1. Lower-Frequency RF Phase Rotation Techniques for Both Muon Signs
Stephen Brooks, RAL
Matthew McCullough, University College, Oxford

2. Low-Frequency Phase Rotation
The UKNF phase rotator evolved from the CERN design
DE reduction occurs in a single RF bucket:
Rees design uses 31.4MHz RF to achieve 180±23MeV intended for a cooling ring
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

3. Problem with Two Signs Negative muons are rotated backwards
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

4. Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

5. Solution (idea) for Two Signs
I. Mixed-sign drifted bunch from decay channel
II. Separate signs with on-peak RF
III. Drift further to get separation in time
IV. Put bunches on opposite sides of two adjacent wave troughs, to get the reverse sign separation and remaining phase rotation simultaneously
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

6. Does Dual-Sign Idea Work?
Initial concept worked moderately well
Some optimisation gave a solution for 31.4MHz
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

7. Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

8. Multi-Harmonic System
Idea: allowing variation of RF frequencies in the optimisation could produce higher yields by better shaped rotation
Allowed harmonics h=n/6 from 1/6 to 4 times the 31.4MHz fundamental
Re-synchronisation every 6 periods (191ns)
My optimisation produced one solution
Summer student produced several others!
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

9. Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

10. Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

11. Comparison of Yields (27.9,58.7)% Arithmetic mean = 43.3%
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

12. Other Parameters Design % Yield # Cells MV sum f / MHz 23.5 30 67.5
Original (single-sign)
23.5 30
67.5
31.4
31.4MHz dual-sign
27.7
131
257.5
Multiharmonic dual-sign
37.8 96
184.4
20-126
Matthew: “New Phase Rotation”
43.3
140
253.0
20-36
“Fifty Three”
42.1
115
201.3
20-43
“Twofreq”
34.8 98
220.5
20.9, x2
“Optimise”
37.2
238.4
22-39
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006

13. Conclusion
The dual-sign problem with lower frequency (few-bucket) phase rotation schemes has been addressed
Bunch train is ns instead of ~300ns as with 200MHz/Neuffer rotation
Yields compare favourably
43.3% into ±23MeV hard limit (48% into 28)
c.f. 57% into 28MeV 1-sigma ( 39% into 28)
Stephen Brooks, Matthew McCullough
BENE meeting, Frascati, November 2006