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Alex Bogacz

Explore novel accelerator topologies and muon acceleration methods for efficient neutrino factories and beyond. Detailed discussion on racetrack vs. dogbone RLA setups, beam dynamics, longitudinal compression, and proof-of-concept optics. Discover how to extend accelerators to higher energies for future applications. Highlights from the Muon Collider Workshop in Padua, Italy, held from July 1-3, 2018.

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Alex Bogacz

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  1. Muon Acceleration for Neutrino Factory and Beyond Alex Bogacz

  2. Overview • Accelerator Topologies: ‘Racetrack vs Dogbone’ • Muon Acceleration for 5 GeV Neutrino Factory • Linac + ‘Dogbone’ RLA: Beam Dynamics Issues • Full bucket acceleration, Longitudinal compression • Longitudinal RF frequency shift: Matching chicane to accommodate μ± • Transverse Optics: Bi-sectedlinacs + ‘Droplet’ Arcs • Extending accelerator complex to 63 GeV Higgs Factory • Dogbone RLA with FFAG-like Arcs • Proof-of-Concept Optics • Demonstration Experiment: JEMMRLA Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  3. Accelerator Topologies ΔE/2 ΔE ΔE/2 ΔE/2 ΔE/2 ΔE Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  4. ‘Racetrack’ vs ‘Dogbone’ RLA ΔE/2 1.5ΔE ΔE/2 ΔE 3 ΔE • Twice the acceleration efficiency • Better separation of passes • Simultaneous acceleration of both charge species • Linac traversed in both direction ⇨ bi-sectedlinac optics Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  5. Linac and RLA to 5 GeV 255 MeV/c 160 m 1.25 GeV 5 GeV 70 m 840 MeV/pass Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  6. 5 5 BETA_X&Y[m] 20 20 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 160 Size_Y[cm] Size_X[cm] 0 0 0 Ax_bet Ay_bet Ax_disp Ay_disp 160 Initial 325 MHz Linac- Transverse Acceptance p = 255 MeV/c 1250 MeV beta functions Aacc= 20 MV/m f = 325 MHz 22 short cryos (2.5 meter, 2-cell cavity) 30 medium cryos (3.5 meter 4-cell cavity) 2.5 s beam envelope eN= 20 mm rad • x,y= 2.3 m • g = 2.1 • a = 15 cm eN= (2.5)2×eN_rms Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  7. 5 5 BETA_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 160 Initial Linac – Longitudinal Matching p = 255 MeV/c 1250 MeV beta functions Aacc= 20 MV/m f = 325 MHz Total RF installed: 1.513 GV 22 short cryos (2.5 meter, 2-cell cavity) 30 medium cryos (3.5 meter 4-cell cavity) Cavity off crest Synchrotron Tune Energy Bucket Area Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  8. 5 5 BETA_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 160 Initial Linac – Longitudinal Acceptance 1250 MeV p = 255 MeV/c beta functions Aacc= 20 MV/m f = 325 MHz Total RF installed: 1.513 GV 22 short cryos (2.5 meter, 2-cell cavity) 30 medium cryos (3.5 meter 4-cell cavity) Initial acceptance 150 mm (blue) Longitudinal compression Longitudinal acceptance eLong= 150 mm Dp/prms = 0.112 Dzrms = 10.3 cm eLong= (2.5)2×eLong_rms Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  9. RLA to 5 GeV 1.25 GeV 5 GeV 70 m 840 MeV/pass 650 MHz Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  10. 5 5 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 240 325 MHz – 650 MHz Transition 1.25 GeV p = 255 MeV/c A325 MHz= 20 MV/m A650 MHz= 25 MV/m beta functions 325 MHz linac 650 MHz linac μ±time structure RF bucket Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  11. 2 20 BETA_X&Y[m] DISP_X&Y[m] -2 0 0 BETA_X BETA_Y DISP_X DISP_Y 15.89 2 20 BETA_X&Y[m] DISP_X&Y[m] -2 0 0 BETA_X BETA_Y DISP_X DISP_Y 16.12 Delay/Compression Chicane q q Dz q q 5 free parameters needed to match: 2 betas + 2 alphas + disp. q q Q2 Q3 Q4 Q3 Q1 Q2 Q1 Q0 Q0 Q’3 Q’3 Q’0 Q’2 Q’0 Q’1 Q’1 Q’4 Q’2 Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  12. 2 15 BETA_X&Y[m] DISP_X&Y[m] -2 0 0 BETA_X BETA_Y DISP_X DISP_Y 173.953 Longitudinal Compression with M56 Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  13. RLA to 5 GeV 1.25 GeV 5 GeV 70 m 840 MeV/pass 650 MHz Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  14. Bi-sectedLinac Optics 5 15 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 35 5 15 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 70 ‘half pass’ , 1250-1625 MeV initial phase adv/cell 90 deg. scaling quads with energy quad gradient 4meter 90 deg. FODO cells 25 MV/m, 650 MHz, 2×4-cell cavity 1-pass, 1625-2475 MeV mirror symmetric quads in the linac quad gradient Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  15. 5 30 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 315 Multi-pass Linac Optics bx = 13.0 m by = 14.4 m ax=-1.2ay=1.5 bx = 7.9 m by = 8.7 m ax=-0.8ay=1.3 Arc 2 Arc 3 Arc 4 Arc 1 bx = 6.3 m by = 7.9 m ax=-1.2ay=1.3 bx,y → bx,y axy → - axy bx = 3.2 m by = 6.0 m ax=-1.1ay=1.5 bx,y → bx,y axy → - axy bx,y → bx,y axy → - axy bx,y → bx,y axy → - axy 4.175 GeV 1.25 GeV 1.625 GeV 2.475 GeV 3.325 GeV 5.025 GeV Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  16. Arc 1 and Arc 3 top view 1.625 GeV 3.325 GeV side view 1.625 GeV  1 m 3.325 GeV Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  17. Arc 1 and 3 – Optics 3 20 BETA_X&Y[m] DISP_X&Y[m] -3 0 0 BETA_X BETA_Y DISP_X DISP_Y 113.595 3 20 BETA_X&Y[m] DISP_X&Y[m] -3 0 0 BETA_X BETA_Y DISP_X DISP_Y 143.611 Arc 1 1.625 GeV 6 m cells 1 m dipoles 2 vertical steps 2 vertical steps Arc 3 3.325 GeV 8 m cells 2 m dipoles Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  18. Switchyard - Arc 1 and 3 1.625 GeV 3.325 GeV 1.625 GeV Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  19. Future Muon Facilities -Muon Acceleration n to Homestake Neutrino Factory LBNE Higgs Factory RLA to 63 GeV NF Decay Ring Linac + RLA to 5 GeV Project XStage III Project XStage II Project XStage I J.-P. Delahaye, MASS (Muon Accelerator Staging Studies) Fermilab Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  20. Higgs Factory: 5-pass RLA 5-63 GeV 5GeV 28.2 GeV 16.6 GeV 63 GeV 51.4 GeV 39.8 GeV 829 m 11.6 GeV/pass Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  21. Multi-pass Arc Muon RLA 5GeV (m±) 63 GeV 11.6 GeV/pass Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  22. Single- vs Multi- pass Droplet Arcs top view 16.6 GeV 39.8 GeV side view 16.6 GeV  1 m 39.8 GeV Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  23. Super-Cell Optics for P2/P1 = 2 • Each arc is composed of symmetric super cells consisting of linear combined-function magnets (each bend: 2.50) P 2xP Proof-of Concept Experiment: JEMMRLA -Jlab Electron Model of Muon RLA q = 600 Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  24. Summary • 5 GeV Neutrino Factory based on multi-pass ‘Dogbone’ RLA • Linac (255 MeV -1.25 GeV) Longitudinal Dynamics • Delay/Compression Chicane - Transition from 325 to 650 MHz SRF • RLA Optics (1.25 - 5 GeV ) - 4 droplet Arcs and multi-pass linac • Optimized RLA scheme for Higgs Factory • RLA with multi-pass arcs • Proof-of-Concept experiments: JEMMRLA and CBETA Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  25. Thank you for your Attention!Questions? Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  26. Backup Slides Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  27. 0.4-1.5 GeVLinac – Transmission Transmission: 1.4% loss Muon decay: 5% loss Total loss: 6.4% Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  28. Beam Loading J.S. Berg J.-P. Delahaye stored energy in a cavity: fractional reduction in the cavity voltage : RF gradient G defined as: fractional voltage reduction: Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  29. Multi-pass Linac – Bisected Optics E = 5-63 GeV Arc 2 Arc 1 Linac pass-1 Linac pass-2 Linac pass-3 RF f[MHz] cells/cavity Grad [MV/m] phase [deg] 650 5 25 22 Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  30. Arc Optics – Longitudinal Distortion 15 0.3 BETA_X&Y[m] DISP_X&Y[m] -0.3 0 303 BETA_X BETA_Y DISP_X DISP_Y 402.975 0 BETA_X BETA_Y DISP_X DISP_Y 100 15 0.3 BETA_X&Y[m] DISP_X&Y[m] -0.3 0 0 BETA_X BETA_Y DISP_X 3.34 E = 24 GeV M56 = -66.7 cm 2 half cells 15 cells out 2 half cells 2 empty cells 15 cells out 83 cells in 2 empty cells 900 FODO Quads L[cm] G[kG/cm] qF 80 10.2924 qD 80 -10.2788 Dipoles L[cm] B[kG] bend angle [deg] 50.00 49.3116 1.7647 Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  31. 300 60 C = 117.6 m Two-pass Arc Layout • Simple closing of arc geometry when using similar super cells • 1.2 / 2.4 GeV/c arc design used as an illustration can be scaled/optimized for higher energies preserving the factor of 2 momentum ratio of the two passes • Droplet arc: • 60 outward bend • 300 inward bend • 60 outward bend Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  32. ‘Droplet’ Arc - Spreader/Recombiner • First few magnets of the super cell have dipole field component only, serving as Spreader/Recombiner * Trajectories are shown to scale Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  33. A pair of 2-pass Arcs - Switchyard • Lower momentum arc is the most challenging because of the highest momentum ratio; have a solution but still plenty of room for optimization * Trajectories are shown to scale Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  34. Vertical Bypass Concept • 3xP • 4xP Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  35. ‘Pulsed’ quad Dogbone RLA 3 GeV 33 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 Workshop, Padua, Italy, July 1 - 3, 2018

  36. 100 5 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 254.651 100 5 DISP_X&Y[m] BETA_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 254.651 ‘Fixed’ vs ‘Pulsed’ linac Optics (8-pass) Fixed Pulsed Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

  37. 120 5 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 254.651 5 120 BETA_X&Y[m] DISP_X&Y[m] 0 0 0 BETA_X BETA_Y DISP_X DISP_Y 254.651 ‘Fixed’ vs ‘Pulsed’ linac Optics (12-pass) Fixed Pulsed Muon Collider Workshop, Padua, Italy, July 1 - 3, 2018

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