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Study of Slow Extraction Relevant to the FAIR Project

Blockseminar, Riezlern, 8 th March 2007. Study of Slow Extraction Relevant to the FAIR Project. Markus Kirk. Fair-Synchrotrons Group GSI mbH. Overview. Theoretical introduction to resonant extraction Technical aspects of the RF „Knock Out“ method

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Study of Slow Extraction Relevant to the FAIR Project

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  1. Blockseminar, Riezlern, 8th March 2007 Study of Slow Extraction Relevant to the FAIR Project Markus Kirk Fair-Synchrotrons Group GSI mbH

  2. Overview • Theoretical introduction to resonant extraction • Technical aspects of the RF „Knock Out“ method • Power supply ripple and its effect on the spill • Summary and outlook

  3. Theory – 3rd integer resonance Effect of a sextupole perturbation on the linear motion Equation of motion (horizontal “sheet” beam) where the B-field of the sextupole is The focussing strength K(s) changes along the lattice. We wish remove this variation by a change of variables… Taken from G. Rees, CERN school, Vol. II

  4. Theory – 3rd integer resonance …normalized coordinates. Viz., Considering just the nth harmonic of the driving term Equation of motion can be reduced to SHM and sextupole driving term

  5. Theory – 3rd integer resonance Change variables again to enable us to find the unstable fixed points, i.e. (u,p)(r,) Thus eventually obtaining The unstable fixed points (A,B,C in figure) are given by Which yield the conditions on r and  …

  6. Theory – 3rd integer resonance … , one obtains For optimum condition, Thereby allowing the jump in x per turn to be calculated which should be greater than the thickness of the septum wires 0.1mm thick. Furthermore, it may be shown that the area of the separatrix is given by Simulation of SIS-300 where

  7. Excitation of the resonance Aim: with as little power as possible create a strong enough resonance whereby we do not shift away from the natural chromaticity. A suitable configuration is to alternate the sextupole strengths according to where subscript variables denote the ith sextupole in the jth arc which follows from the change in chromaticity due to a sextupole

  8. SIS-300 lattice Quadrupole layout modified to accomodate for injection (below) SV ~12m SX11 SH SX12 SH SV

  9. SIS-300 lattice – beta function in x

  10. SIS-300 lattice – beta function in y

  11. SIS-300 lattice – dispersion in x

  12. Magnet parameters of SIS-300 • Dipoles • 12 short dipoles, 24 long • Bending radius 67 m • Max. rigidity 300 Tm • Physical field length 7.76 m (3.88 m short) • Pole gap 1 m • Quadrupoles • FODO structure • 40 focusing and 38 defocusing (2 super periods) • Max. B’=45 T/m • Physical/effect field length 1.0/0.9 m • Pole radius 50 mm • Also…4 long F-quads and 4 D-quads (3m each) • Fast quadrupole • max. 30T/m, 0.5 m effective length, pole radius 55 mm

  13. Magnet parameters of SIS-300 Sextupoles • Resonance excitation • 2 per straight, 12 in total • Max. B’’=750 T/m2 • Physical/effect field length 0.75/0.75 m • Pole radius 47.5 mm • Chomaticity control • 4 per arc (V-H-H-V), 24 in total • Max. B’’=750 T/m2 • Physical/effect field length 0.75/0.75 m • Pole radius 47.5 mm

  14. Ripple in power supplies Time variation in tune of a bunched beam subject to ripple from the power supplies to the quadrupoles where Therefore area of separatrix will also oscillate (effect of ripple in sextupoles is much smaller) Thus, to minimize sensitivity to ripple in the quadrupoles, extract with as high S as possible without distortion to the separatrix.

  15. RF exciter - parameters • Technical details • Stripline electrodes in horizontal plane • Pseudo random noise from a maximum length sequence register • RF carrier digitally modulated with Binary Phase Shift Keying • Carrier frequency at Qff0 • Full width of centre lobe in spectrum 2fbit • Spectrum

  16. RF K.O./BTF system architecture In operation in SIS-18 P. Moritz, GSI

  17. Simulation – Particle tracking • Micromap library (Franchetti, GSI) • Thin lens sextupoles • Thick lens quadrupoles and dipoles • Closed orbit bump made with thin dipoles • Dispersion and chromaticity treated exactly • Kicks from RF exciter treated as thin elements • Sextupole strengths for resonance control calculated from the amplitude and phase • RF exciter amplitude modulation with commissioned ramps

  18. Kick from RF exciter Thin element approximation, viz. where

  19. Ripple in power supplies SIS-300: Tune sensitivity to focussing strength K1

  20. Ripple in power supplies SIS-300: Spill under ideal conditions

  21. Ripple in power supplies SIS-300: Spill degradation due to ripple Tripple

  22. Ripple in power supplies SIS-300: Systematic survey on ripple amplitude

  23. Summary and outlook • Summary • Slow extraction model with RF-K.O. developed • Systematic survey of ripple in quadrupoles undertaken • Outlook • Hardt condition • Stochastic extraction • Introduction of B-clock (all rings) Acknowledgements: P. Spiller, N. Pyka, J. Stadlmann, G. Franchetti from GSI Darmstadt

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