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Beam Dynamics of Low Energy Muon Acceleration

Beam Dynamics of Low Energy Muon Acceleration. Alex Bogacz Jefferson Lab. 7-th International Workshop on Neutrino Factories and Superbeams, LNF Frascati, June 24, 2005. Overview. FFAG acceleration below 5 GeV not cost effective ‘Dogbone’ RLA (3.5-pass) scheme based on 200MHz SRF

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Beam Dynamics of Low Energy Muon Acceleration

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  1. Beam Dynamics of Low Energy Muon Acceleration Alex Bogacz Jefferson Lab 7-th International Workshop on Neutrino Factories and Superbeams, LNF Frascati, June 24, 2005 NuFact’05, INFN Frascati, June 24, 2005

  2. Overview • FFAG acceleration below 5 GeV not cost effective • ‘Dogbone’ RLA (3.5-pass) scheme based on 200MHz SRF • Pre-accelerator (273 MeV/c – 1.5 GeV) based on solenoid focusing • Main Linac (1 GeV/pass) based on triplet focusing • Three ‘droplet’ arcs with horizontal multi-pass separation • Longitudinal phase-space compression in the arcs (M45 and off-crest RF) • M45 and off-crest RF linac acceleration • Large (2) transverse acceptance • Lattices – linear optics, tracking studies, emittance preservation • multi-pass linac optics • tracking studies NuFact’05, INFN Frascati, June 24, 2005

  3. Muon Acceleration Complex • Linear pre-accelerator (273 MeV/c – 1.5 GeV) • ‘Dogbone’ 3.5-pass RLA (1.5 – 5 GeV) • 5 – 10 GeV FFAG • 10 – 20 GeV FFAG NuFact’05, INFN Frascati, June 24, 2005

  4. ‘Dogbone’ RLA (3.5-pass) scheme • Linear pre-accelerator (273 MeV/c – 1.5 GeV) - solenoid focusing • Main Linac (1 GeV/pass) - triplet focusing • Single magnet horizontal multi-pass separation • 3 Arcs based on the same strength of bending magnets (~ 1 Tesla) NuFact’05, INFN Frascati, June 24, 2005

  5. Initial beam emittance/acceptance after the cooling channel at 273 MeV/c NuFact’05, INFN Frascati, June 24, 2005

  6. Beam Parameters NuFact’05, INFN Frascati, June 24, 2005

  7. Pre-accelerator– Longitudinal dynamics longitudinal acceptance, bucket height energy profile along the linac Dp/p=0.17or Df =93 (200MHz) NuFact’05, INFN Frascati, June 24, 2005

  8. Pre-accelerator– Longitudinal acceptance Phase space contours initial, half-way through and at the end of acceleration – contours defined for particles at 2.5s (95% of particles contained inside) NuFact’05, INFN Frascati, June 24, 2005

  9. Linear Pre-accelerator – Longitudinal dynamics, tracking NuFact’05, INFN Frascati, June 24, 2005

  10. ‘soft-edge’ solenoid model • Zero aperture solenoid - ideal linear solenoid transfer matrix: Larmour wave number: NuFact’05, INFN Frascati, June 24, 2005

  11. ‘soft-edge’ solenoid – edge effect • Non-zero aperture - correction due to the finite length of the edge : • It decreases the solenoid total focusing – via the effective length of: • It introduces axially symmetric edge focusing at each solenoid end: • axially symmetric quadrupole NuFact’05, INFN Frascati, June 24, 2005

  12. ‘soft-edge’ solenoid – nonlinear effects • Nonlinear focusing term DF ~ O(r2) follows from the scalar potential: • Scalar potential in a solenoid • Solenoid B-fields NuFact’05, INFN Frascati, June 24, 2005

  13. ‘soft-edge’ solenoid – nonlinear effects • In tracking simulations the first nonlinear focusing term, DF ~ O(r2) is also included: • Nonliner focusing at r = 20 cm for 1 m long solenoid with 25 cm aperture radius NuFact’05, INFN Frascati, June 24, 2005

  14. Linear Pre-accelerator – transverse emittance NuFact’05, INFN Frascati, June 24, 2005

  15. Main Linac - multi-pass Optics • Focusing compromise strategy • focusing optimized for the half-pass (1.5-2 GeV) - 900 phase advance per cell • Uniform focusing restored in the second half of the first full-pass (2.5-3 GeV) NuFact’05, INFN Frascati, June 24, 2005

  16. Main Linac - Multi-pass Optics (lower passes) 1.5-2 GeV 2-3 GeV NuFact’05, INFN Frascati, June 24, 2005

  17. Main Linac - Multi-pass Optics (higher passes ) 3-4 GeV 4-5 GeV NuFact’05, INFN Frascati, June 24, 2005

  18. Main Linac - Multi-pass phase advance slip 2-3 GeV 3-4 GeV NuFact’05, INFN Frascati, June 24, 2005

  19. Main Linac - the half-pass (1.5-2 GeV) longitudinal tracking NuFact’05, INFN Frascati, June 24, 2005

  20. Main Linac - transverse emittance (tracking) the half-pass1.5-2 GeV NuFact’05, INFN Frascati, June 24, 2005

  21. Arc Optics - beam transport choices • Principle of uniform focusing periodicity (900) – cancellation of chromatic effects • Single dipole (horizontal) separation of multi-pass beams in RLA • No need to maintain achromatic Spreaders/Recombiners • Compact Spreaders/Recombiners – minimized emittance dilution • SC dipoles and quads (triplets) in RLA (1 Tesla dipoles/1 Tesla quads) • Requirement of high periodicity and ‘smooth’ transition between different kinds of optics, linac-spreader-arc-recombiner-linac NuFact’05, INFN Frascati, June 24, 2005

  22. ‘Droplet’ return (600 out - 3000 in - 600 out) arc footprint NuFact’05, INFN Frascati, June 24, 2005

  23. Droplet arc – Optics building blocks inward and outward cells, missing dipole cell NuFact’05, INFN Frascati, June 24, 2005

  24. Chromatic properties of the periodic cell Dp/p=0.07 NuFact’05, INFN Frascati, June 24, 2005

  25. Droplet Arc Optics (Spreader and Transition) - Arc 1 Quads: L[cm] G[kG/cm] D 68 -0.32 F 125 0.32 Dipoles: L[cm] B[kG] 150 7.8 NuFact’05, INFN Frascati, June 24, 2005

  26. Arc 1 – Longitudinal dynamics (tracking) NuFact’05, INFN Frascati, June 24, 2005

  27. Arc 1 – Transverse emittance (tracking) NuFact’05, INFN Frascati, June 24, 2005

  28. Arc 2 – Optics NuFact’05, INFN Frascati, June 24, 2005

  29. Summary • Lattice for 3.5-pass, 5 GeV, RLA based on 200MHz SRF - linear optics • Pre-accelerator, three styles of cryo-modules • Proof-of-principle Arc optics lattice - further longitudinal compression in the Arcs, with M56 ~ 3 m • multi-pass linac optics • compact Spr/Rec • matched periodicity (betatron phase advance per cell) between linacs and Arcs • Future work… • Emittance preservation scheme - nonlinear corrections in the Arcs • Chromatic corrections in the Arcs to effectively restore longitudinal space linearity (via three families of sextupoles) • Emittance preservation checked independently by ICOOL NuFact’05, INFN Frascati, June 24, 2005

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