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: TypeProposalsFeaturesIsochronous Linear, scalingJapan, YM et alQ x,y = constFar from Linear, non- scaling CJ, AS, EK, SB et al Q x,y cross integers nearly Non-linear, non- scaling GHR 123 cell  ­ t   ; Q x,y cross integers exactly Non-linear, non- scaling Modif. GHR : HS 66 cell Q­ x,y,  ­t  const. (not yet) exactly

d d F F D D B B F F D D Homogenous Sector Homogenous Sector b Homogenous Rectangular O3 O2 O0 O1 GHR 123 Cell Lattice 8-20 GeV Length [m]B, Bmax [T] Cell19.35 O33 B0.74 O21 F O10.5 D1-2.3 O02 b0.32 Proposed 66 Cell Lattice 10 – 20 GeV Reference Orbit 15 GeV

Basic Parameters Energy Range10 – 20 GeV Circumference m Number of Cells66 Inverted Bending b / B-1/8 Long Straight Sections6 m T101520GeV BB Tm B’±8.42±12.59±16.75T/m for kF, kD = ± 0.25 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

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

10 – 15 – 10 GeV Orbits and Magnets Superimposed (AGILE Code Results) T [Gev]L Halfcell QxQyGamma-t

Plot Evaluate tps.Init15T.Incom.Dx , , e20 -> 0,B r,B r min,B r max, PlotEvaluatekFeff.Incom.Init15T,B r,B r min,B r maxPlotEvaluatetps0 - tps.Init15T.Incom,B r,B r min,B r max Error in Cell ToF for Rectangular inverse b Magnet with added quadratic Dx component [ps] BB BB BB kFkF Cell ToF for lin. Dx = -0.37, -0.36, m Playing with Mathematica..

BeamOptics Representation

sm  mDm OpticsPlot … Graphics …,SigmaEndSigma ,0.,Sigma ,0., Tunes DVectorEndDVector , Path RelativeTimeDispersion BeamOptics Representation

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!)

T101520GeV BB Tm B’±8.42±12.59±16.75 T/m for kF, kD = ± 0.25 Length [m]Bmax [T] Cell19.35 O33 B0.74 O21 F O10.5 D1-2.3 O02 b0.321