1. Impedance in a flat and infinite chamber: a new model
N. Mounet and E. Métral
Impedance meeting - N. Mounet and E. Métral - CERN/BE-ABP-LIS - 14/12/2009

2. Impedance in a flat chamber
Benoît and Carlo showed that the usual Yokoya (or Laslett) factors (used to compute impedance of a flat chamber knowing that of a circular geometry), don’t apply to a SPS ferrite kicker (rectangular shape made of two parallel ferrite plates and two conductors perpendicularly to the ferrite).
More generally, assumptions for the Yokoya factors to hold are:
Ultrarelativistic speed of the beam,
Conductivity of the chamber and frequency range such that we are in the “classic thick wall” regime.
 In the case of ferrite (but also, in principle, for LHC graphite collimators), deviations from this approach are likely to appear.
Impedance meeting - N. Mounet and E. Métral - CERN/BE-ABP-LIS - 14/12/2009

3. Impedance in a flat chamber: a new model
It is possible to get an impedance formula in a “closed form” for infinitely long parallel plates ( a “flat chamber”), even in the multilayer case, for any relativistic velocity factor of the beam and any linear material(s).
Those formulas still imply the computation of integrals that are (apparently) too complicated to compute analytically but can be calculated numerically.
Results in the case of a SPS ferrite kicker seem promising and agree well with Tsutsui’s model, especially when the distance between the perfectly conductive plates (perpendicular to the ferrite) is increased by a factor of ten (see next slides).
Impedance meeting - N. Mounet and E. Métral - CERN/BE-ABP-LIS - 14/12/2009

4. Courtesy of B. Salvant for Tsutsui’s model
Impedance meeting - N. Mounet and E. Métral - CERN/BE-ABP-LIS - 14/12/2009

5. Courtesy of B. Salvant for Tsutsui’s model
Impedance meeting - N. Mounet and E. Métral - CERN/BE-ABP-LIS - 14/12/2009