1. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 1 Bunch Merging in the Helical Channel

2. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 2 We are on the edge of a proof of principle helical channel design that merges 13 bunches exiting a first HCC, which fits the acceptance of a second HCC that cools the merged bunch.

3. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 3  40m of “bunch preparation” that puts different bunches at different energies.  V’ max = 1 MV/m, 204.17 MHz < f < 271.84 MHz  η = 0.43  60m of drift in the same helical channel w/o RF.  η = 0.43  ~5m RF capture into a single bunch  V’max = 10 MV/m, f = 200 MHz  η = 0.43 “Proof of Principle” Design General HCC parameters: λ = longitudinal spatial period = 1 m r ref = 16 cm, κ = pitch = 1, η = 0.43, Bsol(z-axis) = 5.7 T

4. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 4 Parameter list 2/28/11 - 3/04/114 Zbb’bzνEκλεμεμ εTεT εLεL ε 6D unitmTT/mTGH z MV/mmmm rad mmmm 3 Chann el length @ ref RF p ⊥ /p z Trans- missio n RMS normalized 01.021238900 11001.2-0.21-4.20.2161.0 0.751.94.39.4 2911.8-0.42-6.00.4161.00.70.620.861.80.99 3863.1-1.29-10.70.8161.00.40.410.321.00.08 4244.2-2.29-14.00.8161.00.30.380.341.10.07 MAP Winter Meeting 2011, Design study of HCC, K. Yonehara Boundary Conditions (HCC reported by Katsuya at the 2011 Winter MAP Meeting @ JLAB) start of merger end of merger

5. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 5 Parameter list Z±Δr ±Δp/ p bb’bzνκλNμNμ εTεT εLεL ε 6D unitmcm%TT/mTGHzmmm rad mmmm 3 Channe l length Full Width Full width @ ref RF 1015221.3-0.5-4.20.3251.0 38820.442.812900 2408101.3-0.5-4.20.3251.0 3755.9719.7415.9 3497101.4-0.6-4.80.3251.00.93544.0115.010.8 412932.51.7-0.8-5.20.3251.00.83271.024.82.0 52191.71.82.6-2.0-8.50.651.00.53270.582.13.2 62431.61.33.2-3.1-9.80.651.00.43270.421.30.14 72731.3 4.3-5.6-14.10.651.00.33270.321.00.08 83031.21.14.3-5.6-14.11.31.00.33270.341.10.07 12/02/095MC Design workshop @BNL, K. Yonehara Boundary Conditions (HCC reported by Katsuya at the 2011 Winter MAP Meeting @ JLAB) start of merger end of merger

6. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 6 Energy of reference is scaled/accelerated from ~120 MeV out of Katsuya’s HCC to 200 MeV for bunch merging, but emittances are assumed conserved in the acceleration.

7. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 7 Bunch Preparation z = 0 m z = 40 m chosen for end of prep z = 50 m z = 20 m

8. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 8 Bunch Preparation

9. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 9 Drift w/o RF for Bunch Merge z = 40+0 m z = 40+20 m z = 40+40 m z = 40+60 m end of drift; 13 bunches

10. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 10 Drift w/o RF for Bunch Merge z = 40+0 m z = 40+60 m end of drift; 13 bunches z = 40+60 m end of drift; 11 bunches z = 40+60 m end of drift; 9 bunches σ rms (t) = 1.329 ns σ rms (t) = 0.8473 ns σ rms (t) = 0.7912 ns

11. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 11 Capture of 13 Bunches into a Single RF Bucket z = 40+60+0 m z = 40+60+5 m 13 bunches z = 40+60+5 m 13 bunches V’ max = 10 MV/m f = 200 MHz in vacuum Note that this capture sits just upstream of the 2 nd HCC, so incorporating gas to increase V’max is possible (desired). May also use cylindrical wedges to increase longitudinal cooling as well.

12. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 12 HCC acceptance: ε T (200 MHz) ≤ 21 mm ε T (325 MHz) ≤ 20.4 mm Capture of Bunches into a Single RF Bucket

13. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 13 ε L (325 MHz) ≤ 42.8 mm Capture of Bunches into a Single RF Bucket ε L (200 MHz) ≤ 23 mm ?

14. Muons, Inc. 6/21/2011Tuesday Muon Front End Meeting Cary Y. Yoshikawa 14 Conclusions and Future We are on the edge of a proof of principle helical channel design that merges 13 bunches exiting a first HCC, which fits the acceptance of a second HCC that cools the merged bunch. The discrepancy where 200 MHz has a smaller ε L acceptance than the 325 MHz case needs to be understood/rectified. Both used 16 MV/m. Future (assuming HCC ε L for 200 MHz case can be made to accept 9/more bunches): Consolidate frequencies in preparation portion to produce a more practical design. Think about enhanced longitudinal cooling at RF capture (upstream of second HCC). Incorporating cylindrical wedges? (Use lessons learned from “maximal use of wedges” in Quasi studies a few months ago?) ???