Neutrino Factory Facility Overview Alex Bogacz Collider Ring

Neutrino Factory – Facility Overview, Alex Bogacz Collider Ring, Interaction Region – Lattice Design Alex Bogacz Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy

Neutrino Factory – Facility Overview, Alex Bogacz Collider Ring at 1. 5 Te. V CM – Parameters Energy = 750 Ge. V Normalized emittance = 2 mm rad Relative momentum spread = 0. 01 Dipole bending field = 10 Tesla Dipole bend radius = 250 m Number of cells = 12 4 = 48 Cell length = 40 m Number of IRs = 4 IR straight length = 160 m Circumference = 2880 m Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy

Neutrino Factory – Facility Overview, Alex Bogacz Collider Ring layout Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Periodic FODO cell – 135 deg. phase advance phase adv. /cell (Dfx= 1350, Dfy=1350) Arc dipoles: $B=100; => $E 0=750000; => $rho = 250 m 100 k. Gauss 750000 Me. V $Nin=4*12; => $Ndip=8*$Nin; => $Lcell=4000; => $ang=360/$Ndip; => 48 348 Arc quadrupoles: L[cm] 200 G[k. G/cm] 11. 9 -11. 9 40 m 0. 9375 deg. $Lb=$PI*$Hr*$ang/(180*$B); => 409. 4 cm Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Achromatic Arc Optics – Minimum dispersion pattern 4 cells (4× 1350 = 3× 1800) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Collider Ring Quadrant - Lattice 10 cells Momentum compaction, a = 0. 003 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Interaction Region at 1. 5 Te. V CM – Parameters Energy = 750 Ge. V Number of IRs = 4 Peak Luminosity/IRI = 7 1034 s-1 cm-2 Normalized emittance = 2 mm rad Relative momentum spread = 0. 01 Betas at IR, b*x, y = 5 mm Final Focus Quad strength = 250 Tesla/m Peak betas, bmaxx, y = 36/32 km IR straight length = 160 m Circumference = 2880 m Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy

Neutrino Factory – Facility Overview, Alex Bogacz IR - Linear lattice bxmax = 36, 000 m bymax = 32, 000 m bx* = 5 mm by* = 5 mm 13 m 8 m Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz IR - Final Focus Quads bxmax = 36, 000 m bymax = 32, 000 m bx* = 5 mm by* = 5 mm 13 m 8 m Name L[cm] G[k. G/cm] DD 1 FF DD 2 290 510 290 -21. 8 18. 6 -18. 2 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz IR - Beam envelopes (srms) Peak Luminosity/IP 7 1034 s-1 cm-2 The maximum allowed by the tune shift limit. e. N = 2. 1 mm rad e = 0. 3 nm rad 13 m 8 m bxmax = 36, 000 m bymax = 32, 000 m Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz IR - matching to the Ring bxmax = 36, 000 m bymax = 32, 000 m doublet FODO bx* = 5 mm by* = 5 mm Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz IR - matching to the Ring doublet FODO Name L[cm] G[k. G/cm] F 1 D 1 F 2 200 200 3. 63 14. 1 -13. 2 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz IR - matching to the Ring doublet FODO Name L[cm] G[k. G/cm] F 1 D 1 F 2 200 200 3. 63 14. 1 -13. 2 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Collider Ring Quadrant Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Chromatic Aberrations and Mitigation schemes Chromatic aberrations beta chromaticity in the IR natural chromaticity of the collider ring Mitigation schemes Chromaticity correction in the Arcs (two families of sextupoles) Sextupoles in the IR quads Dynamic Aperture – octupoles in the IR quads Localized Chromatic corrections outside the IR Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy

Neutrino Factory – Facility Overview, Alex Bogacz Natural Chromaticity Compensation with two families of Sextupoles Dfx = 3 1800 Dfy = 3 1800 Cancellation of geometric aberrations generated by sextupoles through ‘pairing’ them with a minus identity transformation between them Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz IR - beta chromaticity bxmax = 36, 000 m bymax = 32, 000 m bx* = 5 mm by* = 5 mm Dp/p= 0. 003 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Beta Chromaticity IR beta functions strongly vary for off momentum particles It is measured by the beta chromaticity functions: or by is the so called ‘envelope’ dispersion Typical values of the w-functions ~ 100, need to be ~10 Could be corrected with sextupoles placed in the FF quads (not in a the Arcs) - dispersion must be generated/controlled in IR dipoles in the IR so that D = D ‘= 0 at the IP dipoles outside the IR so that D = 0 but D ‘ 0 at the IP Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Chromatic Compensation Concepts (S. Derbenev) Optimize the IR to provide the smallest beta star – no correcting multipoles Use a long section of the beam extension/matching for the chromatic compensations (i. e. insertion of a Compensating Block (CB) before the IR). Design a chicane (snake) CB with a special Optics (to introduce dispersion) Design a symmetric quadrupole/sextupole lattice of the CB self-compensated for emittance and squared momentum spread parasitic effects of sextupoles Compensation for higher order effects (spherical aberrations, the third order forces…) Expansion of the s-Hamiltonian (2 -nd, 3 -rd, 4 -th order terms) Reduction of tuning equations Compensation for aberrations with multipoles Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Chromatic Compensation Block - Prototype L R R L Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Chromatic Compensation with Sextupoles no sextupole corrections correction with 3 sextupole families ·Dispersion-prime ·M 56 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Dynamic Aperture Considerations Large cross-detuning makes the dynamic aperture small – octupole corrections may be necessary Due to larger dispersion at IR sextupoles the requires sextupole gradient is lower reducing adverse 2 nd order effects The 2 nd order dispersion will be corrected with sextupoles in the matching section/Arcs Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007

Neutrino Factory – Facility Overview, Alex Bogacz Summary Proposed Optics design for the Collider Ring and IR - Linear Lattice Periodic dispersion achromat arcs Natural chromaticity compensation with 2 families of orthogonal sextupoles Compact matching from IR to the arcs Uniform focusing periodicity Ring parameters: Energy = 750 Ge. V Total Length=2880 m Dp/p= 0. 01 Tunes: Qx=13. 8043 Qy=10. 2107 Chromaticity: nuxp=-4011. 85 nuyp=-2393. 76 Momentum compaction=0. 003 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Muon Collider Design Workshop, BNL, Dec. 3 -7, 2007