Berkeley Lab Generic Presentation

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Collider RingNonlinear Compensations
Alex Bogacz
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Muon Collider Ring at 1.5 TeV CM
Low Emittance MC Scenario
Energy 750 GeV Normalized emittance 2 mm
rad Relative momentum spread 0.005 Dipole
bending field 10 Tesla Quadruople gradient
250 Tesla/m Number of IRs 4 Betas at IR,
bx,y 10 mm Peak Luminosity/IP 7?1034 s-1
cm-2 (maximum allowed by the tune shift limit
New SBIR proposal with Muons Inc (submitted)
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IR Collider Ring Design Goals
Energy 750 GeV Low ?? 1 cm Small momentum
compaction factor ?c 10-5 Small circumference
4 km Momentum acceptance 0.005 Dynamic aperture
( gt 3? at normalized emittance 2 mm rad)
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Periodic FODO cell 135 deg. phase advance
phase adv./cell (Dfx 1350, Dfy1350)
Arc dipoles B100 gt 10
Tesla E0750000 gt 750 GeV rho 250
m N450 gt 200 Lcell1600 gt
16 m ang360/Ndip gt 0.45
deg. LbPIHrang/(180B) gt 196.5 cm
Arc quadrupoles Lcm GkG/cm 260
25.1 260 -25.1

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Quadrant Arc Momentum compaction
2 trans cells
2 trans cells
48 full cells
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Collider Ring layout
Circumference 3846 m
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IR - Linear lattice
bxmax 18,500 m bymax 18,600 m
bx 10 mm by 10 mm
13 m
8 m
Name Lcm GkG/cm DD1 290 -20.1 FF 510
18.2 DD2 290 -23.5
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IR - Beam Envelopes (srms)
eN 2 mm rad e 0.3 nm rad
13 m
8 m
bxmax 18,500 m bymax 18,600 m
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IR - matching to the Ring
bxmax 18,500 m bymax 18,600 m
IP
FF
FODO
doublet
bx 10 mm by 10 mm
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IR Dispersion wave (negative M56)
bxmax 18,500 m bymax 18,600 m
IP
FF
FODO
doublet
bx 10 mm by 10 mm
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IR - beta chromaticity
bxmax 36,000 m bymax 32,000 m
bx 5 mm by 5 mm
Dp/p 0.005
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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
  Matching region where dispersion is generated in
  a controlled fashion
• dipoles outside the IR so that D 0 but D ? 0
  at the IP

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Beta Chromaticity correction with sextupoles
(- I)
(- I) (- I) (- I)
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Beta Chromaticity correction with sextupoles
sS1 Lcm90 SkG/cm/cm)0.1
Tiltdeg0 sS2 Lcm90
SkG/cm/cm)-0.1 Tiltdeg0
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T126/T226 and T346/T446 correction with
sextupoles
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ELEGANT (Michael Borland) studies
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T126/T226 and T346/T446 correction with
sextupoles
1 turn uncorrected
initial
1 turn S10.1 S2-0.1
x x
y y
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Chromatic Aberrations and Mitigation schemes

• Chromatic aberrations
• Beta chromaticity in the IR
• Second order chromaticity and momentum
  compaction
• Mitigation schemes
• Localized Beta chromaticity correction with
  sextupoles in the IR-to-Arc matching sections
• Chromaticity correction in the Arcs (two
  families of sextupoles)
• Dynamic Aperture octupoles in the IR quads

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Chromaticity Compensation with two families of
Sextupoles
Dfy 3 1800
Cancellation of geometric aberrations generated
by sextupoles through pairing them with a minus
identity transformation between them
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Dynamic Aperture studies Multi turn tracking
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ELEGANT (Michael Borland) studies
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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 2nd order effects
• The 2nd order dispersion will be corrected with
  sextupoles in the matching section/Arcs

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Summary

• Proposed Optics design for the Collider Ring and
  IR - Linear Lattice
• Periodic dispersion achromat arcs
• Beta chromaticity corrections with sextuoples
  outside the FF region
• Natural chromaticity compensation with 2 families
  of orthogonal sextupoles
• Compact matching from IR to the arcs
• Ring parameters

Energy 750 GeV Total Length3880 m Tunes
Qx13.8043 Qy10.2107 Chromaticity
nuxp-4011.85 nuyp-2393.76 Momentum compaction
10-5
Dp/p 0.003