1. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 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

2. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 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 (M 45 and off-crest RF) M 45 and off-crest RF linac acceleration Large (  2) transverse acceptance Lattices – linear optics, tracking studies, emittance preservation multi-pass linac optics tracking studies

3. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 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

4. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 ‘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)

5. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Initial beam emittance/acceptance after the cooling channel at 273 MeV/c Study IIa  rms A = (2.5) 2  normalized emittance:  x /  y mm  rad 4.830 longitudinal emittance:  l (  l =   p  z /m  c) momentum spread:   p/p bunch length:  z mm 27 0.07 176 150  0.17  442

6. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Beam Parameters Study IIa Final energyGeV5 Number of bunches per pulse89 Number of particles per per pulse 3  10 12 Bunch/accelerating frequencyMHz200/200 Average repetition rateHz15 Average beam powerkW144

7. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Pre-accelerator– Longitudinal dynamics longitudinal acceptance, bucket height energy profile along the linac  p/p=  0.17or  =  93 (200MHz)

8. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Pre-accelerator– Longitudinal acceptance Phase space contours initial, half-way through and at the end of acceleration – contours defined for particles at 2.5  (95% of particles contained inside)

9. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Linear Pre-accelerator – Longitudinal dynamics, tracking

10. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 ‘soft-edge’ solenoid model Zero aperture solenoid - ideal linear solenoid transfer matrix: Larmour wave number:

11. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 ‘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

12. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 ‘soft-edge’ solenoid – nonlinear effects Nonlinear focusing term  F ~ O(r 2 ) follows from the scalar potential: Scalar potential in a solenoid Solenoid B-fields

13. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 ‘soft-edge’ solenoid – nonlinear effects In tracking simulations the first nonlinear focusing term,  F ~ O(r 2 ) is also included: Nonliner focusing at r = 20 cm for 1 m long solenoid with 25 cm aperture radius

14. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Linear Pre-accelerator – transverse emittance

15. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Main Linac - multi-pass Optics Focusing compromise strategy focusing optimized for the half-pass (1.5-2 GeV) - 90 0 phase advance per cell Uniform focusing restored in the second half of the first full-pass (2.5-3 GeV)

16. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Main Linac - Multi-pass Optics (lower passes) 1.5-2 GeV 2-3 GeV

17. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Main Linac - Multi-pass Optics (higher passes ) 3-4 GeV 4-5 GeV

18. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Main Linac - Multi-pass phase advance slip 3-4 GeV 2-3 GeV

19. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Main Linac - the half-pass (1.5-2 GeV) longitudinal tracking

20. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Main Linac - transverse emittance (tracking) the half-pass 1.5-2 GeV

21. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Arc Optics - beam transport choices Principle of uniform focusing periodicity (90 0 ) – 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

22. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 ‘Droplet’ return (60 0 out - 300 0 in - 60 0 out) arc footprint

23. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Droplet arc – Optics building blocks inward and outward cells, missing dipole cell

24. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Chromatic properties of the periodic cell  p/p=  0.07

25. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Droplet Arc Optics (Spreader and Transition) - Arc 1 Dipoles: L[cm] B[kG] 150 7.8 Quads: L[cm]G[kG/cm] D68 -0.32 F125 0.32

26. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Arc 1 – Longitudinal dynamics (tracking)

27. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Arc 1 – Transverse emittance (tracking)

28. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 Arc 2 – Optics

29. Operated by the Southeastern Universities Research Association for the U.S. Depart. Of Energy Thomas Jefferson National Accelerator Facility Alex Bogacz, Beam Dynamics of Low Energy Muon Acceleration NuFact’05, INFN Frascati, June 24, 2005 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