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## PAMELA lattice studies

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**PAMELA lattice studies**Dynamics of the Machida lattice**Outline**• Linear lattice options • Non-linear lattice options • Machida lattice dynamics • Future directions PAMELA lattice studies – Dynamics of the Machida lattice**Linear NS-FFAG lattices**• Quadrupole & dipole elements • e.g. KST (Keil, Sessler, Trobjevic) 48 cell lattice • F/D doublet cells • Small orbit excursion • Large tune excursion • Resonance crossing E. Keil, A. M. Sessler, and D. Trbojevic. “Three ring FFAG complex for H+ and C6+ therapy” pg. 1681. EPAC Proceedings, 2006. PAMELA lattice studies – Dynamics of the Machida lattice**Resonance crossing in linear lattices**• Two significant factors: • Acceleration rate – need to cross quickly! • Number of cells • Number of machine resonances crossed • Ability to have long straight sections 21.6 19.2 Horiz. Cell tunes 16.8 Total tunes Vert. 14.4 12.0 9.6 7.2 4.8 2.4 Δp/p PAMELA lattice studies – Dynamics of the Machida lattice**Resonance crossing with alignment errors**• Simulated KST Ring 2 using ZGOUBI • Particles on closed orbit accelerated & tracked to extraction • Alignment errors (gaussian distributed) introduced • 20 error sizes, 10 lattices simulation for each • Amplification factor defined as: • Ax ~ 315 • (nb. Without acceleration COD 4.4) • 100μm error gives ~31.5mm orbit distortion! PAMELA lattice studies – Dynamics of the Machida lattice**Emittance change through resonances**• Real emittance change - crossing through integer resonance • E.g. isolated integer resonance • 36 macro particles on 5 π mm mrad emittance ellipse • 100 turns from KE=142 MeV Linear NS-FFAG(average Bn), T.Yokoi PAMELA lattice studies – Dynamics of the Machida lattice**Avoidance strategies…**• Cross resonances very quickly ? • Accelerate very quickly • RF voltage must be large • Pushing RF limits as it is… • Reduce number of resonances crossed ? • Reduce number of cells – fewer machine integer resonances • Reduce machine tune excursion to within an integer • i.e. reduce cell tune excursion to 1/N, where N is number of cells PAMELA lattice studies – Dynamics of the Machida lattice**How to reduce tune excursion**1. Take NS-FFAG and add higher order components • Severely reduced dynamic aperture • Small dispersion makes chromatic correction hard OR 2. C.Johnstone – wedge shaped quadrupoles (see T.Yokoi’s talk) • edge focusing & path length of quads a function of momentum • effective focal length of lattice similar & independent of momentum • almost flat tune over the wide momentum range of factor 6 OR 3. S.Machida – different approach • Start from scaling FFAG with large k • Relax scaling law to get “non-scaling” PAMELA lattice studies – Dynamics of the Machida lattice**Machida lattice: aim**• Non-linear NS-FFAG (“tune stabilised”) • The aim: • Small orbit excursion • Few cells • Compact magnets • Small tune excursion • Long straight section for inj/extr. • Stability Diagram • Orbit excursion is inv. prop. to k (or dB/dr) • Take the largest possible k-value • For scaling – end of design procedure…? S. Machida, from PAMELA Design Review, June 08 PAMELA lattice studies – Dynamics of the Machida lattice**Machida lattice: the idea**• 8 Cell triplet FDF lattice • Approximate scaling r-k • Remove scaling law – only to decupole • Rectangular magnets (instead of wedge) • Magnets on straight line (easy alignment) • Long straight sections of over 2m • Orbit excursion < 30cm PAMELA lattice studies – Dynamics of the Machida lattice**Machida lattice – ZGOUBI model**• Total tune excursion within an integer Horiz. Vert. PAMELA lattice studies – Dynamics of the Machida lattice**Dynamic Aperture**• Simulations using ZGOUBI • (no fringe fields at present) • Close to 1/3 at extraction – can easily be shifted to achieve dynamic aperture D. Kelliher, from PAMELA Design Review, June 08 PAMELA lattice studies – Dynamics of the Machida lattice**Alignment errors**• ZGOUBI study with alignment errors (as before) • Ax ~ 1 (cf. 315 for linear lattice) • Expected – as no major resonances crossed! • Need to check with fringe fields PAMELA lattice studies – Dynamics of the Machida lattice**Future directions**• Understand resonance crossing • Include fringe fields in ZGOUBI for Machida lattice • Orbit/optics studies with errors • Optimise lattice PAMELA lattice studies – Dynamics of the Machida lattice**Conclusions**• Densely packed, linear lattices very sensitive to alignment errors when crossing resonances • Want sparse lattice, few cells, no resonance crossing • Machida lattice achieves this – though further studies needed! PAMELA lattice studies – Dynamics of the Machida lattice**Questions?**• Thanks for listening PAMELA lattice studies – Dynamics of the Machida lattice