Collider Ring—Nonlinear Compensations

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

Thomas Jefferson National Accelerator Facility

NFMCC Meeting, Fermilab, March 20, 2008

Collider Ring—Nonlinear Compensations , Alex Bogacz

Collider Ring—Nonlinear Compensations

Alex Bogacz





Energy = 750 GeV

Normalized emittance = 2 m rad

Relative momentum spread =

±0.005

Dipole bending field = 10 Tesla

Quadruople gradient = 250 Tesla/m

Number of IRs = 4

Betas at IR, *x,y = 10 mm

Peak Luminosity/IP = 71034 s-1 cm-

2

(maximum allowed by the tune

shift limit

Muon Collider Ring at 1.5 TeV CM

Low Emittance MC Scenario:

*New SBIR proposal with Muons Inc (submitted)





Energy = 750 GeV

Low = 1 cm

Small momentum compaction factor c ~ 10-5

Small circumference ~ 4 km

Momentum acceptance ±0.005

Dynamic aperture ( > 3 at normalized

emittance = 2 m rad)

IR Collider Ring – Design Goals





160

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0.5

0P

HA

SE

_X

&Y

Q_X Q_Y

Periodic FODO cell – 135 deg. phase advance

4

222

2

102.2sin

cellNL

Larcsp

Arc dipoles: $B=100; => 10 Tesla$E0=750000; => 750 GeV$rho = 250 m

$N=4*50; => 200

$Lcell=1600; => 16 m

$ang=360/$Ndip; => 0.45 deg.

$Lb=$PI*$Hr*$ang/(180*$B); => 196.5

cm

Arc quadrupoles:

L[cm]

G[kG/cm] 260 25.1

260 -25.1

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

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60

0

0.3

-0.3

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y

56xDM ds





Quadrant Arc – Momentum compaction

56dip dip dip totxx x rad x rad

D sM ds D d D d D

3562 0.14

2.2 103846

mML m

48 full cells

2 trans cells 2 trans cells

320176

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60

0

0.3

-0.3

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]

BETA_X BETA_Y DISP_X DISP_Y1440


60

0

0.3

-0.3

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]


3562 1.5

2.5 103846

mML m





Collider Ring layout

Collider Ring - footprint

-90000

-70000

-50000

-30000

-10000

10000

-40000 -20000 0 20000 40000 60000

z [cm]

x [cm]

Circumference = 3846 m





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20

00

00

50

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


IR Linear lattice

xx* = 10 mmyy* = 10 mm

xxmax = 18,500 m

yymax = 18,600 m

8 m

2

2max * 2 max *

*

( )

,

tripltripl

ss

ff

13 m

Name L[cm] G[kG/cm]

DD1 290 -20.1FF 510 18.2DD2 290 -23.5





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0.3

0

0.3

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 m rad

= 0.3 nm rad

8 m

13 m

xxmax = 18,500 m

yymax = 18,600 m





doublet FODO

IR - matching to the Ring

xx* = 10 mmyy* = 10 mm

xxmax = 18,500 m

yymax = 18,600 m

FF

283.680

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20

00

00

2-2

BE

TA_

X&

Y[m

]

DIS

P_

X&

Y[m

]


IP





doublet FODO

IR – Dispersion wave (negative M56)

283.680

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20

00

00

2-2

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


xx* = 10 mmyy* = 10 mm

xxmax = 18,500 m

yymax = 18,600 m

FFIP





IR - beta chromaticity

xx* = 5 mmyy* = 5 mm

xxmax = 36,000 m

yymax = 32,000 m

p/p= ±0.005





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 Matching region where

dispersion is generated in a controlled fashion

dipoles outside the IR so that D = 0 but D ‘ 0 at the IP





Beta Chromaticity correction with sextupoles

2400

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0.5

0P

HA

SE

_X

&Y

Q_X Q_Y

(- I)(- I) (- I) (- I) (- I)(- I) (- I) (- I)

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20

00

00

2-2

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]






Beta Chromaticity correction with sextupoles

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20

00

00

2-2

BE

TA

_X

&Y

[m]

DIS

P_

X&

Y[m

]


sS1 sS1 L[cm]=90 L[cm]=90 S[kG/cm/cm)]=0.1S[kG/cm/cm)]=0.1 Tilt[deg]=0Tilt[deg]=0sS2 sS2 L[cm]=90 L[cm]=90 S[kG/cm/cm)]=-0.1 S[kG/cm/cm)]=-0.1 Tilt[deg]=0Tilt[deg]=0





961.60

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20

00

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2-2

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_X

&Y

[m]

DIS

P_

X&

Y[m

]


×4

T126/T226 and T346/T446 correction with sextupoles

ELEGANT (Michael Borland) studies





T126/T226 and T346/T446 correction with sextupoles

0.005-0.005 X [cm] View at the lattice beginning

1-1

X`[

mra

d]

0.005-0.005 Y [cm] View at the lattice end

1-1

Y`[

mra

d]

0.005-0.005 X [cm] View at the lattice end

1-1

X`[

mra

d]

0.005-0.005 Y [cm] View at the lattice beginning

1-1

Y`[

mra

d]


1-1

Y`[

mra

d]


1-1

Y`[

mra

d]

initial 1 turn uncorrected 1 turn: S1=0.1 S2=-0.1

x x’

y y’





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





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

transformation between them

Chromaticity Compensation with two families of Sextupoles

x = 3 1800

y = 3 1800

320176


600

0.3

-0.3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]

BETA_X BETA_Y DISP_X DISP_Y1440


600

0.3

-0.3

BE

TA_X

&Y

[m]

DIS

P_X

&Y

[m]






Dynamic Aperture studies – Multi turn tracking

961.60

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_X

&Y

[m]

DIS

P_

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]


×4

ELEGANT (Michael Borland) studies





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

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 Length=3880 m

Tunes: Qx=13.8043 Qy=10.2107

Chromaticity: nuxp=-4011.85 nuyp=-2393.76

Momentum compaction ~ 10-5

p/p= 0.003

Documents

Collider Ring—Nonlinear Compensations