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Stephen BrooksNuFact’06, UC-Irvine, August 2006
Lower-Frequency RF Phase Rotation Techniques for Both
Muon Signs
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Low-Frequency Phase Rotation
• The UKNF phase rotator evolved from the CERN design – E reduction occurs in a single RF bucket:
• Rees design uses 31.4MHz RF to achieve 180±23MeV intended for a cooling ring
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Problem with Two Signs
• Negative muons are rotated backwards
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Single-Sign Rotator
• Negative muons are rotated backwards
RF Frequency 31.4 MHz
efficiency (,) 35.2 (61.0, 9.4)
98% train length 19.5 ns (½ b)
L (rectangular) 0.897 eV.s
Total peak voltage 67.5 MV
Channel length 42 m, 30 cells
Stephen BrooksNuFact’06, UC-Irvine, August 2006
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 BrooksNuFact’06, UC-Irvine, August 2006
Does Dual-Sign Idea Work?
• Initial concept worked moderately well
• Some optimisation gave this solution for 31.4MHz
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Dual-Sign Rotator
• Less of each sign, but more in total
RF Frequency 31.4 MHz
efficiency (,) 41.0 (36.9, 45.1)
98% train length 61.8 ns (1½ b)
L (rectangular) 2.84 eV.s
Total peak voltage 257 MV
Channel length 183 m, 131 cells
Stephen BrooksNuFact’06, UC-Irvine, August 2006
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)
• Optimisation produced this solution; not yet clear if this can be improved further
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Multi-Harmonic Rotator
• Better in most regards, produces more b’s
RF Frequencies 21.0 - 126 MHz
efficiency (,) 51.3 (46.6, 55.9)
98% train length 51.7 ns (3 b)
L (rectangular) 2.38 eV.s
Total peak voltage 184 MV
Channel length 134 m, 96 cells
Stephen BrooksNuFact’06, UC-Irvine, August 2006
FS2a Neuffer Rotator
• Attempted comparison
RF Frequencies 201 - 333 MHz
efficiency 57
98% train length 289 ns (58 b)
L (“150mm”/b) 5.2 eV.s (24.9?)
Total peak voltage ~650 MV
Channel length 100 m, 140 cells
Stephen BrooksNuFact’06, UC-Irvine, August 2006
FS2a Bunch Population
30 b
58 b
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Alternative Calculation
80 MeVc.f. 46 MeV
2 nsc.f. 11 ns
0.16 eV.s (rectangular) per b 4.8 eV.s for 30 b, 9.3 eV.s for 58 b
Stephen BrooksNuFact’06, UC-Irvine, August 2006
Conclusion
• The main differences between LF schemes and the Neuffer buncher are:– LF schemes use less ‘voltage’ (~3x)– Bunch train length is much less (~4x)
– Resultant total L is somewhat less (~½)• Though each individual bunch is longer
• But so far:– Efficiency is not quite as good (-10%)– LF channels are slightly longer (+35%)