Thomas RoserJ-Parc workshop

November 30, 2005

Possibility for polarized beam at J-PARCSummary of Satellite Workshop on Polarized Proton Beam at J-PARC

Satellite Workshop Program:Overview of the status of J-PARC (Shin'ya Sawada)Feasibility of Polarized Proton Beam at J-PARC (Hikaru Sato)Overview and Source, RCS (Thomas Roser )50 GeV Main Ring numerical studies (Alfredo Luccio)Polarimeter (Kazu Kurita)

Spin dynamic overview

AGS experience with strong partial snake

Possible plans for J-Parc

Spin Dynamics in Rings

Precession Equation in Laboratory Frame:(Thomas [1927], Bargmann, Michel, Telegdi [1959])

dS/dt = - (e/m) [(1+GB + (1+G) BII ] S

Lorentz Force equation:

dv/dt = - (e/m) [ B ] v

• For pure vertical field:Spin rotates Gtimes faster than motion, sp = G

• For spin manipulation:At low energy, use longitudinal fieldsAt high energy, use transverse fields

Spin tune and Depolarizing Resonances

Depolarizing resonance condition:

Number of spin rotations per turn = Number of spin kicks per turn

Imperfection resonance (magnet errors and misalignments):

G = sp = n

Intrinsic resonance (Vertical focusing fields):

G = sp = Pn ± Qy

P: Superperiodicity [AGS: 12]Qy : Betatron tune [AGS: 8.75]

Weak resonances: some depolarizationStrong resonances: partial or complete spin flip

Illustration by W.W. MacKay

Siberian Snakes (Local Spin Rotators)

cos(180 sp) = cos(/2) · cos(180 G)

0 sp n

No imperfection resonancesPartial Siberian snake (AGS)

= 180 sp = ½No imperfection resonances andNo Intrinsic resonancesFull Siberian Snake(Ya.S. Derbenev and A.M. Kondratenko)

Two Siberian Snakes in RHIC

(Naïve) Limits for Siberian Snakes

Spin rotation of Siberian snake () > Spin rotation of driving fields ()“Spin rotation of Siberian snake drives strong imperfection resonance”

Imperfection resonances Energy

Intrinsic resonances Energy

Partial Siberian snake (AGS, = 9° ) < /360°

One full snake < 1/2

Two full snakes (RHIC) < 1

N full snakes (LHC? N 16) < N/2

RHIC – first polarized hadron collider

BRAHMS

STAR

PHENIX

AGS

LINACBOOSTER

Pol. H- Source

Spin Rotators(longitudinal polarization)

Solenoid Partial Siberian Snake

Siberian Snakes

200 MeV Polarimeter Internal Polarimeter

Rf Dipole

pC PolarimetersAbsolute Polarimeter (H jet)

pC Polarimeter

25% Helical Partial Siberian Snake

5% Helical Partial Siberian Snake

PHOBOS

Spin Rotators(longitudinal polarization)

Spin flipper

Siberian Snakes

Without Siberian snakes: sp = G = 1.79 E/m ~1000 depolarizing resonancesWith Siberian snakes (local 180 spin rotators): sp = ½ no first order resonances

Achieved ~ 50% beam polarization at 100 GeVAchieved ~ 30% beam polarization at 205 GeV on first try!

High intensity polarized H- source

KEK OPPISupgraded at TRIUMF

80 - 85 % Polarization

151011 protons/pulse at source

61011 protons/pulse at end of LINAC

Proton polarization at the AGS

• Full spin flip at all imperfection and strong intrinsic resonances using partial Siberian snake and rf dipole

• Ramp measurement with new AGS pC CNI polarimeter:

• Remaining polarization loss from coupling and weak intrinsic resonances

• New helical partial snake (RIKEN funded) eliminated coupling resonances

• Strong super-conducting helical partial snake will eliminate all depolarization.

raw

asy

mm

etry

= A

N ·

PB

19972000200220032004

Simulation and measurement at 25 GeV

2005: 55%, 1x1011 ppb

Strong Partial Siberian Snake in AGS

desired vertical betatron tune to avoid depolarization

partial snake resonance

Pola

riza

tion

Challenges:1. SC element in warm machine2. Lattice disturbances

Intrinsic resonance

Imperfection resonance

cos(180 sp) = cos(/2) · cos(180

G)

Multiple partial Siberian snakes

Gsp cos2/coscos1 1

Gm

mGsp

)2(cos

2sin

2sincos

2cos

2coscos

1 21211

Single partial snake rotating by angle

Two partial snakes rotating by angle andand separated by 1/m of ring:

Max. effective snake strength at G = mn: (n: integer)Min. effective snake strength at G = mn + m/2:

For max. strength at intrinsic resonances m needs to be a common factor of both vertical tune and super-periodicity (G = Pn ± y)

To avoid minimum strength at imperfection resonances m needs to be an odd integer.

Two partial Siberian snakes in the AGS (J-PARC MR)

GGsp 3cos

2sin

2sincos

2cos

2coscos

1 21211

Vertical tune ~ 9 (21), super-periodicity = 12 (3) m = 3

Two partial snakes rotating by angle andand separated by 1/3 of ring:

Max. effective snake strength at G = 3n (energy of AGS intrinsic resonances): tot =

Min. effective snake strength at G = 3n + 1.5 (energy of AGS injection/extraction): tot =

At this energy the stable spin direction is close to vertical, which simplifies spin matching. Two equal partial snakes give perfect spin matching.

Warm helical partial Siberian snake

Replaced solenoidal partial snake Same design as cold snake (dual pitch) 1.5 Tesla field ~ 6 % partial snake (w/o generating

coupling) Funded by RIKEN, built by Takano

Ind.

25 % AGS super-conducting helical snake

Completed helical dipole coil

Correction solenoid and dipoles

Measured twist angle2 deg/cm in the middle~ 4 deg/cm at ends

Vertical component of stable spin

Fractional part ofspin tune

Injection First intrinsic resonance (0+)G

Two partial snakes in the AGSD

evia

tion

fro

m in

tege

r

Tune Measurement on Ramp (Haixin Huang)

(Jeff Wood)

3 6+ y

3 7+ y

3 5+ y

4 8-

y

2 4+ y

3 6-

y

1 2+ y

0 + y

1 + y

-1+ y

8.98

2T+1.53T Snake:Spin tune (7)=.957Spin tune (8)=.957Spin tune (9)=.925

Tune Scan around 36+ (2T+1.53T) (Haixin Huang)

The vertical tune should be > 9.985 for 2T case.For tune range of 8.90-8.96, the depolarization is a combination of 36+nu and 37+.

For vertical tune >8.97, there is no effect from 37+ and 55-: the betatron tune is already high enough for all G. It is possible a few percents polarization loss due to the tight tune space.

Ramp Measurement

The ramp measurements pattern look similar, there is no catastrophic polarization drop. Higher asymmetry with cold snake. There may still be polarization loss around 36+.

2.5T

2T 1.5T

Horizontal resonances

38+Qy

38+Qx

Horizontal resonances are much weaker than the counterparts of vertical ones.

55-Qy

41.4/49.8=.83

34.9/49.2=.71

Caused by horizontal component of stable spin directionHorizontal resonances are always weak but there are many of them

Polarization losses

C2.5T C2.5T,W1.5T C2T,W1.5T AC dipole

Hori. res.1: 0.94 0.89 0.94 0.99

Low y at 36+1: 0.95 0.95 0.95 1.00

Inj./Ext.: 0.92 0.97 0.99 0.99

Weak intrinsic 1.00 1.00 1.00 0.85

Total2 0.82 0.82 0.89 0.83

Measured3 0.77 0.76 0.80 0.801. The polarization loss due to horizontal res. and low y at 36+ is given as the

upper limit, especially in the two snake cases (total snake strength varies). 2. There is also possible loss at early part of ramp when vertical tune is outside

the tune window. It is estimated to be no more than a couple percents but spin tracking will follow.

3. 80% source polarization assumed.

Polarized proton beams at J-Parc

50 GeV polarized protons for slow extracted beam primary fixed target experimentsLow intensity (~ 1012 ppp), low emittance (10 mm mrad) beams

Pol. H- Source

180/400 MeV Polarimeter

Rf Dipole

25-30% Helical Partial Siberian Snakes

pC CNI Polarimeter

Extracted BeamPolarimeter

Polarized proton beams in J-PARC Linac and RCS

Optically Pumped Polarized Ion Source: 1012 Hminus per 0.5 ms pulse and > 5 Hz rep. rate, 85% polarization

Bunch emittance: ~ 5 mm mrad and 0.3 eVs for 2 x 1011 protons (required for polarized beam acceleration)

Linac: No depolarization RCS (y = 6.35, P = 3, Ekin = .18 … 3 GeV, G = 2.2 … 7.5)

Harmonic correction of 5 imperfection resonances Intrinsic resonances:

G = 2.65 (9- y), 3.35 (-3+ y), 5.65 (12- y), 6.35 (0+ y) Full spin flip with rf dipole: 20 Gm gives > .99 spin-flip (seems feasible) Avoid depolarization with tune jump: y = 0.2 in 6 turns large

aperture ferrite quadrupoles with fast pulsing power supplies (difficult)

Intrinsic resonances in RCS (Mei Bai)

• emittance: 10 mm-mrad, 95%• repetition rate 25Hz• sinusoidal ramping• kinetic energy: 180MeV – 3GeV

• intrinsic resonance strength for a particle at an emittance of 10 mm-mrad Full spin flip by a rf dipole

=2.33x10-5

=6.18x10-5

=7.63x10-5 =6.60x10-5Fast tune jump?

Polarized proton beams in J-PARC Main Ring

Main ring (y ~ 20.8, P = 3, Ekin = 3 … 50 GeV, G = 7.5 … 97.5) Two strong 30% partial Siberian snakes installed in two of the three straight

sections: Avoid all vertical depolarizing resonances if vertical tune is set to ~ 20.92 For injection and extraction energies of 3 GeV (G = 7.5) and 50 GeV

(G = 97.5), respectively, perfect spin matching at injection and extraction.

Setting horizontal tune to 22.88 (or 22.12) avoids depolarization from horizontal motion with stable spin direction not vertical.

Vertical component of stable spin

Fractional part ofspin tune

Injection Intrinsic resonance

G

Two partial snakes in J-PARC MR

1

0.

preaxis OT gg( )( )T

2

sptune OT gg( )( )

13.57.5 gg8 9 10 11 12 13

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

y x

Possible locations of partial snakes in MR

First 30% snake Second 30% snake

x,y = 22.128,20.960

Two 30% snakes

12 particles at 1.5 beam sigma

Spin tracking in 50 GeV MR (Alfredo Luccio)

Conclusions

Strong partial Siberian snakes can overcome intrinsic depolarizing resonances. Operation is analogous to full snake situation.

If vertical tune and super-periodicity have common factor that is odd multiple partial snakes can be used to give larger effective strength

With proper choice of injection and extraction energy multiple partial snakes can solve the spin matching problem

Horizontal resonances can be avoided by placing horizontal tune close to integer also.

Polarized beam acceleration in J-Parc is possible with a rf dipole in the RCS and two strong partial Siberian snakes in Main Ring.