An Alternative to Grahame Rees’ Isochronous FFAG

1. An Alternative to Grahame Rees’ Isochronous FFAG Lattice for the Acceleration of Muons from 10 – 20 GeV Horst Schönauer, CERN Proposed FFAG-type Muon Accelerators:

2. d F D D F d O1 O0 B O2 F D Homogenous Sector b b O3 D Homogenous F B Rectangular Homogenous Sector GHR 123 Cell Lattice 8-20 GeV Proposed 66 Cell Lattice 10 – 20 GeV Reference Orbit 15 GeV

3. Design Principles: • Extended Triplet Cell • One high-field SC homogenous bending per half cell • One low-field room temp. homogenous bending per half cell • Approx. Constant Tune – no integer crossing • Simple Elements (for tracking …): Rectang. F, D magnets • Local Phase Slip accepted → Off-crest acceleration

4. Consequences of kF,D const. At y = 0 (Central Energy, T = 15 GeV), B=0 and B’ = B’0 : , YFmax 10 PBF , gPBF , y , YFmin Evaluate Plot As the Gradients B’ are given by k (=0.25 m-2) , the maximum fields can be < 2T if |ymax, min | < 0.1m

5. 10 – 15 – 10 GeV Orbits and Magnets Superimposed (AGILE Code Results)

6. Cell ToF for lin. Dx = -0.37, -0.36, -0.34 m Playing with Mathematica.. B Error in Cell ToF for Rectangular inverse b Magnet with added quadratic Dx component [ps] tps Evaluate . Init15T . Incom . Dx70 0.37 , 0.36 , 0.34 . Plot - - - e20 0 , B , B min , B max , -> r r r kF B B Plot Evaluate kFeff . Incom . Init15T , B , B min , B max Plot Evaluate tps0 tps . Init15T . Incom , B , B min , B max r r r - r r r

7. BeamOptics Representation

8. BeamOptics Representation 25 20 15 m D m  10 5 0 0 5 10 15 s m OpticsPlot Graphics , SigmaEnd Sigma 14.3333 , 0. , Sigma 8.07818 , 0. , … … Tunes 0.389993 0.243576 DVectorEnd DVector 0.304343 0. , Path 0.0164295 RelativeTimeDispersion 0.000849186

10. Open Questions : • (After finalizing and optimizing the lattice) • Consequences of local   t • Classical acceleration at high s feasible? • RF acceptance • Orbit control in isochronous lattice • Dynamic aperture (Sextupole!)