Non-Scaling FFAG (NS_FFAG) design for PRISM

1. Non-Scaling FFAG (NS_FFAG) design for PRISM Y. Shi/J. Pasternak Imperial College London, UK PRISM Session at FFAG’11, Oxford, 14.09.2011

2. Outline Scaling or Non-Scaling? Different designs Simulations and comparison Tracking results Summary

3. Design scheme R Ring Design Options • NS_FFAG, • Main motivation for Non-Scaling • design is a possibility to obtain • „infinite” acceptance. • Problems to be addressed: • confirmation of a large DA • no insertion scheme • very difficult injection/extraction • Scaling FFAG, • standard lattice, • periodic with extended cell • superperiodic (proposed by S. Machida) • advanced (proposed by Y. Mori and • collaborators, see J-B.Lagrange’s lattice)

4. Working applications Fig. Scaling PRISM-FFAG at Osaka Fig. 10Cell simulation by A. Kurup EMMA

5. Non-Scaling Design (conventional) D-magnet: g= 0.03742 T/m B= 0.11461 T F-magnet: g= 0.190532 T/m B= -0.113369 T *each magnet is 0.707m long and the short drift among them is 0.3 m • In order to obtain ”classical” NS-FFAG tune behaviour: • number of cells ~20. • results in relatively large ring (h=2) • requires more RF voltage. • parameters: • Lattice symmetric DFD (FDF) triplet • N ~20 • p0 68 MeV/c

6. New Non-Scaling Design type-I • parameters: • Lattice symmetric FDF triplet • N 10 • p0 68 MeV/c • Circumference 43 m • Drift length 2.2 m Quad: g=0.054504 T/m Central magnet:g= 0.098986 T/m B=0.25 T Both magnets are 0.5m long with a 0.3m short drift between each other *Two types of quadrupole focussing magnets **Vertical stability is due to edge focusing

7. New Non-Scaling Design Type-II • parameters: • Lattice asymmetric doublet • N 10 • p0 68 MeV/c • Cencumference 35.5 m • Drift length 2.2 m F-quad: gradient= 0.6 T/m X-offset=0.3 m Length=0.3 m D-quad: gradient= -0.14 T/m X-offset=0.813 m Length=0.75 m *Asymmetric cell configuration **Bending achieved by displacing the quadrupole from the central beam line in the G4Beamline simulation

8. G4beamline visualization of the doublet cell G4beamline does not provide the option of field clamp, the figure on the left shows how the fringe field would affect the particle orbit. The other fig was visualized using hard edge approximation for which the vertical focusing is incorrect

9. NS-FFAG ring parameters

10. Orbits and tunes • Chromaticity are relatively flat in • both vertical and horizontal planes • All nicely separated. Tune/Cell Triplet Doublet Red-vertical tune Black-horizontal tune K.E/GeV • Orbit excursion • Orbits are very linear with • momentum X/m Doublet orbit is the most compacted K.E/GeV

11. Resonance diagram This region gives large dynamical acceptance. Parabolic Operation Point for doublet

12. Tracking simulations for different emittance (differ by a factor of 10) • The initial distributions are Gaussian in all 6D for 1000 particles, • 3.75 MV per turn, • 6.5 turns, Small emittance Transverse plane x' vs x Red-injection Black-final

13. Tracking simulations_longitudinal Small emittance Large emittance • Phase rotation performed with the ideal ”sawtooth” RF voltage. • Matching is done at the central momentum (68MeV/c)

14. Summary • Non-scaling PRISM lattices were tried. • The drift length (2.2 m) and the need for the h=1 operation with current RF type • dictates small number of cells ~10. Still the “classical behaviour” of the tunes in • NS-FFAG can be obtained in certain lattices. • Visualization program (G4beamline) can not simulate the fringe field for complex • magnet designs. Fieldmaps are desired for more accurate simulation. • Tracking in hard edge approximation shows no distortion for large amplitudes, • which promises a very large acceptance, but the transverse – longitudinal coupling • needs to be further studied. • Injection/extraction and matching needs yet to be designed for the non-scaling • design.