Te V Scale Muon RLA Complex Large Emittance

Te. V Scale Muon RLA Complex – ‘Large Emittance’ MC Scenario Alex Bogacz and Kevin Beard Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Outline ‘Large Emittance MC’ Neuffer’s Collider Acceleration Scheme with three Dogbone RLAs Linac + RLA I: 0. 3 -4 Ge. V 4. 5 -pass (200 MHz SRF) RLA II: 4 -52 Ge. V 12 -pass (400 MHz SRF) RLA III: 52 - 1000 Ge. V 12 -pass (800 MHz SRF) Muon RLA – Beam dynamics choices Fesibility/Cost considerations Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Muon RLA – Beam dynamics choices ‘Dogbone’ (Single Linac) RLA – better orbit separation at the linac ends Longitudinal Compression via synchrotron motion ‘Bisected’ linac Optics – mirror symmetric quad gradient along the linac Pulsed linac Optics…. even larger number of passes is possible if the quadrupole focusing can be increased as the beam energy increases (proposed by Rol Johnson) Flexible Momentum Compaction return arc Optics to accommodate two passes (two neighboring energies) – NS-FFAG like Optics (proposed by Dejan Trbojevic) Pulsed arcs? – ramping arc magnets to further reuse the arcs Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

How to get ms from 3 Ge. V to 2 Te. V before they all decay away? average gradient over whole path determines m survivability N/No = e -l Dt m = (Ef/Ei) -l m /gc o TELSA cavities ~ real estate g ~ 31 Me. V/m è 64. 4 km linac è 97% survival è ~$40, 000 M* *@Jlab ~ $20 M/Ge. V g Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Large Emittance MC’ Scenario Proton Linac 8 Ge. V Accumulator, Buncher Hg target Drift, Bunch, Cool 200 m Linac Dave Neuffer RLAs Detector Collider Ring Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Bunch train for ‘Large Emittance’ MC Drift, buncher, rotator to get “short” bunch train (n. B = 10): 217 m ⇒ 125 m 57 m drift, 31 m buncher, 36 m rotator Rf voltages up to 15 MV/m (× 2/3) Obtains ~0. 1 μ/p 8 in ref. acceptance At < 0. 03, AL <0. 2 Choose best 12 bunches ~0. 008 μ/p 8 per bunch ~0. 005 μ/p 8 in acceptance 3 × 1013 protons 1. 5× 1011 μ/bunch in acceptance Dave Neuffer εt, rms, normalized ≈ 0. 003 m (accepted μ’s) εL, rms, normalized≈ 0. 034 m (accepted μ’s) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Large Emittance MC’ – Front End Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Large Emittance MC’ – Front End 3. 0 34 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Pre-accelerator – Longitudinal dynamics Transverse acceptance (normalized): (2. 5)2 e. N = 25 mm rad Longitudinal acceptance: (2. 5)2 Dp z/mmc = 200 mm 6 short cryos 8 medium cryos 16 long cryos 12 MV/m 1. 1 Tesla solenoid 1. 2 Tesla solenoid 2. 4 Tesla solenoid Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Longitudinal matching – Synchrotron motion Longitudinal acceptance: Dp/p= 0. 17 or Df = 93 (200 MHz) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009 10

4 Ge. V RLA – Longitudinal compression Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

4 Ge. V RLA – Accelerator Performance Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Beam envelopes end of RLA II (50 Ge. V) Pass 12 Transverse acceptance (normalized): (2. 5)2 e. N = 25 mm rad Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

A few thoughts on scaling… • for dipoles, the stored energy ~ power ~ cost → ┴ 2 ∙ B 2 • for quadrupoles, stored energy ~ power ~ cost → ┴ 4 ∙ G 2 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Hybrid magnets… 3. 0 T is the best we can do ± 1. 8 T 8. 8 T Ln/2 ± 1. 8 T Ls Ln/2 Don Summers Pmax/Pmin= Bmax/Bmin = (Bs∙Ls + Bn∙Ln) (Bs∙Ls - Bn∙Ln) x≡ (Pmax/Pmin-1)/(Pmax/Pmin+1) Bavg[T] Bavg= f (x+1)/(x/Bn+1/Bs) Pmax/Pmin→∞, Bavg→ 3. 0 T Pmax/Pmin→∞, Bs→∞ Bavg→ 2 Bn Pmax/Pmin Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Large Emittance’ MC vs LEMC …. rough numbers for normal 1. 8 T magnets… • LEMC emittance (153 Ge. V, ≈200 m) ┴N ≈2. 1 mm-mrad → 10 ┴≈5 mm 90 mm • small aperture → little stored energy ~ 37 J/m • power ~ 22 k. W/m 11. 5 k. J/m 7 MW/m Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Large Emittance’ MC - Conclusions ramped dipole magnets mean large arcs low emittance makes for small apertures → little stored energy, power, costs most schemes require fast pulsed magnets of some kind Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Multi-pass ‘bisected’ linac Optics ‘half pass’ , 4 -6 Ge. V initial phase adv/cell 90 deg. scaling quads with energy quad gradient 1 -pass, 6 -10 Ge. V mirror symmetric quads in the linac quad gradient Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Multi-pass linac Optics 4 -pass, 18 -22 Ge. V quad gradient 7 -pass, 30 -34 Ge. V quad gradient Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Linac-to-Arc Beta Match E =5 Ge. V Matched ‘by design’ 900 phase adv/cell maintained across the ‘junction’ No chromatic corrections needed Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Mirror-symmetric ‘Droplet’ Arc – Optics ( out = in and aout = -ain , matched to the linacs) E =5 Ge. V 2 cells out transition 10 cells in 2 cells out Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Pulsed’ linac Dogbone RLA (8 -pass) 4 Ge. V 34 Ge. V/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 k. Gauss/cm (5 cm bore radius) ramped over t = 10 -3 sec from the initial gradient of G 0 =0. 1 k. Gauss/cm (required by 900 phase advance/cell FODO structure at 3 Ge. V). G 8 =13 G 0 = 1. 3 k. Gauss/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 k. Hz capability Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Fixed’ vs ‘Pulsed’ linac Optics (8 -pass) Fixed Pulsed Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

‘Fixed’ vs ‘Pulsed’ linac Optics (12 -pass) Fixed Pulsed Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Multi-pass Arc besed on NS-FFAG Dejan Trbojevic 1. 2. 3. 4. Large energy acceptance Very small orbit offsets Reduce number of arcs Very compact structure , FMC Optics (NS-FFAG-line) Compact triplet cells based on opposed bend combined function magnets Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Flexible Momentum Compaction Cells Guimei Wang , Strong focusing (middle magnet) yields very small beta functions and dispersion Momentum offset of 60% corresponds to the orbit displacement of about 4. 3 cm. Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

NS-FFAG multi-pass ‘Droplet’ Arc , 600 outward 3000 inward MADX-PT - Polymorphic Tracking Code is used to study multi-pass beam dynamics for different pass beams: path length difference, optics mismatch between linac and arcs, orbit offset and tune change is being studied. Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Beta functions vs. Energy Inward bending cell Outward bending cell For different energy spread, ~the same beta function in opposite bending cell. With MADX- Polymorphic Tracking Code. Energy spread changes from -30% to 90% Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009

Summary ‘Large Emittance’ MC - Acceleration Scheme with three Dogbone RLAs Linac + RLA I: 0. 3 -4 Ge. V 4. 5 -pass (200 MHz SRF) RLA II: 4 -52 Ge. V 12 -pass (400 MHz SRF) still large tr. beam size RLA III: 52 - 1000 Ge. V 12 -pass (800 MHz SRF) serious problems with big magnets FODO bisected linac Optics - large number of passes supported (8 passes) Pulsed linac Optics - further increase from 8 to 12 -pass Flexible Momentum Compaction (FMC) return arc Optics allows to accommodate two passes (two neighboring energies) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, December 1 -3, 2009