric structures
Axial Symmetric Structures

  • Pillbox cavaity

Presentation title - 3


Axial symmetric structures1
Axial Symmetric Structures

  • Energy Loss vs beam offset

Presentation title - 4


Axial symmetric structures2
Axial Symmetric Structures

  • Magnitude of wake field depends on displacement of source charge and is independent of test charge position !

Presentation title - 5


Axial symmetric structures3
Axial Symmetric Structures

  • Transverse kicks vs test charge position

Presentation title - 6


Non axially symmetric structures
Non-axially-symmetric structures

  • Elliptic Model of LEP Shielded bellows

Presentation title - 7


Non axially symmetric structures1
Non-axially-symmetric structures

  • Elliptic Model of LEP Shielded bellows

Presentation title - 8


Non axially symmetric structures2
Non-axially-symmetric structures

  • Transverse kicks vs test charge position

Presentation title - 9


Non axially symmetric structures3
Non-axially-symmetric structures

  • Generalized Impedance

Presentation title - 10


Non axially symmetric structures4
Non-axially-symmetric structures

  • Transverse kicks for on axis beam:

  • Ansatz: Subtract this wake for beams with finite offset !

Presentation title - 11


Non axially symmetric structures5
Non-axially-symmetric structures

  • Transverse kicks vs test charge position minus contribution of on-axis beam

Presentation title - 12


Non axially symmetric structures6
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


Non axially symmetric structures7
Non-axially-symmetric structures

  • Electrostatic Separators

Presentation title - 14


Non axially symmetric structures8
Non-axially-symmetric structures

  • Electrostatic Separators

Presentation title - 15


Non axially symmetric structures9
Non-axially-symmetric structures

  • Transverse kicks vs test charge position

Presentation title - 16


Non axially symmetric structures10
Non-axially-symmetric structures

  • Transverse kicks vs test charge position minus contribution of on-axis beam

Presentation title - 17


Calculation of quadrupolar wakes
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


Wakes in non axially symmetric structures
Wakes in non-axially-symmetric structures

  •  To describe a non-axially-symmetric structure one needs typically 4 transverse wake tables

Presentation title - 19


  • Thank you for your attention !

  • Questions ?

Presentation title - 20


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