Collider Ring, Interaction Region – Lattice Design

Collider Ring, Interaction Region – Lattice Design Alex Bogacz Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Collider Ring at 1.5 TeV CM – Parameters Energy = 750 GeV Normalized emittance = 2 mm rad Relative momentum spread = 0.01 Dipole bending field = 10 Tesla Dipole bend radius = 250m Number of cells = 124 = 48 Cell length = 40 m Number of IRs = 4 IR straight length = 160 m Circumference = 2880 m Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Collider Ring layout Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Periodic FODO cell – 135 deg. phase advance phase adv./cell (Dfx= 1350, Dfy=1350) Arc dipoles: $B=100; => 100 kGauss $E0=750000; => 750000 MeV $rho = 250 m $Nin=4*12; => 48 $Ndip=8*$Nin; => 348 $Lcell=4000; => 40m $ang=360/$Ndip; => 0.9375 deg. $Lb=$PI*$Hr*$ang/(180*$B); => 409.4 cm Arc quadrupoles: L[cm] G[kG/cm] 200 11.9 200 -11.9 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Achromatic Arc Optics – Minimum dispersion pattern 4 cells (4×1350 = 3×1800) Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Collider Ring Quadrant - Lattice 10 cells Momentum compaction, a = 0.003 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Interaction Region at 1.5 TeV CM – Parameters Energy = 750 GeV 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 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

IR - Linear lattice bxmax = 36,000 m bymax = 32,000 m bx* = 5 mm by* = 5 mm 13 m 8 m Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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[kG/cm] DD1 290 -21.8 FF 510 18.6 DD2 290 -18.2 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

IR - Beam envelopes (srms) Peak Luminosity/IP 71034 s-1 cm-2 The maximum allowed by the tune shift limit. eN = 2.1 mm rad e = 0.3 nm rad 13 m 8 m bxmax = 36,000 m bymax = 32,000 m Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

IR - matching to the Ring bxmax = 36,000 m bymax = 32,000 m doublet FODO bx* = 5 mm by* = 5 mm Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

IR - matching to the Ring doublet FODO Name L[cm] G[kG/cm] F1 200 3.63 D1 200 14.1 F2 200 -13.2 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Collider Ring Quadrant Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Dfx = 3 1800 Dfy = 3 1800 Natural Chromaticity Compensation with two families of Sextupoles Cancellation of geometric aberrations generated by sextupoles through ‘pairing’ them with a minus identity transformation between them Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

IR - beta chromaticity bxmax = 36,000 m bymax = 32,000 m bx* = 5 mm by* = 5 mm Dp/p= 0.003 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Chromatic Compensation Block - Prototype R L L R Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Chromatic Compensation with Sextupoles correction with 3 sextupole families no sextupole corrections • Dispersion • Dispersion-prime • M56 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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 reducingadverse2nd order effects • The 2nd order dispersion will be corrected with sextupoles in the matching section/Arcs Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

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 GeV Total Length=2880 m Tunes: Qx=13.8043 Qy=10.2107 Chromaticity: nuxp=-4011.85 nuyp=-2393.76 Momentum compaction=0.003 Dp/p= 0.01 Muon Collider Design Workshop, BNL, Dec. 3-7, 2007

Collider Ring, Interaction Region – Lattice Design