RHIC Spin Flipper

M. Bai, T. Roser

Collider Accelerator DepartmentBrookhaven National Laboratory, Upton, NY 11973

Outline Goal: achieve full spin flip in RHIC without detuning the snake setting

How to obtain full spin flip of polarized protons with spin precession tune of 1/2

RHIC spin flipper parameters

Traditional spin flipping technique

How to spin flip?

θcosQ

Bρ

ΔBL)Gγ1(GγS sfdθ

Sd xy

ψ(θ)2

1)e(eσ

Bρ

ΔBL)Gγ1(Gγ

2θQiσ-θQiσ

13dθψd sp3sp3

i

Adiabatically crossing an artificial spin resonance induced by an ac dipole.

This technique has been demonstrated in the Brookhaven AGS, IUCF Cooler Ring as well as the Cozy 3 GeV storage ring

0.5QspinQsf

Traditional spin flipping technique However, this technique excites not only an resonance at

Qsf but Also an resonance at –Qsf. Hence, the condition of adiabatic resonance crossing is broken when the beam spin precession tune is at or close to ½, and one can not achieve full spin flipping.

It is critical for this technique to have spin precession tune stay away from 1/2 requires to detune the snake settings. This requirement it can not be an operational tool to realize routine spin flipping at high energy colliders like RHIC.

Spin flipper for operational high energy pp accelerators Has to provide full spin flip in the presence of the nominal snake configuration, i.e.

the beam spin precession tune is at or close to ½

Use a rotating spin kick field instead of an oscillating spin kick field by a single ac dipole to eliminate the resonance at –Qsf.

θsinQθcosQ

Bρ

ΔBL)Gγ1(GγS sfsfdθ

Sd zxy

ψ(θ)eσBρ

ΔBL)Gγ1(Gγ

2θQiσ

13dθψd sp3

i

)sin(cos2 21 sfsf QQi

liperidealSpinF eM

B

BLG

1

Implementation of spin flipper Schematic layout

Ac dipole 1:)cos( sfQBL

Ac dipole 2:)sin( sfQBL

Spin rotator 1:Axis: verticalAngle 0: 90o

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

130130 cos22

sin22

inf

sfsf Qii

Qii

lippersp eeeeM

120103030 cos2

sincossin222

sfsf Qi

Qiii

eeee

]cossincossin[2 12010 sfsf QQi

e

)cos(sin2

inf

12 sfsf QQi

lippersp eM

For small , the equation then becomes:

Let =90o, we then get:

Simulation results

Single particle with spin tune = 0.5 Spin flipper:

Amplitude: 20 Gauss-m Tune: 0.49 -> 0.51 Sweep in half million turns

0 100000 200000 300000 400000 500000 600000

-1.0

-0.5

0.0

0.5

1.0

Sy

Number of Turns

Spin tune meter Instead of sweeping the spin flipper tune across the beam spin

precession tune, one can also keep the spin flipper tune fixed nearby the beam spin tune. In this case, the stable spin direction is given by

The beam spin tune can be calculated by measuring the turn by turn horizontal and vertical asymmetry

)cos(22

sf

sfspinsf

sfx Q

QQP

)sin(22

sf

sfspinsf

sfz Q

QQP

22

sfspinsf

spinsfy

QQ

QQP

Using rotating field

Using a single ac dipole

Spin vector in the rotating frame

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 1 2 3 4 5 6 7

Px Py

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7

Py Px

Using rotating field

Using a single ac dipole

How to construct a rotating field with ac dipoles

208.03o

-167.493o

Specs:• Ac dipole:

• field amplitude: 20 Gauss-m• frequency:

• 90o Spin rotator:• magnet: a DC dipole with vertical field• integrated field strength: 2.7 Tesla-m • dipole deflection:

• 100 GeV: 8.2 mrad• 250 GeV: 3.2mrad

90o Spin rotator

-45o Spin rotator