Driven Spin Coherent Driven Spin Coherent Precession at RHICPrecession at RHIC

Mei Bai, G. Bunce, R. Gill, T. Roser

Brookhaven National Lab. Upton, NY 11973

IntroductionIntroduction

Spin motion near an isolated resonance

spin vector gets away from vertical and precesses around vertical direction. The closer the spin tune to the resonance, the further the spin vector gets away from vertical.

Spin vector vertical component: remains constant. The vertical component averages to zero when on resonance

Spin vector horizontal component: precesses at an amplitude proportional to the strength of the resonance

The ratio of the average vertical component and horizontal precession amplitude can be used to determine the spin tune

€

dr

ψ

dθ= −

i

2Gγσ 3 + φrese

iσ 3Qresθσ 1[ ]r

ψ (θ)

Coherent PrecessionCoherent Precession

Vertical component

€

Px =

φres

2π

Qres − Qspin

2+

φres

2π

2cos(Qresθ)

€

< Py >=Qres − Qspin

Qres − Qspin

2+

φres

2π

2

Horizontal component

Spin motion driven by a single ac Spin motion driven by a single ac dipoledipole

Spinor motion driven by a single ac dipole with horizontal magnetic field

€

dr

ψ

dθ= −

i

2Gγσ 3 + (1+ Gγ )

ΔBL

Bρ

e iσ 3Qspθ + e-iσ 3Qspθ

2σ 1

⎡

⎣ ⎢

⎤

⎦ ⎥r

ψ (θ)

Drives two resonances at Qs=Qsp and Qs=-Qsp. This introduces extra motion to the spin precession

Oscillating field

Rotating field

Simulation of spin motion driven by a single ac Simulation of spin motion driven by a single ac dipoledipole

Spin vector not only gets bent away from vertical but also wobbles from turn to turn

Experimental SetupExperimental Setup

RHIC injection Gγ=45.5

RHIC polarization setup: two Siberian snakes

opposite side of the ring

axes about which spin rotates: perpendicular

spin tune Qs=1/2

A single ac dipole at 4RF Maximum strength:

79 Gauss-m

Fill pattern: two sets of 12 bunches with alternating spin signs

Data Analysis (1)Data Analysis (1)

Data was taken with the RHIC CNI polarimeter

Events for each detector each orbital revolution

Horizontal asymmetry Y45 and vertical asymmetry X45 for each bunch in the frame which rotates at the ac dipole frequency

€

asymmetry =N top, j _ bin − Nbottom, j _ bin

N top, j _ bin + Nbottom, j _ bin

€

Nk, j _ bin = Nk,i

i

nturn

∑

€

for i : ( j _ bin −1)2π

Nbin

⟨ sin 2πQspi + χ( )⟨ j _ bin2π

Nbin

Data Analysis (2)Data Analysis (2)

Average all the asymmetries for all bunches with the same spin sign, either up or down

Asymmetry due to the coherent spin precession

False asymmetry due to systematic€

average_ asymmetryspin up − average_ asymmetryspin dn

2

€

average_ asymmetryspin up + average_ asymmetryspin dn

2

Data AnalysisData AnalysisAverage horizontalasymmetry for all the spin down (left)and spin up (right)bunches

Down Up

€

Up + Down

2

€

Up − Down

2

Data AnalysisData AnalysisAverage verticalasymmetry for all the spin down (left)and spin up (right)bunches

€

Up + Down

2

€

Up − Down

2

Experimental Results (1)Experimental Results (1)

Observed a large false asymmetry.

Source of False AsymmetrySource of False Asymmetry

The vertical coherent oscillation. This causes the oscillation of solid angle Ω

False asymmetry ~ Ω2

Scattering angle θ False asymmetry due to coulomb scattering cross section θ

dependence

Need actual geometry of the CNI polarimeter to estimate

€

θΩ

⎛

⎝ ⎜

⎞

⎠ ⎟~ sin Qsp 2πi + χ( )

Silicon detectorultra-thin Carbon ribbon

18 cm

€

σ c ~1

sin4 (θ

2)

Experimental Results (2)Experimental Results (2)

Multiple data sets show the measured spin precession in horizontal plane is insignificant.

Another look of the vertical Another look of the vertical asymmetryasymmetry

€

Px,amp =

φres

2π

Qres − Qspin

2+

φres

2π

2

Experimental Results (3)Experimental Results (3)

Large polarization loss at the vicinity of the spin tune

The data suggests a rather large spin tune spread

In the presence of two full snakes, the source of spin tune spread Difference in the

divergence of the beam at the two snakes: ~ 0.002 for a 25 pi mm-mrad

Difference between the snake orbital angle due to dispersion: ~ 0.0001

Simulation indicates spin tune spread modulate at low frequency like synchrotron oscillation can lead to large polarization loss

ConclusionConclusion

It is very difficult to excite coherent spin precessions with the single ac dipole setup at RHIC.

Repeat the experiment with the new design of RHIC spin flipper Ac dipole 1:

)cos( θsfQBLAc dipole 2:

)sin( θsfQBL

Spin rotator 1:Axis: verticalAngle 0: 90o

Spin rotator 2:Axis: verticalAngle 0: -90o

AcknowledgementAcknowledgement

Special thanks to E. Stephenson for helping the false asymmetry analysis

Also would like to thank all the RHIC CNI polarimeter crew