Slide 1

Polarized Proton Acceleration in theAGS with Two Helical Partial Snakes

October 2, 2006

SPIN 2006

H. Huang, L.A. Ahrens, M. Bai, A. Bravar, K. Brown,E. D. Courant, C. Gardner, J.W. Glenn, A.U.Luccio, W.W. MacKay, V. Ptitsyn, T. Roser, S.Tepikian, N. Tsoupas, J. Wood, K. Yip, A.Zelenski, K. Zeno

Depolarizing Resonances in the AGS

Imperfection Resonances

arising from sampling of error fields, fields due to closed orbit errors, etc.

G=n (integer) G=5,6,…45partial snake(s)

Spin tune is given by coss=cos (/2) cos G

s can not be an integer, avoided all imperfection resonances

Vertical Intrinsic Resonances

arise from sampling of focusing fields due to finite beam emittance.

G=kPy

Strong ones: G=0+y,12+y,36y AC dipole, strong partial snakes

Weak ones: G=24y,48-y fast crossing speed , strong partial snakes

Horizontal Intrinsic Resonances

1. horizontal non-vertical stable spin direction due to strong partial snakeinteraction with horizontal motion.

2. betatron motion coupled to the vertical betatron motion by coupling elements:solenoid, helical magnet.

G=kx fast crossing speed, strong partial snakes

Partial Snake Resonances

strength proportional to nearby intrinsic resonance strength.

G=kPmy , m>1 avoid the resonance tunes

Spin Tune and Fractional Vertical Tune

With two helical magnetsinstalled, the lattice islargely distorted at lowenergies. It took quite a lotefforts to set the verticaltune close to integer.Vertical tune is higher than8.98 at all major intrinsicresonances. It is even ashigh as 8.99 at 36+.

Ramp Measurement

RHIC injection energy was lowered by 1 unit of G for better spintransmission. Note that there is not much data before G=7.

Polarization as Function of Vertical Tunes

Snake resonance effect is clearly seen.

9th Harmonic at 36+

Estimated imperfection resonance strengthswith large sin 9th harmonics. As can be seen,with 8mm sin 9th harmonic amplitude, theresonance strength is comparable to the 16%partial snake in the AGS. With certain phasebetween them, the effect of partial snakes iscanceled by the large orbit distortion at G=45(near 36+y).

Measured polarization as functionof the sine 9th harmonicamplitude at 36+y. The dashedline is to guide the eyes. Thelocation of the polarization dipagrees with model prediction.

(Mei)

Horizontal Polarization Profile

Polarization

Target Position (mm)

15% Cold Snake

10% Cold Snake

Target Position (mm)

Normalized

Rate

15% ColdSnake

10% ColdSnake

The horizontal resonance effect is measurable over the whole ramp.The following snake setup gave the best polarization: 10% cold snake,5.9% warm snake.

2002

2003

2004

2005

2006

Intensity (1011)

0.7

1.0

1.5

Polarization

30%

40%

50%

65%

AGS Polarization Evolution

Slow

ramp rate

Normal

ramp rate

New warm

snake

Cold

snake

Booster

Scraping

Source polarization and intensity gradually improved over this period.

Horizontal Tune Near Integer

•The idea is to put horizontal tune near 9 (~8.95) whilemaintain vertical tune close to 9 (~8.98). Both tunes arewithin the spin tune gap.

•With the fractional part of the two tunes are so close, thecoupling has to be corrected very well. The old solenoidsnake will be ramped to overcome the coupling.

•Since the horizontal resonance strength are very weak,the horizontal tune does not need to be so as close tointeger as vertical tune.

•The idea has been tested with beam. With addedstrength from nearby quad strings, we should be able toput the tunes into the gap as needed.

Horizontal Tune Near Integer (2)

Horizontal Tune Near Integer (3)

Summary

•65% polarization with 1.51011 intensity achieved with two partialsnakes in the AGS.

•The following snake setup gave the best polarization: 10% coldsnake, 5.9% warm snake.

•Added four compensation quads for warm snake worked verywell. The lattice is easier to handle than last year without them.

•The intensity dependence is very benign with this setup.

•There is polarization loss of 5% due to each of vertical andhorizontal resonances. The injection and extraction mismatch isabout 1%. We expect 73% polarization with 82% input. There isstill an relative 10% polarization loss unexplained.

•Move horizontal tune into the spin tune gap next run.

•Spin tracking effort is underway to understand the polarizationloss.

•More polarization ramp measurements during next run.

Spare slides

AGS Stability

RHIC injection measurements with very long measuring time. Averagedover 420 million events. Error bar for each bunch is 4.7%. Trying to lookfor AGS variation from shot to shot. Need more statistics.