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.