1. RFA Simulations Joe Calvey LEPP, Cornell University 6/25/09

2. RFA Simulation RFA behavior can be complicated We need to simulate the RFAs in order to compare directly with data RFA modeling so far has been done with a postprocessing script –Calculates beam pipe and grid efficiencies based on incident angle and energy, deposits an appropriate amount of current on the grid and collector Preliminary simulations are good to within a factor of 2 –Data shown for a 45 bunch positron beam at 1 mA/bunch in a drift region We are beginning to do systematic comparisons with data in order to pin down simulation parameters RFA Simulations, CTA09

3. Wigglers Wiggler data is fit fairly well using a low SEY (~ 1.0) –Plots below are for 1x45x1.25 mA e+, 14ns However, some structure is missing –Data has spike at nonzero retarding voltage(~10 V in this case) –Problem is more obvious at shorter bunch spacing (e.g. 4ns, right plot) RFA Simulations, CTA09 Data, 14ns Simulation, 14ns Data, 4ns

4. The “Trampoline Effect” Because electrons are so strongly pinned to the field lines, secondaries generated on the retarding grid can escape through the same hole they entered in (motion is one-dimensional) These electrons gain energy from the retarding field If they are given the right amount of energy, they will be near the center of the pipe during the next bunch passage This leads to a resonance condition that depends on bunch spacing and retarding voltage (the shorter the bunch spacing, the more energy is needed to get close to the beam) RFA Simulations, CTA09

5. 4ns 12 ns 8ns 20 ns Center Collector Plots vs Bunch Spacing 1x45x1.25 mA e+, 5 GeV

6. An Analytical Model If you assume that beam kicks are very large and that the time spent in the RFA is negligible, resonance occurs when the time to get from the wall to the center of the beam pipe equals the bunch spacing From this condition you can derive the resonance voltage, given below –Note the 1/(bunch spacing) 2 dependence Plot shows location of peak vs bunch spacing Note that this does not explain the ~2V peak in the 4ns data (unless that is a n=2 resonance) RFA Simulations, CTA09 ParameterMeaningValue hBeam pipe height5.5 cm tbBunch spacing4-20ns veVelocity of emitted secondaries 1.3*10^6 ybBunch height2.5cm

7. Grid Center Collector A Closer Look Plots show 12ns spike in more detail The grid current exactly mirrors the enhancement in the center collector –Supports assertion that the effect is caused by secondary emission from the grid There are actually two separate peaks (14V and 22V) Speculation: maybe there is more than one resonant mode When an electron interacts with the beam, it can either be kicked toward the RFA or away from it –Towards RFA: want energy minus retarding voltage to correspond to peak SEY on the grid –Away from RFA: want energy to correspond to the peak SEY on the beam pipe

8. Dipole Effect is present but attenuated in the dipole –“One dimensional” assumption is less justified Peak has moved to ~36V for 8ns, 160V(?) for 4ns –This is actually closer to the model prediction –Consistent with idea for more sophisticated model, since the dipole is in an Aluminum chamber Al has a higher peak SEY than Cu Higher beam kick needed to get to SEY peak “Infinite kick” assumption more justified RFA Simulations, CTA09 4 ns 8 ns

9. Conclusions and Future Work Mapping RFA measurements to actual cloud densities required a solid understanding of RFA behavior The RFA can have an effect on the cloud in the region it is sampling –This effect gets stronger with higher magnetic field –Since it may depend on peak SEY, maybe this could be used as an indirect measurement of that parameter? –In any case it should be attenuated with the finer grids in the new RFAs Efforts are underway to incorporate RFAs directly into cloud simulation programs –ECLOUD (Cornell): semi-analytic model –POSINST (LBNL): full particle tracking RFA Simulations, CTA09