1. MEW Meeting 28/05/15 Aaron Farricker

2. Outline Wakefield ahead of a bunch Wakefield in CST comparison of Eigenmode and Wakefield solvers

3. Wakefield Ahead of a Bunch Last time the place where the assumption v=c was highlighted. It was noted that the assumption comes in the form of the charge density and current when deriving the wakefield (c.f SLAC-PUB-3528)

4. The Approach Taken Delta function wake does not make any sense for beta<1 as no field can exist in front of the charge. To replicate the effects it mat be possible to use a charge distribution that produces a field identical to a non-ultra relativistic bunch. Fields for a relativistic charge were found as a function of gamma and an attempt to replicate them was made

5. Attempt One As we have the field profile applying Gausses (Div (E)= rho/epsilon_0) law should reproduce the charge density distribution. However the result is zero This is because solutions to Poissons equation are unique and a point charge which has a singularity (Problem) produces it This approach will not work

6. Attempt 2 (Under Study) Calculate the point wake at v=c and use a Gaussian bunch of width sigma to produce the wake Allow this bunches width to tend to zero and look at the resulting wake I am currently testing if the field profiles are similar for a Gaussian bunch and a non relativistic charge

7. Summary Little progress have been made but a couple of approaches have been ruled out. Any ideas for alternative approaches?

8. Comparison between CST wakefield and eigenmode solver CST wakefield solver data for a pillbox at 1.5 GHz with various beta’s Gaussian bunch of 5 mm RMS was used Clearly the magnitude drops and also the number of high frequency modes contributing Beta=1 red Beta=0.86 blue Beta=0.67 green Beta=0.4 orange In meters

9. Eigenmode Solver The wakefield is reconstructed from the first 100 modes that pass 90 degree MM boundary conditions in CST A similar behaviour to that seen in the wakefield solver is observed This suggests that the varying loss parameter as a function of beta is pretty dominant This sum however is not take up to the highest frequency seen in the wakefield solver (about half way there) Beta=1 blue Beta=0.86 red Beta=0.67 green Beta=0.4 orange

10. Summary Variation in the wake appears to be dominated by variations in the R/Q I want to confirm this by excluding the higher frequency modes by taking the Fourier transform and then removing the contribution before reversing it