The typical approaches to Muon acceleration at higher energies: Recirculating linacs

An Isochronous 10-20GeV Muon Ring with Constant Tunes, Operating Above Transition H.O. 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 H. Schönauer CERN

FFAG Family H. Schönauer CERN

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 Periodic Half-Cell 66 Cells make C=1250 m (fits inside JPARC Ring) O2 4 m B (hom., 4T) F 1.2 m D 1 m O1 0.5 m O3 0.5 m -b (hom.) O0 2m Small kF, kD Values <0.1 m-2 -> max. Field < 2T 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): H. Schönauer CERN

Strategy for Lattice Design II 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: 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 … 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 0.5Normal 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 H. Schönauer CERN

bd(-) BF(±) BD (+) BF(±) bd(-) O0.5 0.5 0.5 0.5O 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 H. Schönauer CERN

2.92 Periodic Cell as Seen by BeamOptics bd bF bD bF bd All Combined-Function Magnets are Rectangular H. Schönauer CERN

Orbits 8 – 20 GeV Rotation by /123 8 10 20 GeV O o bd o bF bD H. Schönauer CERN

Focusing Parameters 8 – 20 GeV kD 8 GeV 10 GeV 20 GeV kF kd H. Schönauer CERN

Focusing Parameters T [GeV] B [Tm] kd kF kD [m-2] H. Schönauer CERN

Tune Variation 8 – 20 GHz H. Schönauer CERN

T [GeV]ToF [ps] t Dx [m] H. Schönauer CERN

Lattice Functions at 10 GeV and 20 GeV 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: H. Schönauer CERN

The typical approaches to Muon acceleration at higher energies: Recirculating linacs