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%)