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Dejan Trbojevic

Muon acceleration by RLA using non-scaling FFAG. Dejan Trbojevic. RLA for Muons. Introduction: Present design of the muon RLA’s Problems: Matching of the circular non-scaling FFAG to the straight linac. Time of flight adjustments for each pass. Goals:

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Dejan Trbojevic

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  1. Muon acceleration by RLA using non-scaling FFAG Dejan Trbojevic Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  2. RLA for Muons • Introduction: • Present design of the muon RLA’s • Problems: • Matching of the circular non-scaling FFAG to the straight linac. • Time of flight adjustments for each pass. • Goals: • Try to make four or five times in muon energy by either a race track or dog-bone acceleration with a single arc (2.5-10 GeV or 10-40 GeV). • Match the betatron and dispersion functions from the arc to the linac. • Design a chicane to adjust the time of flight for different energy passes. Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  3. Few references for Mike Craddock: D. Trbojevic E.D. Courant, and A. Garren, September 30, 1999, Montauk, Long Island High Energy Muon Collider Workshop Lee Teng: 1956 Non-scaling FFAG proposal at the conference A year later a book Conference Proceedings came out: D. Trbojevic, E.D. Courant, and A. Garren, “FFAG lattice without opposite bends” , AIP Conf. Proc. August 17, 2000 -- Volume 530, pp. 333-338 Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  4. ‘Racetrack’ vs ‘Dogbone’ RLA (both m+ and m- species ) m+ m- m- m+ m+ m- m- m- m- m+ m+ m+ m+ m- m- m+ DE/2 From Alex Bogacz presentation at the previous LEMC: • better orbit separation at linac’s end ~ energy difference between consecutive passes (2DE) • allows both charges to traverse the Linac in the same direction (more uniform focusing profile • the droplets can be reduced in size according to the required energy • both charge signs can be made to follow a Figure-8 path (suppression of depolarization effects) Chuck Ankenbrandt DE Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  5. FODO vs Triplet focusing - ‘flat focusing' linac profile* Bob Palmer* From Alex Bogacz presentation at the previous LEMC: Triplet 1-pass, 3-5 GeV 256.82 meters phase adv. drops much faster in the horizontal plane Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  6. Design of the arcs – from the densely populated FODO cells for the 2.5 -> 10 GeV muons N=142 cells L=1.9 m LBD=0.9 m LQF=0.6 m For the: dp/p=+-60% BBD=1.64 T BQF =-1.09 T GF=20.8 T/m GD=-10.2 T/m r=42.94 m 85.9 m Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  7. Arc cells for two different lattices 1.9 m x max=69 mm 0.9 m 0.3 m x min= -34 mm FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  8. Arc cells for two different lattices FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  9. Matching cell – geometrical constraint - arc to linac The matching cell length is: L=3 * 1.9 m = 5.7 m Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  10. Matching cell to the non-scaling FFAG arcs Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  11. Non scaling FFA arcs with matching cells without linac Orbits from 2.5 – 10 GeV through the matching cells and arcs: Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  12. Non scaling FFA arcs with matching cells without linac Betatron Functions from 2.5 – 10 GeV through the matching cells and arcs: Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  13. Non scaling FFA arcs with matching cells without linac Dispersion from 2.5 – 10 GeV through the matching cells and arcs: Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  14. The linac – Betatron Function dependence on energy Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  15. Matching cell with linac – arc to linac Orbits magnified 100 times From 2.5 GeV- 10GeV Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  16. Multipass Linac - racetrack FFAG Chicane 20 Cavities Chicane Non-scaling FFAG arc Non-scaling FFAG arc Chicane Chicane 20 Cavities Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  17. 20 cells linac Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  18. Multipass Linac with combined function triplets Details of the orbits with Chicanes: Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  19. Path length difference from the arc celldp/p=(0,-80%) Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  20. Path length difference from the arc cell (Ds=0.55m for arc) Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  21. -2q L q Lo Details of the chicane calculations: Lo /L=cos q Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  22. Details of the Chicane CAVITY TRIPLET Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  23. New approach: What do we need to came from a remainder by Yoshimaru Mori yesterday:IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983 Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  24. New matching cell Input parameters are: xmaxand xminfrom the arc NS-FFAG pmax, po, and pmin, Dx, bx, by, Unknowns: BD, BF, Ffo, Fdo , andlo rfmax ffo rfo amax fdo amin rfmin lo ffo fdo umax rdmin xmax umin fdo rdo xmin fdo rdmax To be matched to the input parameters of the linac: bx, by, ax,ay Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  25. Matching Cell - @ zero dispersion end amax amin lo rdmin fdmin umax rdo umin fdo rdmax fdmax Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  26. Matching Cell @ entrance w Ffmax rfmax j rfmax Ffo amax amin Ffo- Ffmax rfo Ffo- Ffmax= Fdo- Fdmax Ffmin lo Ffmin- Ffo rfmin Ffmin- Ffo= Fdmin- Fdo umax pmin umin xmax umax=amax+lo tan(Ffo-Ffmax) po xmin umin=amin+lo tan(Ffmin-Ffo) pmax Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  27. Mike Craddock’s approach: D/2 rfmax xd+=0 ffo rfo Xd+ xd-=0 fdo Xd- rfmin lo ffo fdo umax rdmin xfp+ umin fdo high p+ rdo xfp- fdo po rdmax F/2 low p- Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  28. p>pcent orbits matched to linac -> zero dispersion for each momentum p=pmax p=pcent Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  29. orbits almost matched to linac -> zero dispersion for each momentum 10 GeV 2.5 GeV Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

  30. Conclusions: • It looks like a combination of the non-scaling FFAG with linac is possible this could reduce present number of arcs. • Multiple pass linac by the triplet combined function dipoles cells. • Time of flight adjustments is necessary due to 0.6 m delay for the lowest energy pass through the arc. A details of chicane design has to be studied. • Initial matching between the two arcs and linac could be improved. • The simulation of acceleration with many particles is already set-up by the PTC (Polymorphic Tracking Code). • Thanks to Muon Inc. for the support Dejan Trbojevic FFAG’08 Workshop, Manchester, 15:00, September 2, 2008

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