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Alex Bogacz

Pulsed ‘Dogbone’ RLA for Muon Collider. Alex Bogacz. RLA for Muons. ‘Dogbone’ (Single Linac) RLA has advantages over the Double-Linac RLA ‘Racetrack’ FODO Optics is superior to Triplet focusing - more passes are possible with the FODO scheme

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Alex Bogacz

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  1. Pulsed ‘Dogbone’ RLA for Muon Collider Alex Bogacz Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  2. RLA for Muons • ‘Dogbone’ (Single Linac) RLA has advantages over the Double-Linac RLA ‘Racetrack’ • FODO Optics is superior to Triplet focusing - more passes are possible with the FODO scheme • Pulsed linac Optics…. proposed by Rol Johnson ....even larger number of passes is possible if the quadrupole focusing can be increased as the beam energy increases…..subject to a new SBIR with Muons Inc. Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  3. m+ m- m- m+ m+ m- m- m- m- m+ m+ m+ m+ m- m- m+ DE/2 ‘Racetrack’ vs ‘Dogbone’ RLA (both m+ and m- species ) • 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 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  4. FODO vs Triplet focusing - ‘flat focusing' linac profile* Bob Palmer* FODO phase adv. diminish uniformly in both planes 1-pass, 3-5 GeV Triplet phase adv. drops much faster in the horizontal plane Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  5. FODO vs Triplet focusing - ‘flat focusing' linac profile FODO phase adv. diminish uniformly in both planes 2-pass, 5-7 GeV Triplet phase adv. drops much faster in the horizontal plane Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  6. FODO vs Triplet focusing - ‘flat focusing' linac profile FODO 3-pass, 7-9 GeV Triplet no phase adv. in the horizontal plane Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  7. FODO vs Triplet focusing - ‘flat focusing' linac profile FODO phase adv. diminish uniformly in both planes 4-pass, 9-11 GeV Triplet no phase adv. across linac- beam envelopes not confined Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  8. FODO vs Triplet focusing - ‘flat focusing' linac profile FODO phase adv. diminish uniformly in both planes 5-pass, 11-13 GeV Triplet no phase adv. Across the linac- beam envelopes not confined Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  9. FODO vs Triplet focusing - ‘flat focusing' linac profile FODO phase adv. diminish uniformly in both planes 6-pass, 13-15 GeV Triplet no phase adv. Across the linac- beam envelopes not confined Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  10. ‘Dogbone’ RLA with FODO Focusing • RLA requirements • Simultaneous acceleration of both m+m- species • Manageable orbit separation at recirculation arcs • Beam dynamics challenges -RLA Optics solutions • Phase slippage in the linacs • Multi-pass linac optics • ‘Droplet’ arc lattice • Orbit separation - switchyard • 7.5-pass Dogbone RLA - Linear Optics/Lattices designed Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  11. Ef Ef = 13 = 23 E0 E0 2.5 GeV 0.3 GeV Dogbone RLA II 7 pass 32.5 GeV 753.5 GeV ILC Linac 103 GeV/pass Possible RLA based Acceleration Scenario for MC Dogbone RLA I 7.5 pass 32.5 GeV 4 GeV/pass Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  12. Possible RLA based Acceleration Scenario for MC • Low EnergyRLA (2.5 GeV to 32.5 GeV) • 7.5-pass ‘Dogbone’ RLA: Linac (4 GeV/pass) + 7 droplet Arcs • SRF: 200-400 MHz • Top-to-injected energy ratio = 13 • High EnergyRLA (32.5 GeV to 753.5 GeV) • 7-pass ‘Dogbone’ RLA: Linac (ILC 4000 m, 103 GeV/pass) + 7 droplet Arcs • Tesla SRF: 1300 MHz, 25 MeV/m • Top-to-injected energy ratio =23 • No injection at the middle of linac necessary Harold Kirk Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  13. Phase Slippage in the Linacs Phase slippage of a semi-relativistic muon beam injected with the initial energy E0 and accelerated by DE in a linac of length, L - assuming uniformly spaced RF cavities phased for a speed-of-light particle RLA II (32.5 GeV to 753.5 GeV) RLA I (2.5 GeV to 32.5 GeV) Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  14. ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) 3 GeV 35 GeV 4 GeV/pass • Quad pulse would assume 500 Hz cycle ramp with the top pole field of 1 Tesla. • Equivalent to: maximum quad gradient of Gmax =2 kGauss/cm (5 cm bore radius) ramped over t = 10-3 sec from the initial gradient of G0 =0.1 kGauss/cm (required by 900 phase advance/cell FODO structure at 3 GeV). G8 =13 G0 = 1.3 kGauss/cm • These parameters are based on similar applications for ramping corrector magnets such as the new ones for the Fermilab Booster Synchrotron that have 1 kHz capability Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  15. ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) • For simplicity, we consider a linear ramp according to the following formula: • A single bunch traveling with a speed of light along the Linac with quads ramped as above ‘sees’ the following quad gradient passing through i-th cell along the Linac (i = 1,…20) where is the cell length and i defines the bunch position along the Linac. • For multiple passes through the Linac (the index n defines the pass number) the above formula can be generalized as follows: where is the full Linac length and is the length of the lowest energy droplet arc. Here we also assume that the energy gain per linac is much larger than the injection energy. Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  16. ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) Pulsed 1-pass, 3-7 GeV Fixed Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  17. ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) Pulsed 8-pass, 28-32 GeV Fixed phase adv. diminishes down to 1800 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  18. ‘Pulsed’ vs ‘Fixed’ Dogbone RLA (8-pass) Pulsed phase adv. diminishes down to 1800 12-pass, 47-51 GeV Fixed no phase adv. across the linac- beam envelopes not confined Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  19. ‘Pulsed’ Dogbone ILC - example number of passes Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  20. dipole dipole spreader 5 GeV 21 GeV septum 13 GeV 29 GeV Mirror-symmetric ‘Droplet’ Arc – Optics (bout = bin ,and aout = -ain , matched to the linacs) 2 cells 2 cells 16 cells Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

  21. Conclusions • ‘Dogbone’ RLA – preferred configuration • better orbit separation for higher passes • offers symmetric solution for simultaneous acceleration of m+ and m- • FODO lattice (900 deg. phase adv/cell) allows to accommodate large number of passes in the linac (8-pass RLA example) • uniform phase advance decrease in both planes • smaller variation of Twiss function – easier match to the Arcs • Pulsed linac Optics Dogbone RLA looks very encouraging…needs further studies... • Increase from 8-pass (Fixed Optics) to 12-pass (Pulsed Optics) for 500 m long 4 GeV pass example • Muon Collider Acceleration Scheme with two Dogbone RLAs • RLA I: 2.5-32 GeV • RLA II: 32-753 GeV Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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