Effect of special magnets in FFAG

1. Effect of special magnets in FFAG David Kelliher ASTeC/STFC/RAL 13/05/09 UKNF Conceptual Design Meeting, Imperial College

2. Contents Special magnets for extraction (2 slides) Effect of special magnets (3) FFAG modelled by PTC (4) UKNF Conceptual Design meeting, Imperial College

3. Special magnets for extraction UKNF Conceptual Design meeting, Imperial College

4. Vertical extraction – 6 kickers • Kick vertically with 6 kickers at 0.067 T in consecutive drifts • Septum at 2T • Gap between kicked and circulating beam at septum entrance is 2cm • Magnets immediately before the septum require large aperture UKNF Conceptual Design meeting, Imperial College

5. Special magnet apertures F D 41.6 cm 39.06 cm Magnet apertures determine fringe field extents UKNF Conceptual Design meeting, Imperial College

6. Effect of special magnets UKNF Conceptual Design meeting, Imperial College

7. Closed orbit distortion due to special magnets Peaks in closed orbit distortion at integer tunes UKNF Conceptual Design meeting, Imperial College

8. Accelerated orbit distortion • Orbit distortion due to 1 special D magnet per half ring • In general, optimal initial (x,x’) is not the closed orbit at injection UKNF Conceptual Design meeting, Imperial College

9. Linear Approximation method • Use differential algebra (DA) to find, to first order, dependence of orbit distortion on corrector magnet strengths. • Build up set of first order Taylor coefficients that relates the horizontal position measurement made at each BPM and at each turn to each corrector magnet strength. • Linear least squares problem solved to find optimal . The target is to cancel the orbit distortion measured at each BPM, turn-by-turn. • Differential Algebra (DA) is implemented in PTC with the result that Taylor maps of arbitrary order can be generated.

10. FFAG modelled by PTC UKNF Conceptual Design meeting, Imperial College

11. Cell geometry • FODO specifications – magnets rotated w.r.t to one another • Sum of rotations is 2π/ncell • Modelled in Zgoubi F D • In PTC magnets aligned with faces parallel • Coordinate rotation done after the D magnet • Should be possible to fix this F D UKNF Conceptual Design meeting, Imperial College

12. Zgoubi/PTC comparison TOF Closed Orbit UKNF Conceptual Design meeting, Imperial College

13. Zgoubi/PTC comparison - tunes Cell tunes (no fringe field) Cell tunes (fringe field) UKNF Conceptual Design meeting, Imperial College

14. Simulate special magnet in PTC • Model effect of special magnet in PTC as a kick e.g. by displacing the magnet • Find magnitude of kick from Zgoubi results –calculate difference in integral of magnetic field in special magnet UKNF Conceptual Design meeting, Imperial College

15. Conclusion Vertical extraction from the FFAG looks feasible but requires large aperture “special” magnets Accelerated orbit distortion ~1cm due to special magnets This can be reduced by optimising (x,x’) at injection Work is underway to achieve this using PTC UKNF Conceptual Design meeting, Imperial College