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Dejan Trbojevic Work with the Muons Inc.

FFAG – Type Multipass Arcs for RLA’s. Dejan Trbojevic Work with the Muons Inc. FFAG – Type Multipass Arcs for RLA’s:. Introduction: Present design of the muon RLA’s A short introduciotn to the non-scaling FFAG Problems: Matching of the circular non-scaling FFAG to the straight linac.

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Dejan Trbojevic Work with the Muons Inc.

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  1. FFAG – Type Multipass Arcs for RLA’s Dejan Trbojevic Work with the Muons Inc. Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  2. FFAG – Type Multipass Arcs for RLA’s: • Introduction: • Present design of the muon RLA’s • A short introduciotn to the non-scaling FFAG • 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

  3. ‘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: • 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

  4. FODO vs Triplet focusing - ‘flat focusing' linac profile* From Alex Bogacz: Triplet 1-pass, 3-5 GeV 256.82 meters phase adv. drops much faster in the horizontal plane Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  5. From CYCLOTRONS to FFAG’s: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  6. PSI – (Paul Scherrer Institute) CYCLOTRON 4.5 meter outer orbit Compared to TRIUMF 7.6 m Presently runs at 590 MeV with energy on target of 1.2 MW 2 mA in CW mode Upgrade to 1.8 MW at the beam energy of 590 MeV Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  7. The first SCALING FFAG MURA-KRS-6 Phys.Rev. 103, 1837 (1956) November 12, 1954 K. R. Symon: The FFAG SYNCHROTRON – MARK I This is why FFAG had lost: Dr~60-100 cm N=N1+N2, Q=2p/(N1+N2) r = r1sin(q/2)/sin(b/2)=r q/b Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  8. Many scaling FFAG’s have been built:latest complex at KURRI-Kyoto Japan Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  9. Proton driven reactor:latest complex at KURRI-Kyoto Japan Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  10. First current in KURRI’s FFAG Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  11. Non-scaling FFAG concept • Orbit offsets are proportional to the dispersion function: Dx = Dx*dp/p • To reduce the orbit offsets to ±4 cm range, for momentum range of dp/p ~ ± 50 % the dispersion function Dx has to be of the order of: Dx ~ 4 cm / 0.5 = 8 cm • The size and dependence of the dispersion function is best presented in the normalized space and by the H function:  = Dx /xand  = D’x x + x Dx x with H: H = 2 + 2 Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  12. The minimum emittance lattice: • The minimum emittance lattice requires reduction of the function H: • The normalized dispersion amplitude corresponds to the <H>1/2 • Conditions are for the minimum of the betatron function bx and dispersion function Dx to have small values at the middle of the dipole (combined function dipole makes it even smaller). bmin= Ld/215 Dxmin=q*Ld/24 Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  13. Our first publication: Lee Teng: 1956 Non-scaling FFAG proposal at the conference D. Trbojevic E.D. Courant, and A. Garren, September 30, 1999, Montauk, Long Island High Energy Muon Collider Workshop Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  14. Lattice got simplified with smaller number of magnets: just two kinds Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  15. Basic Properties of the non-scaling FFAG • Extremely strong • focusing with small • dispersion function. • large energy acceptance. • - tunes variation • very small orbit offsets • small magnets • linear magnetic field Muon acceleration Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  16. Basic Properties of the Non-Scaling FFAG A . Particle orbitsB. Lattice Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  17. Scaling FFAG – Non scaling FFAG B = Bo+r Go B =Bo(r/ro)k • Scaling FFAG properties: • Zero chromaticity. • Orbits parallel for different dp/p • Relatively large circumference. • Relatively large physical aperture (80 cm – 120 cm). • RF - large aperture • Tunes are fixed for all energies. • Negative momentum compaction. • B =Bo(r/ro)k non-linear field • Non-Scaling FFAG properties: • Chromaticity is changing. • Orbits are not parallel. • Relatively small circumference. • Relatively small physical aperture (0.50 cm – 10 cm). • RF - smaller aperture. • Tunes move 0.4-0.1 in basic cell. • Momentum compaction changes. • B = Bo+x Go linear field Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  18. EMMA: first non-scaling FFAG Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  19. EMMA: first non-scaling FFAG Two already built magnets: EMMA’s cavity: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  20. EMMA: first non-scaling FFAG: six cells on a girder Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  21. 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

  22. Single arc cells 1.9 m x max=69.7 mm 1.08 m 0.3 m x min= -35.1 mm FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV 35.1 mm LBD = 1.08 m , LQF=0.6 m Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  23. FODO cell for the dp/p=+-60 % -> 2.5 - 10 GeV Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  24. Matching cell – geometrical constraint - arc to linac The matching cell length is: L=3 * 1.9 m = 5.7 m Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  25. Matching cell to the non-scaling FFAG arcs Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  26. Non scaling FFA arcs with matching cells without linac Orbits from 2.5 – 10 GeV through the matching cells and arcs: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  27. Non scaling FFAG arcs with matching cells without linac Betatron Functions from 2.5 – 10 GeV through the matching cells and arcs: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  28. Non scaling FFA arcs with matching cells without linac Dispersion from 2.5 – 10 GeV through the matching cells and arcs: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  29. The linac – Betatron Function dependence on energy Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  30. Matching cell with linac – arc to linac Orbits magnified 100 times From 2.5 GeV- 10GeV Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  31. Multipass Linac - racetrack FFAG Chicane 20 Cavities Chicane Non-scaling FFAG arc Non-scaling FFAG arc Chicane Chicane 20 Cavities Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  32. Multipass Linac with combined function triplets Details of the orbits with Chicanes: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  33. Path length difference from the arc cell (Ds=0.55m for arc) Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  34. -2q L q Lo Details of the chicane calculations: Lo /L=cos q Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  35. Details of the Chicane CAVITY TRIPLET Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  36. Phil Meads: IEEE Transactions on Nuclear Science, Vol. NS-30, No. 4, August 1983 Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  37. Analytical formulae from the combined function magnet: LINAC p_max p_min Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  38. 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

  39. Analytical formulae from the combined function magnet: Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  40. Matching Cell - @ zero dispersion end amax amin lo rdmin fdmin umax rdo umin fdo rdmax fdmax Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  41. 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

  42. A solution for zero offsets at the end 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

  43. p>pcent orbits matched to linac -> zero dispersion for each momentum p=pmax p=pcent Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  44. Orbits matched to linac -> zero dispersion for each momentum 10 GeV Linac 2.5 GeV FFAG cell Matching cell Dejan Trbojevic Muon ColliderDesign Workshop, 9:00, December 11, 2008

  45. Conclusions: • A solution of the non-scaling FFAG arcs with RLA’s looks very good. • This multiple pass linac is designed 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 for any energy without orbit offsets in the linac ! • 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 Muon ColliderDesign Workshop, 9:00, December 11, 2008

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