1. MEW Meeting 05/06/14 Aaron Farricker 1

2. Effect Of HOMs Near Machine lines HOMs on or near machine lines get resonantly excited. Modes in real cavities have a shift of up to 0.04% in frequency As a worst case scenario what happens when a mode is shifted directly onto the nearest machine line in a single cavity? The position of this cavity in the linac has been varied to see the effects with Q=10^9 All other cavities have the same mode with a Gaussian spread in f 2

3. Conclusion By shifting the mode onto the machine lines we see the worst possible case. The overall effect of one cavity lying on a machine line is not always disastrous depending on where in the linac the cavity is. A cavity lying on a machine line may cause significant growth however if the cavity modes are measured accurately before hand it may be possible to position the such that they are still not an issue 3

4. Potential issues within the code Some of the definitions used in the code may be inconsistent resulting in some errors particularly the definition of R/Q and the voltage induced in a monopole mode Our fundamental R/Q come out to be equal in magnitude however if i do it they way it is done in the paper mine doubles Its the usual factor of 2 in these problems but what is the right definitions to use? The code only implements equation 5.0.37 4

5. Transverse Similar analysis to previously There is one mode present in each cavity and it is the highest transverse R/Q Gaussian frequency spread is applied to all modes The growth observed is very small and suggests Dipoles aren't an issue 5 62.5mA red 75 mAblue 100mAGreen

6. Concerns Rob observed very little growth when doing is alignments studies even with offsetting cavities by 10mm or so Highest R/Q mode offset by 10 mm only induces 20 V in the cavity with 5000 bunches and it seems small Modes near machine lines by extrapolating a 5000 bunch test in mathematical will only induce on the kV scale with the same offset This results in almost no effect as it is significantly smaller than the longitudinal momentum 6

7. Is this right? 7 This is the only place that an obvious error could be made The code is implementing this method correctly as far as i can see after several looks through