SPIN FEST 2012 Spin Dynamics M Bai CA

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SPIN FEST 2012 Spin Dynamics M. Bai, C-A Dept. , BNL

SPIN FEST 2012 Spin Dynamics M. Bai, C-A Dept. , BNL

Spin motion: Thomas BMT Equation SPIN FEST 2012 Spin vector in particle’s rest frame

Spin motion: Thomas BMT Equation SPIN FEST 2012 Spin vector in particle’s rest frame Magnetic field along the direction of the particle’s velocity Ø G is the anomoulous g- factor, for proton, G=1. 7928474 Ø : Lorenz factor Magnetic field perpendicular to the particle’s velocity

Spin motion in a circular accelerator SPIN FEST 2012 l In a perfect accelerator,

Spin motion in a circular accelerator SPIN FEST 2012 l In a perfect accelerator, spin vector precesses around its guiding field along the vertical direction B beam l Spin tune Qs: number of precessions in one orbital revolution. In general,

Depolarizing mechanism in a synchrotron SPIN FEST 2012 l horizontal field kicks the spin

Depolarizing mechanism in a synchrotron SPIN FEST 2012 l horizontal field kicks the spin vector away from its vertical direction, and can lead to polarization loss Ø Ø dipole errors, misaligned qadrupoles, imperfect orbits betatron oscillations other multipole magnetic fields other sources y y beam z x Initial y 1 st full betatron Oscillation period z x 2 nd full betatron Oscillation period

Depolarizing resonance SPIN FEST 2012 l when the spin vector gets kicked at a

Depolarizing resonance SPIN FEST 2012 l when the spin vector gets kicked at a frequency close to the frequency it processes. The location of a spin depolarizing resonance is at l For protons, imperfection spin resonances are spaced by 523 Me. V

imperfection spin resonance SPIN FEST 2012 ¢ Source l ¢ dipole errors, quadrupole mis-alignments

imperfection spin resonance SPIN FEST 2012 ¢ Source l ¢ dipole errors, quadrupole mis-alignments Resonance location: G = k, k is an integer ¢ Resonance strength: l Proportional to the size of the vertical closed orbit distortion

Intrinsic spin resonance SPIN FEST 2012 ¢ Intrinsic resonance l Source: focusing field due

Intrinsic spin resonance SPIN FEST 2012 ¢ Intrinsic resonance l Source: focusing field due to the intrinsic betatron oscillation l Resonance location: G = k. P±Qy, P is the super periodicity of the accelerator, Qy is the vertical betatron tune l Resonance strength: • Proportional to the size of the betatron oscillation • When crossing an isolated intrinsic resonance, the larger the beam is, the more the polarization loss is

Spin depolarization resonance in RHIC SPIN FEST 2012 the higher energy, the stronger the

Spin depolarization resonance in RHIC SPIN FEST 2012 the higher energy, the stronger the resonance

Single resonance crossing SPIN FEST 2012 ¢ Frossart-Stora formula ε is the strength of

Single resonance crossing SPIN FEST 2012 ¢ Frossart-Stora formula ε is the strength of the resonance. α is the speed of resonance crossing

overcoming spin depolarizing resonances SPIN FEST 2012 l Harmonic orbit correction • to minimize

overcoming spin depolarizing resonances SPIN FEST 2012 l Harmonic orbit correction • to minimize the closed orbit distortion at all imperfection resonances • Operationally difficult for high energy accelerators Tune jump Vertical betatron tune l • Operationally difficult G =Qy G because of the number of resonances • Also induces emittance blowup because of the non-adiabatic beam manipulation acceleration time

overcoming spin depolarizing resonances SPIN FEST 2012 l AC dipole • Induce full spin

overcoming spin depolarizing resonances SPIN FEST 2012 l AC dipole • Induce full spin flip by using an AC dipole to adiabatically excite a coherent betatron oscillation with large amplitude Quadrupole: horizontal Magnetic field linearly Proportional to the offset From magnet center w. o. correct coherent oscillation With coherent oscillation • Can only strong intrinsic spin resonances

Innovative polarized proton acceleration technique: Full Siberian snake SPIN FEST 2012 q First invented

Innovative polarized proton acceleration technique: Full Siberian snake SPIN FEST 2012 q First invented by Derbenev and Kondratenko from Novosibirsk in late 1976 q A group of dipole magnets with alternating horizontal and vertical dipole fields q rotates spin vector by 180 o

Particle trajectory in a Helical snake: SPIN FEST 2012

Particle trajectory in a Helical snake: SPIN FEST 2012

Principle of full Siberian snake SPIN FEST 2012 q Use one or a group

Principle of full Siberian snake SPIN FEST 2012 q Use one or a group of snakes to make the spin tune to be at ½ q Break the coherent build-up of the perturbations on the spin vector y y beam z

partial Siberian snake: solution for medium energy accelerators SPIN FEST 2012 ¢ ¢ rotates

partial Siberian snake: solution for medium energy accelerators SPIN FEST 2012 ¢ ¢ rotates spin vector by an angle of <180 o Keeps the spin tune away from integer Primarily for avoiding imperfection resonance Can be used to avoid intrinsic resonance as demonstrated at the AGS, BNL.

Snake depolarization resonance SPIN FEST 2012 q Condition 16 3/4 Py current working point

Snake depolarization resonance SPIN FEST 2012 q Condition 16 3/4 Py current working point 11/16 7/10 old working point q even order resonance l Disappears in the two snake case if the closed orbit is perfect q odd order resonance l Driven by the intrinsic spin resonances

Snake resonance observed in RHIC SPIN FEST 2012 7/10 snake resonance polarized protons were

Snake resonance observed in RHIC SPIN FEST 2012 7/10 snake resonance polarized protons were accelerated to an energy of G =63, a location of a strong intrinsic spin resonance 17 Spin. Fest, August 7, 2008

Polarization Tune Scan: 250 Ge. V acceleration 7/10 resonance Working pt for 250 Ge.

Polarization Tune Scan: 250 Ge. V acceleration 7/10 resonance Working pt for 250 Ge. V run 11/16 resonance SPIN FEST 2012 3/4 resonance

SPIN FEST 2012 BRAHMS(p) Absolute Polarimeter (H jet) RHIC p. C Polarimeters Siberian Snakes

SPIN FEST 2012 BRAHMS(p) Absolute Polarimeter (H jet) RHIC p. C Polarimeters Siberian Snakes Spin flipper PHENIX (p) STAR (p) Spin Rotators (longitudinal polarization) Spin Rotators Solenoid Partial Siberian Snake (longitudinal polarization) LINAC Pol. H Source 200 Me. V Polarimeter BOOSTER AGS Helical Partial Siberian Snake AGS Polarimeters Strong AGS Snake 19 Spin. Fest, August 7, 2008

Polarized proton setup in the Booster SPIN FEST 2012 q Booster l l l

Polarized proton setup in the Booster SPIN FEST 2012 q Booster l l l Kinetic Energy: 200 Me. V ~ 1. 42 Ge. V Intrinsic spin resonances are avoided by setting the vertical betatron tune above the spin precession tune at extraction A total of 2 imperfection resonances and they are corrected by the harmonic correction of the vertical closed orbit

Polarized proton setup in the AGS SPIN FEST 2012 q AGS (Alternating Gradient Synchrotron)

Polarized proton setup in the AGS SPIN FEST 2012 q AGS (Alternating Gradient Synchrotron) l l Energy: 2. 3 Ge. V ~ 23. 8 Ge. V A total of 41 imperfection resonances and 7 intrinsic resonances from injection to extraction Ø One 5. 9% partial snake plus one 10~15% partial snake E 20 5. 9% A 20 10~15%

Courtesy of T. Roser Spin tune with two partial snakes SPIN FEST 2012 Spin

Courtesy of T. Roser Spin tune with two partial snakes SPIN FEST 2012 Spin tune Extraction Vertical component of stable spin Vertical betatron tune 36+Qy intrinsic resonance G

Polarized protons in the AGS SPIN FEST 2012 Beam intensity AGS bending magnet field

Polarized protons in the AGS SPIN FEST 2012 Beam intensity AGS bending magnet field 9. 0 Vertical betatron tune (8. 98) 8. 8 Horizontal betatron tune 8. 6 23 Courtesy of L. Ahrens and K. Brown Spin. Fest, August 7, 2008

Polarized proton acceleration setup in RHIC SPIN FEST 2012 q Energy: 23. 8 Ge.

Polarized proton acceleration setup in RHIC SPIN FEST 2012 q Energy: 23. 8 Ge. V ~ 250 Ge. V (maximum store energy) l A total of 146 imperfection resonances and about 10 strong intrinsic resonances from injection to 100 Ge. V. Ø Two full Siberian snakes

How to avoid a snake resonance? SPIN FEST 2012 q Keep the spin tune

How to avoid a snake resonance? SPIN FEST 2012 q Keep the spin tune as close to 0. 5 as possible l snake current setting • set the vertical tune to 0. 745 • measure the beam polarization with different snake current • expect no depolarization if the corresponding spin tune is very close to 0. 5 25 Spin. Fest, August 7, 2008

How to avoid a snake resonance? SPIN FEST 2012 q Keep the vertical closed

How to avoid a snake resonance? SPIN FEST 2012 q Keep the vertical closed orbit as flat as possible Flat orbit: Sum of kicks on the spin vector from quads as well as the dipole correctors = 0 26 Spin. Fest, August 7, 2008

Precise orbit control SPIN FEST 2012

Precise orbit control SPIN FEST 2012

How to avoid a snake resonance? SPIN FEST 2012 q Keep the vertical closed

How to avoid a snake resonance? SPIN FEST 2012 q Keep the vertical closed orbit as flat as possible Flat orbit: Sum of kicks on the spin vector from quads as well as the dipole correctors = 0 q Keep the betatron tunes away from snake resonance locations l Precise tune control 28 Spin. Fest, August 7, 2008

Precise Beam Controls: Betatron Tune SPIN FEST 2012

Precise Beam Controls: Betatron Tune SPIN FEST 2012

Achieved Polarization: 100 Ge. V SPIN FEST 2012

Achieved Polarization: 100 Ge. V SPIN FEST 2012

Achieved Polarization: 255 Ge. V SPIN FEST 2012

Achieved Polarization: 255 Ge. V SPIN FEST 2012

Achieved Polarization: 255 Ge. V SPIN FEST 2012

Achieved Polarization: 255 Ge. V SPIN FEST 2012