Multiple Partial Siberian Snakesin the AGS

Junpei Takano

BRAHMS & PP2PP (p)

STAR (p)

PHENIX (p)

AGS

LINACBOOSTER

Pol. Proton Source500 mA, 300 ms

Spin Rotators

Solenoidal snakefor imperfection res.but produce coupling res.Achieved P=40% in 2003

SuperconductingSiberian Snakes

RHIC pC PolarimetersAbsolute Polarimeter (H jet)

RHIC

SuperconductingSiberian Snakes

Cold snake for imperfection res. and intrinsic res. Achieved P=65% in 2006 with Warm snake

Warm snake for imperfection res. Reduced coupling res. Achieved P=50% in 2004 and P=55% in 2005

0 10 20 30 40 504

6

8

10

12

14

16

18

20

22

24

Snak

e st

reng

th [

%]

G

CSNK_1.5T CSNK_2.0T CSNK_2.5T SSNK WSNK

Snake strength has energy dependence

Injection Extraction

Merit 1: large spin tune gapMerit 2: small spin mismatch

Double snake scheme

1

2: CSNK strength

: WSNK strength

A20:CSNK E20:WSNK

AGS

to RHIC

from Booster

120°

)}cos(2

{coscos1 1

Gsp

)}3

cos(2

sin2

sin)cos(2

cos2

{coscos1 21211

GGsp

← Spin tune Eq. for “single” snake

↓ Spin tune Eq. for “double” snake

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

4 5 6 7 8 9 10Ggamma

spin

tun

e

WSNK+CSNKWSNKIntrinsic res.

WSNK=8.4%CSNK=15%

12k±νy (νy = 8.9)

Injection energy

Large spin tune gap

Spin tune around first intrinsic resonance with 2 snakes

= 3m

Stable spin direction

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

0 10 20 30 40 50

AGS location

n_xn_yn_zmismatch

injinj ext

Spin mismatch

CSNK WSNK

CSNK@A20=20%, WSNK@E20=8%

Coldsnake%

vertcomp

Pol. at injection

0 1.000 80.00

5 0.997 79.75

10 0.988 79.02

15 0.972 77.79

20 0.951 76.09

25 0.924 73.91

30 0.891 71.28

Without Warm Snake(Cold Snake only)

Coldsnake%

vertcomp

Pol at injection

0 0.992 79.37

5 0.999 79.91

10 0.999 79.96

15 0.994 79.52

20 0.982 78.58

25 0.965 77.17

30 0.941 75.27

With 8% Warm Snake(Double snake)

Snake strength at “injection” energy

If the SSNK is relocated from I10 to I20....Spin tune gap will be larger.

)3

cos(2

sin2

sin)cos(2

cos2

cos2

{coscos1 213211

GGsp

)}3

cos(2

sin2

sin)3

cos(2

sin2

sin 1332 GG

SSNKI20←I10

A20:CSNK E20:WSNK

AGS

to RHIC

from Booster

1 2 3: CSNK strength : WSNK strength : SSNK strength( )

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

4 5 6 7 8 9 10

Ggamma

spin

tun

e WSNK+CSNK+SSNKWSNK+CSNKWSNKIntrinsic res.

Large spin tune gap

CSNK=16%

WSNK=8%

SSNK= 10%

Spin tune around first intrinsic resonance with 3snakes

CSNK=15%, WSNK=8%, SSNK=-7%

Stable spin direction

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

0 10 20 30 40 50

AGS location

n_xn_yn_zmismatch

injinj ext

SSNKWSNKCSNK

Spin mismatch with 3snakes

No spin mismatch

33100 33200 33300 33400 335000.00.20.40.60.81.01.21.41.61.82.0

Inte

nsit

y (1

e11)

run#

33100 33200 33300 33400 335000

1020304050607080

Pol

ariz

atio

n [%

]

Red: 10%CSNK+6%WSNKBlue: 6%CSNK+6%WSNK

Result in RUN6

Summary

The triple snake scheme was simulated. ・ Larger spin tune gap ・ No spin mismatch

6%CSNK+6%WSNK was operated. Achieved same level polarization to 10%CSNK +6%WSNK

If the 6%+6% machine is optimized, the polarization might be improved.

Extra slides

SSD at Ggamma=4.5

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

AGS location

spin

com

pon

ent

n_x

n_y

n_z

C15 H10 L20L20 A20 E20C20

4. Double partial snakes scheme

Spin mismatch

CSNK = 24% Injection energy

Vertical component at L20 = 0.930

SSD at Ggamma=4.5

-1.2-1

-0.8-0.6-0.4-0.2

00.20.40.60.8

11.2

AGS location

spin

com

pon

ent

n_x

n_y

n_z

C15 H10 I20 L20L20 A20 E20 I10C20

No spin mismatch

CSNK = 10%, WSNK = 6%, SSNK = 4% Extraction energy

Operation of SSNK for triple snake scheme

0%

10%

injection

extraction

ramp upS

SN

K s

tren

gth

%

-7.6%

4%

The current at injection is negative for no spin mismatch.Then the sign should be turned to positive to open the spin tune gap larger, but the bipolar PS is needed in this case.