# Presentation: 846988

## Collider Ring, Interaction Region – Lattice Design

- Alex Bogacz

## Collider Ring at 1.5 TeV CM – Parameters

**Energy = 750 GeV ****	**
**Normalized emittance = 2 ********m 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

- Collider Ring at 1.5 TeV CM – Parameters

## Collider Ring layout

## Periodic FODO cell – 135 deg. phase advance

**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

- phase adv./cell (x= 1350, y=1350)

## Achromatic Arc Optics – Minimum dispersion pattern 

- 4 cells (4×1350 = 3×1800)

## Collider Ring Quadrant - Lattice

- Momentum compaction,  = 0.003

- 10 cells

## Interaction Region at 1.5 TeV CM – Parameters

**Energy = 750 GeV ****	**
**Number of  IRs  =  4**
**Peak Luminosity/IRI  =  7********10****34 ****s****-1 ****cm****-2**
**Normalized emittance = 2 ********m rad**
**Relative momentum spread = 0.01**
**Betas at IR, *************x,y**** =  5 mm**
**Final Focus Quad strength = 250 Tesla/m**
- Peak betas, maxx,y =  36/32 km
- IR straight length = 160 m
- Circumference = 2880 m

- Interaction Region at 1.5 TeV CM – Parameters

## IR Linear lattice 

**IR ********Linear lattice **

- x* = 5 mm
- y* = 5 mm

- xmax = 36,000 m
- ymax = 32,000 m

- 8 m

- 13 m

## IR Final Focus Quads 

**IR ********Final Focus Quads **

- x* = 5 mm
- y* = 5 mm

- xmax = 36,000 m
- ymax = 32,000 m

- 8 m

- 13 m

**Name ****	****L[cm] ****	****G[kG/cm]**
- DD1 	290 	-21.8
- FF 	510 	18.6
- DD2 	290 	-18.2

## IR Beam envelopes (rms)

**IR ********Beam envelopes (********rms****)**

- N = 2.1 m rad
-  = 0.3 nm rad

- 8 m

- 13 m

- xmax = 36,000 m
- ymax = 32,000 m

- Peak Luminosity/IP 	 71034 s-1 cm-2
- The maximum allowed by the tune shift limit.

## IR - matching to the Ring 

- y* = 5 mm

- xmax = 36,000 m
- ymax = 32,000 m

- doublet

- FODO

**IR - matching to the Ring **

## IR - matching to the Ring 

- doublet

- FODO

**IR - matching to the Ring **

**Name ****	****L[cm] ****	****G[kG/cm]**
- F1 	200 	3.63
- D1 	200 	14.1
- F2 	200 	-13.2

## IR - matching to the Ring 

- doublet

- FODO

**IR - matching to the Ring **

**Name ****	****L[cm] ****	****G[kG/cm]**
- F1 	200 	3.63
- D1 	200 	14.1
- F2 	200 	-13.2

## Collider Ring Quadrant 

## 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

## 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

## IR - beta chromaticity 

- x* = 5 mm
- y* = 5 mm

- xmax = 36,000 m
- ymax = 32,000 m

- p/p= 0.003

## 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

## 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

## Chromatic Compensation Block  Prototype

- L

- R

- R

- L

## Chromatic Compensation with Sextupoles 

- Dispersion
- Dispersion-prime
- M56

- correction with 3 sextupole families

- no sextupole corrections

## 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

## 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

- p/p= 0.01