1. MCDW 2008, JLAB, Dec 8-12, 2008 1 Multi-pass Droplet Arc Design Guimei WANG (Muons Inc./ODU) Dejan Trbojevic (BNL) Alex Bogacz (JLAB)

2. MCDW 2008, JLAB, Dec 8-12, 2008 2 Outline Requirements of Muon collider acceleration Baseline design Prototype design Proposed new lattice design Ongoing…

3. MCDW 2008, JLAB, Dec 8-12, 2008 3 Requirements of Muon collider acceleration Economical system with multi pass acceleration 1.Single Accelerator 2.Single arc Short life time 1.High gradient accelerator 2.Short circumference

4. MCDW 2008, JLAB, Dec 8-12, 2008 4 Baseline design —— Separate droplet arc for different energies Alex Bogacz and Rol Johnson: single linac (with Pulsed linac Optics)+ multi droplet Arcs to accommodate multi pass beam acceleration Reference: RECIRCULATING LINEAR MUON ACCELERATOR WITH RAMPED QUADRUPOLES, S.A Bogacz, R.P. Johnson, EPAC, 2629-2631 Ramped Quads field gradient with time 4 GeV/pass 3 GeV 35 GeV  

5. MCDW 2008, JLAB, Dec 8-12, 2008 5 Baseline design — Linac Optics Increase from 8-pass (Fixed Optics) to 12-pass (Pulsed Optics) for 500 m long 4 GeV pass 8-pass Fixed linac Optics Pulsed linac Optics 12-pass 1-pass

6. MCDW 2008, JLAB, Dec 8-12, 2008 6 5 GeV 13 GeV 21 GeV 29 GeV septum spreader dipole 16 cells 2 cells Baseline design — Mirror-symmetric ‘Droplet’ Arc Optics Different energy beams coming out of a linac are directed into different ‘droplet’ arcs for recirculation. Cost moves from accelerator to arcs.

7. MCDW 2008, JLAB, Dec 8-12, 2008 7 Prototype design —— NS-FFAG (Non-Scaling Fixed Field Alternating Gradient) Dejan Trbojevic: Double linac + two 180 degree Arcs to accommodate large momentum spread (~60%) Basic cell structure in ARC (combined function magnet with extremely strong focusing ) Reference: FLEXIBLE MOMENTUM COMPACTION RETURN ARCS FOR RLAS, D. Trbojevic, R.P. Johnson, EPAC, 2578-2580 1.Large energy acceptance 2.Very small orbit offsets 3.Reduce number of arcs 4.Very compact structure

8. MCDW 2008, JLAB, Dec 8-12, 2008 8 Single Linac (pulsed linac optics) + Single Droplet arc (NS-FFAG) for two or more passes acceleration Or Single Linac +Single Droplet arc (pulsed linac optics + pulsed arc optics) for two or more passes acceleration Proposed new lattice design Basic arc design requirements: 1.Mirror symmetry arc structure for muon +/- acceleration 2.Large momentum acceptance 3.Path length control to match beam phase in the linac            

9. MCDW 2008, JLAB, Dec 8-12, 2008 9 New lattice design Tools： Optim, Madx-PTC, Cosy-Infinity … Linac: use Alex ’ s design Arc: Combine the droplet design and idea of NS-FFAG basic cell design. Mirror Symmetric droplet Arc with large momentum acceptance Basic cell of Large momentum acceptance with combined bending magnet: Extremely strong focusing to suppress dispersion function

10. MCDW 2008, JLAB, Dec 8-12, 2008 10 Strong focusing yields very small beta functions and dispersion (Gr/B ~50, optics dominated by quads) The maximum betatron in x and y plane are 4.9m and 3.4m. The maximum dispersion are 7.21cm and -7.21cm. Flexible Momentum Compaction Symmetric Cells, Inward bending cell Outward bending cell

11. MCDW 2008, JLAB, Dec 8-12, 2008 11 NS-FFAG multi-pass ‘Droplet’ Arc, 300 0 inward 60 0 outward The total length is 199 m, with 74 m long and 27 m wide.

12. MCDW 2008, JLAB, Dec 8-12, 2008 12 Cells for different energy spread —— Beta function Outward bending cellInward bending cell With MADX- Polymorphic Tracking Code. Energy spread changes from -30% to 90% For different energy spread, ~the same beta function in opposite bending cell.

13. MCDW 2008, JLAB, Dec 8-12, 2008 13 Cells for different beam energy — orbit offset and dispersion Outward bending cellInward bending cell For different energy spread, opposite offset and dispersion in opposite bending cell. Beam offset <10cm, dispersion < 0.1 m. Possible solution: (1) Matching cell with – I matrix in x plane, and +/- I matrix in y plane.

14. MCDW 2008, JLAB, Dec 8-12, 2008 14 Analysis with multipoles components Beam offset VS energy spread Same bending raduis, same optics, same chromaticity

15. MCDW 2008, JLAB, Dec 8-12, 2008 15 Ongoing More optimizations on the basic cell design, such as use multipoles Dispersion and opposite bending cells match study Pathlength difference and adjustment study Orbit offset Optics match between Linac and Arc and Optics mismatch sensitivity Error sensitivity study, beam dynamics study … Pulsed droplet arc optics study

16. MCDW 2008, JLAB, Dec 8-12, 2008 16

17. MCDW 2008, JLAB, Dec 8-12, 2008 17 1-pass, 3-7 GeV Pulsed Fixed ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (1-pass)

18. MCDW 2008, JLAB, Dec 8-12, 2008 18 8-pass, 28-32 GeV ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) Pulsed Fixed phase adv. diminishes down to 180 0

19. MCDW 2008, JLAB, Dec 8-12, 2008 19 12-pass, 47-51 GeV ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (12-pass) Pulsed Fixed no phase adv. across the linac- beam envelopes not confined phase adv. diminishes down to 180 0