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NMC lattice for PS2

PS2 meeting. NMC lattice for PS2. Y. Papaphilippou. September 28 th , 2007. Towards a feasible Negative Momentum Compaction (NMC) module Starting point Alternative NMC The short NMC Tunability Transition energy versus linear optics parameters Summary. Outline. The starting point.

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NMC lattice for PS2

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  1. PS2 meeting NMC lattice for PS2 Y. Papaphilippou September 28th, 2007

  2. Towards a feasible Negative Momentum Compaction (NMC) module Starting point Alternative NMC The short NMC Tunability Transition energy versus linear optics parameters Summary Outline PS2 Meeting, Y. Papaphilippou

  3. The starting point • The “high-filling” factor arc module • Phase advances of 280o,320o per module • γt of 8.2i • Four families of quads, with max. strength of 0.095m-2 • Max. horizontal beta of 67m and vertical of 43m • Min. dispersion of -6m and maximum of 4m • Chromaticities of -1.96,-1.14 • Total length of 96.2m • Slightly high horizontal beta and particularly long module, leaving very little space for dispersion suppressors and/or long straight sections C. Carli et al. PAC07 • Reduce further the transition energy by moving bends towards areas of negative dispersion and shorten the module PS2 Meeting, Y. Papaphilippou

  4. An alternative NMC module • 1 FODO cell with 4 + 4 bends and an asymmetric low-beta triplet • Phase advances of 320o,320o per module • γt of 6.2i • Five families of quads, with max. strength of 0.1m-2 • Max. beta of 58m in both planes • Min. dispersion of -8m and maximum of 6m • Chromaticities of -1.6,-1.3 • Total length of 90.56m • Fifth quad family not entirely necessary • Straight section in the middle can control γt • Flexible phase advance tuning between 240o and 330o • Main disadvantage the length of the module, giving an arc of around 560m (5 modules + dispersion suppressors), versus 510m for the FODO cell arc PS2 Meeting, Y. Papaphilippou

  5. The “short” NMC module Remove middle straight section and reduce the number of dipoles 1 asymmetric FODO cell with 4 + 2 bends and a low-beta doublet Phase advances of 280,260o per module γt of 9.4i Five families of quads, with max. strength of 0.1m-2 Max. beta of around 60m in both planes Min. dispersion of -2.5m and maximum of 5m Chromaticities of -1.1,-1.7 Total length of 72.84m • Considering an arc of 6 modules + 2 dispersion suppressors of similar length, the total length of the arc is around 510m PS2 Meeting, Y. Papaphilippou

  6. “Tunability” • Phase advance tunable between 240o and 420o in the horizontal and between 250o and 320o in the vertical plane PS2 Meeting, Y. Papaphilippou

  7. Transition energy versus horizontal phase advance imaginary

  8. Beta functions imaginary real

  9. Dispersion • The smaller the amplitude of the imaginary γt, the wilder the excursion of the dispersion imaginary real • For γt>10, dispersion evolution is strikingly similar • The low γt solutions correspond to high horizontal phase advances

  10. Max/Min Dispersion versus transition energy imaginary • Clear symmetry between maximum and minimum dispersion, with respect to transition energy

  11. Transition energy versus chromaticity imaginary • Higher in absolute horizontal chromaticities for smaller transition energies • Vertical chromaticities between -1.8 and -2 (mostly depending on vertical phase advance) PS2 Meeting, Y. Papaphilippou

  12. Dispersion suppressor • Two working examples, with 4 quadrupole families: • Large beta functions but well equilibrated focusing • Beta functions much lower but not well matched PS2 Meeting, Y. Papaphilippou

  13. Summary • Short NMC cell leaving comfortable space for straight sections (same as the FODO arc) • Reasonable optics functions • Wide range of transition energies can be achieved • Very good tunability • In progress • Dispersion suppressor refinement • Matching to the straight section • Module length optimisation • Minimise quadrupole families number • Systematic phase advance scanning • Working point matching • Chromaticity correction • Dynamic aperture evaluation done Not necessary done PS2 Meeting, Y. Papaphilippou

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