1. Effects of wake fields in ATF2 low aperture kicker and IP nano-BPMs Karl Bane April 19, 2005

2. Extraction with low aperture kicker & slow orbit bump cross-section of the vacuum chamber built-in low aperture kicker damping ring working aperture nominal orbit bumped orbit kicked beam septum (B. Grishanov, F. Podgorny talk at ATF2 meeting in Jan 2005)

3. Detail of the drawing: low aperture kicker One of the plates is split so that the beam could be slowly moved into the kicker. Ø 5 mm 1mm Schematics of the low-aperture kicker Note: Wakes in the 1mm gap during multi-turn orbit bump need to be studied (B. Grishanov, F. Podgorny talk at ATF2 meeting in Jan 2005)

4. Parameters: charge, Q= 5 nC bunch length,  z = 8 mm energy, E= 1.28 GeV normalized emittance,  yn = 3e-8 m beta function,  y = 10 m rms beam divergence,  y’ = 1  r A: kicker --consider 2 aspects of kicker separately: (1) 2.5 mm radius pipe, with transitions (2) 1 mm gap, with transitions --separate wakes into resistive wall wake (rw) and geometric wake (g)

5. --rw dipole wake ~s -1/2 (see A. Chao) --for a gaussian bunch rms wake is: s/zs/z shape of rw wake for gaussian bunch --g wake, for collimator, with  z>~a, for a gaussian bunch wake shape is gaussian with rms (2 edges): (see Bane and Morton) --rms kick on beam:

6. --assume beam has 100  m offset beam pipe with a= 2.5mm model: --length, L= 20 cm; Cu --note: collimator approx for geometric wake is pessimistic, since electrode thickness is small, ~ 1mm --rw: (  y’/  y’ )= 0.002; g: (  y’/  y’ )= 0.07  effect is small 1 mm gap model: --model as round beam pipe with a= 0.5 mm --rw: (  y’/  y’)= 0.25; g: (  y’/  y’)= 0.35 =>effect is not small

7. 1mm 3mm better model for geometric wake --Cho ran MAFIA on this problem --100  m offset gives wake of 0.47 V/pC (compared to 0.25 V/pC from the earlier model) MAFIA wake

8. B: Nano-bpm (thanks to Z. Li) (from V. Vogel’s slide)

9. model used in MAFIA --scaled from Vogel’s picture, but changed iris radius from 3 mm to 2.5 mm --assumed cylindrically symmetric

10. MAFIA output: wake for bunch offset by 2.5 mm --wake for gaussian bunch (per cavity segment): total: 1160 V/nC/mm without bellows: 860 without bellows/flange: 334

11. --considering all 3 cavity segments, kick angle at center of 3 nC bunch, with 1  m offset, at 1 GeV, is 15 nr --if beam pipe radius is increased, wake probably reduces ~linearly with 1/a --effect of cavity is due to many higher order modes -- first two modes {f/GHz, k_loss/(V/nC/mm^2), k_perp/(V/nC/mm)}: {7.155, 7.0, 46.8}, {11.623, 71.8, 295.1}. 2 nd mode has 10 times stronger signal than 1 st --Vogel’s plot shows y signal at 9 GHz, x (much weaker) signal at 11 GHz; must have broken symmetry that I don’t have