1. NUFACT’05 24-June-2005 H. Schönauer CERN The typical approaches to Muon acceleration at higher energies: Recirculating linacs Scaling FFAG’s : constant tune, non-isochronous Non-scaling FFAG’s in various variants, most are weakly non-isochronous: Current investigations try to reduce RF phase slip An Isochronous 10-20GeV Muon Ring with Constant Tunes, Operating Above Transition H.O. Schönauer, CERN

2. NUFACT’05 24-June-2005 H. Schönauer CERN FFAG Family Scaling FFAG’s f RF ~ 10 MHz non-isochronousConstant tuneJapan’s Neutrino Factory Non-scaling FFAG’s f RF ~ 200 MHz non-isochronous, operating around transition Varying tune, Linear lattice Off-bucket acceleration Mainstream Non-scaling FFAG’s f RF ~ 200 MHz Isochronous, operating at transition Varying tune non-linear lattice On-crest acceleration GHR Non-scaling FFAG’s f RF ~ 200 MHz Isochronous, operating above transition : locally non-isochronous Constant tune non-linear lattice In-bucket acceleration HOS

3. NUFACT’05 24-June-2005 H. Schönauer CERN Periodic Half-Cell B (hom., 4T) -b (hom.) D 1 m F 1.2 m Small kF, kD Values max. Field < 2T O0 2m O2 4 m O3 0.5 m O1 0.5 m 66 Cells make C=1250 m (fits inside JPARC Ring) In order to keep the tunes constant, the kF, kD values have to be constant the gradients are prop. B , For lin. Dispersion -> Quads are pure sextupoles

4. NUFACT’05 24-June-2005 H. Schönauer CERN Strategy for Lattice Design The following is a starting assumption for the orbit at the entrance of the cell (O0). Here a (initially linear) Dx= -0.31m is assumed. Abscissa is Brho for 10 -20 GeV in Tm. This gives a ToF error as you expect it (in ps/cell):

5. NUFACT’05 24-June-2005 H. Schönauer CERN Calculate numerically a non-linear correction to this entrance orbits to make ToF =const. Adding this to the linear orbit dependence of the 1st plot gives a non-linear dispersion at the entrance: With this orbit dependence, one obtains the ToF error as a function of Brho in ps: Strategy for Lattice Design II

6. NUFACT’05 24-June-2005 H. Schönauer CERN Strategy for Lattice Design III The inverse homogenous bending may have a curved entrance face to adjust the closing angle. Alternatively, one may add a correction to the F magnet. Both approaches spoil the focusing structure and upset the tune constancy… Are two focusing elements per half cell not enough..? G.H. Rees’ lattice cell offers three …

7. NUFACT’05 24-June-2005 H. Schönauer CERN bd(-) BF(±) BD (+) BF(±) bd(-) O 0.5 0.5 0.5 0.5 O 0.45 0.62 1.26 0.62 0.45 0.5 Normal cell (3º, 6.4 m) 0.5 2.4 Insertion cell (3º, 10.2 m) 2.4 Four superperiods, each of 20 normal & 10 insertion cells New and old ring circumferences: 920.0 and 1254.6 m Present GHR Scheme

8. NUFACT’05 24-June-2005 H. Schönauer CERN bd(-) BF(±) BD (+) BF(±) bd(-) O 0.5 0.5 0.5 0.5 O 0.45 0.62 1.26 0.62 0.45 2.4 Periodic cell (2.92º, 10.2 m) 2.4 123 Periods, Circumference = 1254.6 m Periodic Cell Derived from Earlier GHR Scheme

9. NUFACT’05 24-June-2005 H. Schönauer CERN Periodic Cell as Seen by BeamOptics 2.92  All Combined-Function Magnets are Rectangular bDbFbdbFbd

10. NUFACT’05 24-June-2005 H. Schönauer CERN Orbits 8 – 20 GeV 8 10 20 GeV bd bFbD o o O Rotation by  /123

11. NUFACT’05 24-June-2005 H. Schönauer CERN Focusing Parameters 8 – 20 GeV kD kd kF 8 GeV10 GeV 20 GeV

12. NUFACT’05 24-June-2005 H. Schönauer CERN Focusing Parameters T [GeV] B  [ Tm] kd kF kD [m -2 ]

13. NUFACT’05 24-June-2005 H. Schönauer CERN Tune Variation 8 – 20 GHz

14. NUFACT’05 24-June-2005 H. Schönauer CERN T [GeV]  ToF [ ps]  t Dx [m]

15. NUFACT’05 24-June-2005 H. Schönauer CERN Lattice Functions at 10 GeV and 20 GeV

16. NUFACT’05 24-June-2005 H. Schönauer CERN RF Issues For 200 MHz RF (h=800) and 750 MV we have One synchrotron period during acceleration for gamma-t ~20 … Bucket height: