1. Stephen Brooks NuFact’06, UC-Irvine, August 2006  Lower-Frequency RF Phase Rotation Techniques for Both Muon Signs

2. Stephen Brooks NuFact’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

3. Stephen Brooks NuFact’06, UC-Irvine, August 2006 Problem with Two Signs Negative muons are rotated backwardsrotated backwards

4. Stephen Brooks NuFact’06, UC-Irvine, August 2006

5. Stephen Brooks NuFact’06, UC-Irvine, August 2006 Single-Sign Rotator Negative muons are rotated backwards RF Frequency31.4 MHz  efficiency ( ,  ) 35.2 (61.0, 9.4) 98% train length19.5 ns (½ b)  L (rectangular) 0.897 eV.s Total peak voltage67.5 MV Channel length42 m, 30 cells

6. Stephen Brooks NuFact’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

7. Stephen Brooks NuFact’06, UC-Irvine, August 2006 Does Dual-Sign Idea Work? Initial concept worked moderately well Some optimisation gave this solution for 31.4MHzthis solution

8. Stephen Brooks NuFact’06, UC-Irvine, August 2006

9. Stephen Brooks NuFact’06, UC-Irvine, August 2006 Dual-Sign Rotator Less of each sign, but more in total RF Frequency31.4 MHz  efficiency ( ,  ) 41.0 (36.9, 45.1) 98% train length61.8 ns (1½ b)  L (rectangular) 2.84 eV.s Total peak voltage257 MV Channel length183 m, 131 cells

10. Stephen Brooks NuFact’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 furtherthis solution

11. Stephen Brooks NuFact’06, UC-Irvine, August 2006

12. Stephen Brooks NuFact’06, UC-Irvine, August 2006 Multi-Harmonic Rotator Better in most regards, produces more b’s RF Frequencies21.0 - 126 MHz  efficiency ( ,  ) 51.3 (46.6, 55.9) 98% train length51.7 ns (3 b)  L (rectangular) 2.38 eV.s Total peak voltage184 MV Channel length134 m, 96 cells

13. Stephen Brooks NuFact’06, UC-Irvine, August 2006 FS2a Neuffer Rotator Attempted comparison RF Frequencies201 - 333 MHz  efficiency 57 98% train length289 ns (58 b)  L (“150mm”/b) 5.2 eV.s (24.9?) Total peak voltage~650 MV Channel length100 m, 140 cells

14. Stephen Brooks NuFact’06, UC-Irvine, August 2006 FS2a Bunch Population 30 b 58 b

15. Stephen Brooks NuFact’06, UC-Irvine, August 2006 Alternative Calculation 80 MeV c.f. 46 MeV 2 ns c.f. 11 ns 0.16 eV.s (rectangular) per b  4.8 eV.s for 30 b, 9.3 eV.s for 58 b

16. Stephen Brooks NuFact’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%)