What Ive been doing this week Mostly trying

What I’ve been doing this week • Mostly trying to find if there are existing ways to model small perturbations in beam wall • Found models for discontinuities, cavities, rough surfaces – all geometric wakefields • Decided to use rough surfaces as this allows for a small perturbation of the surface – cavities and discontinuities seem to assume an interruption of the beam pipe rather than a change in shape. • Reading up on how to combine both geometric and resistive wakefields in a calculation: • Serigraphy is geometric, ferrite resistance is resistive • Nothing found so far Hugo Day – Manchester Monday Morning Mega. Meeting 25/01/10 1

Rough surface approximation • Assumes a small periodic disruption of the surface • Wakefield Effects due to surface roughness M. Angelici et al • Resulting wakefield not dependant on L -> Derived within a single corrugation Hugo Day – Manchester Monday Morning Mega. Meeting 25/01/10 2

• Gives equation w (V C^-1 m^-1) z/mm Resultant Wakefunction Existing modelled wakefunction. . . Hugo Day – Manchester Monday Morning Mega. Meeting 25/01/10 3

Problems • Surface roughness is a geometric wake function -> Current model will have both geometric and resistive wake functions • Uncertain of the validity of a wake function of a periodic roughness to a single unit. . . But can only really check once I have a complete wake function (or an idea as to how to combine them; linear/non-linear) – Any help? Derivation assumes standing wave structures so probably not valid, atleast a starting point • Other possiblities: Using discontinuities in a circular beam pipe and applying form factors to convert to square pipe, see if possible to derive myself. . . -> Roger B/Adina work on rectangular apertures so will talk to them Hugo Day – Manchester Monday Morning Mega. Meeting 25/01/10 4

To do for next week • Still working on summary of impedance reduction techniques • Figure out how to combine geometric and resistive wall wakefields – open question to anyone? • See if there is any analytical treatment of impedance reduction -> So far have found evaluation of small strip insert – will see to applying MKI for the LHC – can compare to data • If successful with the above, see if its possible to extend roughness to the z-direction. . . • Catch the waskly wabbit Hugo Day – Manchester Monday Morning Mega. Meeting 25/01/10 5