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RHIC Spin Flipper. M. Bai, T. Roser Collider Accelerator Department Brookhaven National Laboratory, Upton, NY 11973. Outline. Goal: achieve full spin flip in RHIC without detuning the snake setting - PowerPoint PPT Presentation
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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
QQP
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