Optics design for NICA collider · 2010. 10. 1. · x, ε y & σ p (σ s -fixed) until Collider Luminosity Increase ε x, ε y & σ p proportionally staying in the ring acceptance

0

Optics design for NICA collider

SKostromin OKozlov IMeshkov VMikhailov ASidorin JINR Dubna VLebedev SNagaitsev

FNAL Batavia Illinois USA YuSenichev IKP Juelich Germany

RuPAC 2010 2709-0110 г Протвино

Россия

1

Main requirements

from physics experiment


Россия

2

bull changeable experiment energy

for heavy ions collisions

Au + Au (45 35 15) GeVu

γ = 58 47 26

with luminosity ~1027 (at 45

GeVu)

bull operation with proton beams

(125 GeV - γ =143)

Possibility of variation of

gamma-tr ~3 divide 15

Main requirements


Objectives for optics design


Россия

3

Luminosity

232

2

1

22pyxyxyxyx

syy

xx

yxs

ip

YSC

SCD

C

A

NZrX

s

ip

SC

C

A

NZr

24 32

2

2

0

4

s

yx

ib HNnf

L

0

221

22

yx

dyexH

y

SCss

b

i

p

HnC

Nf

Zr

AL

0

2

32

2

For bunched beam with Gaussian distribution in all planes

For round beam smooth focusing and sufficiently small dispersion

For x = y

and head-on collisions the luminosity is

assuming x = y one obtains a luminosity limitation

limitation due to Beam Space Charge

- limits beam longitudinal density Ni s


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2

324

65228 SC

sssb

p

HC

n

rZ

cAL

4

For the case of fixed ring acceptance and circumference one should also exclude Ni That

results in

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

Small circumference C

Luminosity limitation due to Beam Space Charge

Short separation length Cnb Large value of σsβ

Large emittance =gt large acceptance

Large luminosity requires




Large acceptance

Small perimeter

Small beta-function at IP

Acceptable IBS rates


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5

Racetrack with 2 IPs

Optics optimized for Au+Au collisions at 45 GeVn

γtr asymp76

bull plusmn 45 m for particle detector

bull Phase advance 90deg per FODO-cell

bull Dispersion zeroing in straight sections

bull Vertical beam separation

bullTunes ~x44 (same as in FNAL Recycler)

(γ asymp58)

Slip factor

η=1γtr2-1γ2

asymp0013

Cross-section view of the NICA Collider dipole magnet


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6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~

- orbit compaction factor

(OCF)

where

Correlated change of

dispersion through the orbit

moves alfha close to zero

or to negative values

Построение laquoрезонансныхraquo магнитооптических структур с контролируемой критической энергией

ЮВ Сеничевa и АН Чеченинb

variation of gamma-trdecrease phase advance per cell

90deg-gt 60deg -gt 30deg

ldquoresonancerdquo optic structure with

variation of D through the ring

7

bull The solution of equation

bull with modulation of gradient and curvature

bull gives the expression for OCF

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS

variation of gamma-tr


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8

Regular structure

Modulated dispersion Modulated radius of curvature


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9

Regular structure

Modulated dispersion

12 Cell 90deg =gt Qxarc=3

4 Superperiods 3 Cell

Dy=0


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10

Cell dimensions

90deg phase advance for Au 45 GeVn


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11

Arc

12 cell x 90deg phase advance


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12

Dispersion suppression

-using special quads

gradients in edges cells

(possible to adjust for the

different γtr ie different

phase advance in arc)

bullD=0 due to 2πn ndash phase advance

per Arc


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13

Straight sections

bullβ at IP ~35 cm

bullvertical beam separation

bull enough space for non

structural equipment RF-

resonators PU for SC injection

spin rotatorshellip

bull keep total tune of the ring x44


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14

Straight sections


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15

Straight insertions in arcs

2π phase advance

bull additional space for non

structural equipment e-cooler

injection spin rotatorshellip


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16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


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17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


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18

Ring tune

x44

Tune diagram (fractional part) with sum resonances up to 12th order

bbsc 2 lt005


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19

Chromaticity correction

1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2

2 3 Au 35 Gevn Au 15 Gevn

All sextupoles in the arc (near each quad) are used for chromaticity

correction (24 total)

Sf1=0054 kGcm2

Sd1=-0085 kGcm2


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20


4 Protons 1245 GeV

Only sextupoles near central lenses (four families) in each superperiod

(where dispersion function are positive) are used

(16 total)

Sf1=0072 kGcm2 Sf2=0110 kGcm2

Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


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Dependence of the ring tune on dpp


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22

Dynamic aperture

helliptracking in MAD OptiM

Au 45 Gevn

Phase space at IP


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23

Dynamic aperture

Au 35 GevnPhase space at IP


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24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


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25

IBS

NICA Conceptual Proposal for Collider Valeri

Lebedev Fermilab January 11 2010

hellipTriplet focusing

looks preferable It

results in

essential increasing

IBS growth timehellip



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26

IBS rates were tested for full ring FODO- amp ODFDO- structures

VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610

IBS rates for full FODO- ring optics is ~60 from ODFDO- ring optics

Difference is due to

different straight

section structure



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27

bbsc 2 lt005

Adjust εx εy amp σp (σs -fixed) until

Collider Luminosity

Increase εx εy amp σp proportionally staying in the ring acceptance

Increase Ni ions in the bunch keeping bbsc 2 lt005

LuminosityIBS rates


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Россия

Collider Luminosity

Energy of the

experiment

Ion-ion and collisions Polarize

d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long

acceptance ppplusmn0005 plusmn0005

Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum

spread06middot10-3 13middot10-3 17middot10-3 12middot10-3

Particle per bunch

corresponding to

tune shift

Q = 005

04middot109 25middot109 49middot109 25middot1011

IBS growth time s 110 600 710 8700

Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29

Main Parameters of the NICA collider Energy of the experiment Ion-ion and ion-proton collisions Polarized

protons512 GeV

15 GeVn 35 GeVu 45 GeVu

Ring circumference m 5342

Transition energy γtr 32 58 76 68

Phase advance per cell deg 30 60 90 varied

Slippage factor 0051 0015 0013 0004

Betatron tune QxQy 844744 10441044 12441244 12441244

Number of bunches nbunch 26

bullTotal chromaticity of the ring(before correction) ξxξy

-288-275

-296-324

-383-366

-372-335

Ring acceptance mmmrad 200300 200200 4040 4070

Ring long acceptance pp plusmn0005 plusmn0005

Maximum acceptable RMS emittance xy mmmrad

1105 1106 1206 1106

RMS momentum spread 06middot10-3 13middot10-3 17middot10-3 12middot10-3

Particle per bunch corresponding to tune shift Q = 005


cm 35 35

Bunch length cm 60 60 60 60


Maximum achievable luminosity cm-2 s-1



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30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks

Classic optic structure

ldquoResonancerdquo optic structure for super-period



minkS-ν =gt maximum influence to orbit compaction factor

kS

10060

2

cellNS

3divide5 Cells per super-period

strs

ss

LLS

LS

Orbit compaction factorfor structure with str sec

33

bullD=0 at straight sections in resonance structure =gt 2πn ndashphase advance per Arc

Qxarc - integer

Sarc a- number of super-periods in Arc 1min arcarc kS

Sextupoles compensationSarc ndash even

Qxarc - odd arcarc

arc

arc S

S

2

2

Phase advance between Cells through Sarc2 super-periods

45 GeVn γ=58 =gt Qxarc γtr gt 6

Narc=2 =gt Qxarc=3 (γtr asympQx)

Min[Qxarc-1Sarc]=-1 =gt Sarc=4

32π ndash ph ad per super-per

3Cell 90deg - superperiod

34



35

Calc of Dynamic Aperture amp compensation of nonlinearities



NicaVAL4- ref point

Tracking in MAD

(XXrsquo) ndashphase plane at IP (YYrsquo) ndashphase plane at IP

Agreement between tracking in MAD and OptiM

(MAD used for further investigationshellip)

bull Large acceptance

36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB

Luminosity Limitation due to Beam-beam EffectsFor bunched beam with Gaussian distribution

For round beam =gt

Combining the above equation with the equation for space charge tune shift one obtains

For NICA parameters the space charge tune shift is significantly smaller than the tune shift due to beam space chargeSmall results small s and consequently small SCLarge value of s

results in phase averaging for high order resonances and significantly mitigates the beam-beam effects

37

38

39

NicaVAL4 Tunes vs dpp first and second order chromaticitycorrection

2

210

p

p

p

pbbsc

lt005 (depends on working

point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







1

Main requirements



Россия

2



Au + Au (45 35 15) GeVu

γ = 58 47 26


GeVu)


(125 GeV - γ =143)



Main requirements




Россия

3

Luminosity

232

2

1

22pyxyxyxyx

syy

xx

yxs

ip

YSC

SCD

C

A

NZrX

s

ip

SC

C

A

NZr

24 32

2

2

0

4

s

yx

ib HNnf

L

0

221

22

yx

dyexH

y

SCss

b

i

p

HnC

Nf

Zr

AL

0

2

32

2



For x = y






Россия

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

4


results in

2

324

65228 SC

sssb

p

HC

n

rZ

cAL









Large acceptance

Small perimeter




Россия

5



γtr asymp76






(γ asymp58)

Slip factor

η=1γtr2-1γ2

asymp0013



Россия

6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where











7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



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12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







2



Au + Au (45 35 15) GeVu

γ = 58 47 26


GeVu)


(125 GeV - γ =143)



Main requirements




Россия

3

Luminosity

232

2

1

22pyxyxyxyx

syy

xx

yxs

ip

YSC

SCD

C

A

NZrX

s

ip

SC

C

A

NZr

24 32

2

2

0

4

s

yx

ib HNnf

L

0

221

22

yx

dyexH

y

SCss

b

i

p

HnC

Nf

Zr

AL

0

2

32

2



For x = y






Россия

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

4


results in

2

324

65228 SC

sssb

p

HC

n

rZ

cAL









Large acceptance

Small perimeter




Россия

5



γtr asymp76






(γ asymp58)

Slip factor

η=1γtr2-1γ2

asymp0013



Россия

6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where











7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







3

Luminosity

232

2

1

22pyxyxyxyx

syy

xx

yxs

ip

YSC

SCD

C

A

NZrX

s

ip

SC

C

A

NZr

24 32

2

2

0

4

s

yx

ib HNnf

L

0

221

22

yx

dyexH

y

SCss

b

i

p

HnC

Nf

Zr

AL

0

2

32

2



For x = y






Россия

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

4


results in

2

324

65228 SC

sssb

p

HC

n

rZ

cAL









Large acceptance

Small perimeter




Россия

5



γtr asymp76






(γ asymp58)

Slip factor

η=1γtr2-1γ2

asymp0013



Россия

6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where











7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







4


results in

2

324

65228 SC

sssb

p

HC

n

rZ

cAL









Large acceptance

Small perimeter




Россия

5



γtr asymp76






(γ asymp58)

Slip factor

η=1γtr2-1γ2

asymp0013



Россия

6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where











7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







5



γtr asymp76






(γ asymp58)

Slip factor

η=1γtr2-1γ2

asymp0013



Россия

6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where











7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







6

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

1

cos11

)(

1

n

n nrR

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where











7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







7




ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

1

cos11

)(

1

n

n nrR

0

cos)(k

k kgk ε

])1(1[)1(4

11

12

2

2

2

k

ks r

kS

gR

kS



Россия

8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







8

Regular structure



Россия

9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







9

Regular structure




Dy=0


Россия

10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







10

Cell dimensions



Россия

11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







11

Arc



Россия

12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







12








per Arc


Россия

13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







13

Straight sections

bullβ at IP ~35 cm





spin rotatorshellip



Россия

14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







14

Straight sections


Россия

15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







15


2π phase advance





Россия

16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







16

Full optics

5342m

perimeter

ξx= -38

ξy= -37

ξx= -29

ξy= -32


Россия

17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







17

ξx= -29

ξy= -28

ξx= -37

ξy= -34

Full optics

5342m

perimeter


Россия

18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







18

Ring tune

x44


bbsc 2 lt005


Россия

19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







19


1 Au 45 Gevn

Two families of

sextupoles

(16 total)

Sf1=0154 kGcm2

Sd1=-0264 kGcm2




Sf1=0054 kGcm2

Sd1=-0085 kGcm2


Россия

20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







20


4 Protons 1245 GeV



(16 total)


Sd1=-0207 kGcm2 Sd2=-0284 kGcm2


Россия

21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







21



Россия

22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







22

Dynamic aperture


Au 45 Gevn

Phase space at IP


Россия

23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







23

Dynamic aperture



Россия

24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







24

Dynamic aperture

Protons 1245 Gevn

Phase space at IP


Россия

25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







25

IBS




looks preferable It

results in





Россия

26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







26


VAL4 optics

V Lebedev

Lring=4542м

45 53

nb=20

60 112

060

179 75

551120 580

622

-0026

-0039

-0007

-0010

6046

ODFDO Au

full optics

Lring=39246м

Fit to VAL4

45 53

nb=20

60 086

086

189 38

761320 580

864

-0026

-0031

-0008

-0008

6628

ODFDO Au

full optics

Lring=4022м

45 53

nb=20

60 090

079

158 45

80770 580

835

-0028

-0034

-0008

-0009

6624

FODO Au full

optics

Lring=36326м

Fit to VAL4

45 53

nb=20

60 114

076

162 45

54890 580

695

-0021

-0029

-0007

-0008

6629

FODO Au full

optics

Lring=37430м

45 53

nb=20

60 093

089

146 45

90560 580

713

-0024

-0030

-0008

-0008

6628

FODO Au full

optics

Lring=34350м

45 53

nb=20

60 126

077

169 101

63760 580

683

-0019

-0026

-0006

-0008

6610



different straight

section structure



Россия

27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







27

bbsc 2 lt005


Collider Luminosity



LuminosityIBS rates


Россия

28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







28


Россия

Collider Luminosity

Energy of the

experiment


d

protons

512

GeV

15

GeVn

35

GeV

u

45

GeVu

Ring acceptance

mmmrad300300 200200 4040 4070

Ring long


Maximum

acceptable RMS

emittance εxεy

mmmrad

1105 1106 1206 1106

RMS momentum


Particle per bunch

corresponding to

tune shift

Q = 005



Maximum

achievable

luminosity cm-2 s-1


scaling

2

324

65228 SC

sssb

p

HC

n

rZ

cAL

29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







29


protons512 GeV









-288-275

-296-324

-383-366

-372-335




1105 1106 1206 1106




cm 35 35






Россия

30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







30

31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







31

Thank you

32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







32

RD 2

RD

2

1

)3(

])1(1[2

1

])1(1)[1(2

1

14

1

])1(1)[1(4

11

1

2

2

2

2

2

22

24

2

jirgO

kS

grR

kSkS

grR

kS

r

kSkS

gR

j

k

i

k

k

kk

k

kk

k

k

k

ks






kS

10060

2

cellNS


strs

ss

LLS

LS


33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







33


Qxarc - integer



Qxarc - odd arcarc

arc

arc S

S

2

2







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







34



35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







35




NicaVAL4- ref point

Tracking in MAD





36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







36

y

x

yx

ip

YBB

BB

A

NZrX

1

11

4

2

2

2

2

1

4

2

2

2

A

NZr ip

BB

22 12

C

sSCBB


For round beam =gt




37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







37

38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







38

39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







39


2

210

p

p

p

pbbsc


point location)

40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







40

41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







41

42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







42

ρ(s)

D=k(s)K(s)+ds

Dd

1

2

2

p

eG(s)K(s)

p

G(s)ek(s)

C

dss

sD

C )(

)(1

0

cos)(k

k kgk ε

dkGp

egk cos

1 sLs 2

1

cos11

)(

1

n

n nrR

dnR

rn

)(

cos

)(~

)( DDD

))(~1(1

)(

1

r

R R

rD

R

D )(~)(~


(OCF)

where





with

where







Documents

Optics design for NICA collider · 2010. 10. 1. · x, ε y & σ p (σ s -fixed) until Collider Luminosity Increase ε x, ε y & σ p proportionally staying in the ring acceptance