Collider Ring, Interaction Region – Lattice Design

Operated by JSA for the U.S. Department of Energy

Thomas Jefferson National Accelerator Facility

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

Neutrino Factory – Facility Overview, Alex Bogacz

Collider Ring, Interaction Region – Lattice

Design

Alex Bogacz





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 = 124 = 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

Collider Ring - footprint

-90000

-70000

-50000

-30000

-10000

10000

-40000 -20000 0 20000 40000 60000

z [cm]

x [cm]





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

400

Mon Dec 03 17:08:35 2007 OptiM - MAIN: - D:\Muon Collider\750GeV Ring\135deg cell_new\cell.opt

12

00

7-7

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y 400

Mon Dec 03 17:09:05 2007 OptiM - MAIN: - D:\Muon Collider\750GeV Ring\135deg cell_new\cell.opt

0.5

0P

HA

SE

_X

&Y

Q_X Q_Y

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





Achromatic Arc Optics – Minimum dispersion pattern

4 cells (4×1350 = 3×1800)

1600

Mon Dec 03 17:31:43 2007 OptiM - MAIN: - D:\Muon Collider\750GeV Ring\135deg cell_new\super_per.opt

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&Y

[m]

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BETA_X BETA_Y DISP_X DISP_Y

1600

Mon Dec 03 17:36:44 2007 OptiM - MAIN: - D:\Muon Collider\750GeV Ring\135deg cell_new\spr.opt

12

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Collider Ring Quadrant - Lattice

7200

Mon Dec 03 22:17:40 2007 OptiM - MAIN: - D:\Muon Collider\750GeV Ring\135deg cell_new\quadrant.opt

14

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30

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Momentum compaction, = 0.00356

dip dip dip totxx x rad x rad

D sM ds D d D d D

3562 1.6

3 102880

mML m

10 cells





Energy = 750 GeV

Number of IRs = 4

Peak Luminosity/IRI = 71034 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





13961

Wed Feb 14 11:10:33 2007 OptiM - MAIN: - D:\Muon Collider\IR\5mm\IR_sym.opt

40

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IR Linear lattice

xx* = 5 mmyy* = 5 mm

xxmax = 36,000 m

yymax = 32,000 m

8 m

2

2max * 2 max *

*

( )

,

tripltripl

ss

ff

13 m





13961


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IR Final Focus Quads


xxmax = 36,000 m

yymax = 32,000 m

8 m

13 m

Name L[cm] G[kG/cm]

DD1 290 -21.8FF 510 18.6DD2 290 -18.2





13961


0.5

0

0.5

0

Siz

e_

X[c

m]

Siz

e_

Y[c

m]

Ax_bet Ay_bet Ax_disp Ay_disp

IR Beam envelopes (rms)

NN = 2.1 m rad

= 0.3 nm rad

8 m

13 m

xxmax = 36,000 m

yymax = 32,000 m

Peak Luminosity/IP 71034 s-1 cm-2

The maximum allowed by the tune shift limit.






199.60


40

00

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&Y

[m]

DIS

P_

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Y[m

]


xxmax = 36,000 m

yymax = 32,000 m

doublet FODO

IR - matching to the Ring





199.60


40

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Y[m

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doublet FODO


Name L[cm] G[kG/cm]

F1 200 3.63 D1 200 14.1 F2 200 -13.2





doublet FODO


Name L[cm] G[kG/cm]

F1 200 3.63 D1 200 14.1 F2 200 -13.2

199.60


20

00

60

0

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[m]

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Collider Ring Quadrant

7200


14

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[m]

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819.80

Tue Dec 04 01:01:00 2007 OptiM - MAIN: - D:\Muon Collider\750GeV Ring\135deg cell_new\IR_R_arc.opt

36

00

00

30

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[m]

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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





7200


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Cancellation of geometric aberrations generated by sextupoles through ‘pairing’ them with a minus identity

transformation between them

Natural Chromaticity Compensation with two families of Sextupoles

x = 3 1800 y = 3 1800





IR - beta chromaticity


xxmax = 36,000 m

yymax = 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

2 2

,

1,

,

xx x x

p x p

x xx p

x x x

a

b

w a b

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

17.620

Mon Sep 24 08:55:05 2007 OptiM - MAIN: - D:\SBIR\chicane\jog_NP.opt

50

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L R R L

4.810

Mon Sep 24 09:33:19 2007 OptiM - MAIN: - D:\SBIR\chicane\straight.opt

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BETA_X BETA_Y DISP_X DISP_Y17.620

Mon Sep 24 08:44:53 2007 OptiM - MAIN: - D:\SBIR\chicane\jog_PN.opt

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Chromatic Compensation with Sextupoles

0.1 0.05 0 0.05 0.110

0

10

20

DeltaP/P

x [c

m]

p1 p2

0.05 0 0.0510

0

10

20

DeltaP/Px

[cm

]

p1 p2

0.1 0.05 0 0.05 0.10.04

0.02

0

0.02

DeltaP/P

x ' [

cm]

p1 p2

0.05 0 0.05

0.02

0

DeltaP/P

x ' [

cm]

p1 p2

0.1 0.05 0 0.05 0.120

10

0

10

DeltaP/P

s [c

m]

p1 p2

0.05 0 0.0520

10

0

10

DeltaP/P

s [c

m]

p1 p2

Dispersion

Dispersion-prime

M56

correction with 3 sextupole familiesno 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

Documents

Collider Ring, Interaction Region – Lattice Design