Ion Polarization in MEIC Vasiliy Morozov on behalf

Ion Polarization in MEIC Vasiliy Morozov on behalf of A. M. Kondratenko, M. A. Kondratenko, Yu. N. Filatov and JLab’s MEIC Study Group The 2 nd Internal MEIC Accelerator Design Review, JLab, January 15, 2014

Outline • Ion polarization requirements • Polarization preservation during acceleration • Polarization control in the collider - using “small” solenoids for deuterons - using “small” radial fields for protons • Compensation of the spin perturbation in the collider - 0 th harmonic of the spin perturbation - Spin response function - Suppression of the spin response function at interaction points • Conclusions V. S. Morozov January 15, 2014 -- 2 --

Ion Polarization Requirements • MEIC major ion complex components Ion source SRF linac Cooling Prebooster (accumulator ring) to high-energy collider ring Large booster Medium-energy collider ring • Polarization design requirements – – High polarization (~80%) of protons and light ions (d, 3 He++, and possibly 6 Li+++) Both longitudinal and transverse polarization orientations available at all IPs Sufficiently long polarization lifetime Spin flipping (can be done e. g. at the source) V. S. Morozov January 15, 2014 -- 3 --

Spin Motion in Figure-8 Ring • Figure-8 structure provides unique capabilities for controlling the polarization – – – In an ideal structure (without perturbations) all solutions are periodic It has an energy-independent (zero) spin tune It allows control of polarization with small fields with little or no orbit perturbation It eliminates depolarization problem during acceleration It provides efficient polarization control of any particles including deuterons Makes possible ultra-high precision experiments with polarized beams n=0 V. S. Morozov January 15, 2014 --

Polarization Control during Acceleration • Polarization is stable if >> w 0 – w 0 is the zero-harmonic spin resonance strength – B||L of only 3 Tm provides deuteron polarization stability up to 100 Ge. V – A conventional ring at 100 Ge. V would require B||L of 1200 Tm or B L of 400 Tm V. S. Morozov January 15, 2014 -- 5 --

Acceleration and Spin Matching Pre-booster (1 solenoid) Large booster (1 solenoid) 0. 785 / 3. 83 0. 06 / 0. 28 60 0. 003 / 0. 01 3. 83 / 20 0. 28 / 1. 5 120 0. 003 / 0. 01 Conventional 20 Ge. V accelerators require B||L of ~70 Tm for protons and ~250 Tm for deuterons V. S. Morozov January 15, 2014 -- 6 --

Solenoid Matching in Prebooster • Prebooster lattice without solenoid • Prebooster lattice with solenoid • No correction needed solenoid V. S. Morozov January 15, 2014 -- 7 --

Solenoid Matching in Large Booster • Large booster straight lattice without solenoid • Large booster straight lattice with solenoid • No correction needed solenoid V. S. Morozov January 15, 2014 -- 8 --

Deuteron Polarization Control in Collider • Scheme for obtaining any polarization direction – Beam injected longitudinally polarized, accelerated and then desired spin direction adjusted § § are the spin rotation angles in the solenoids is the spin rotation angle between the solenoids is the orbit bending angle between the solenoids is the angle between the polarization and beam direction V. S. Morozov January 15, 2014 -- 9 --

Deuteron Polarization Control in Collider (B||L)1, 2 (T m) vs. p (Ge. V/c) longitudinal polarization radial polarization (B||L)1 (B||L)2 V. S. Morozov January 15, 2014 -- 10 --

Proton Polarization Control in Collider Last two arc dipoles (B L)i (T m) vs. p (Ge. V/c) longitudinal polarization (Bx. L)1 (Bx. L)2 (Bx. L)3 (Bx. L)4 V. S. Morozov radial polarization January 15, 2014 -- 11 --

Proton Polarization Control in Collider Vertical excursion of the reference orbit V. S. Morozov January 15, 2014 -- 12 --

Spin Response Function • Zero-harmonic spin resonance strength can be calculated using spin “response function” • Response function is determined by the accelerator’s design lattice and represents the spin response to a -function perturbation at an azimuthal angle : • Such a dipole generates the following strength of the zero-harmonic resonance: • In a flat figure-8 orbit, the response function is given by where is the spin rotation angle in the collider’s bending dipoles, is the Floquet function and are the vertical betatron function and betatron tune V. S. Morozov January 15, 2014 -- 13 --

Response Function of Collider is the periodic response function describing effect of any radial fields and allowing one to calculate the zero-resonance strength. IP IR Highest error sensitivity in the IR’s but error control requirements high anyway for dynamic reasons. IP V. S. Morozov January 15, 2014 --

Zero-Harmonic Spin Resonance Strength • The total zero-harmonic spin resonance strength: is composed of – coherent part due to closed orbit excursions – due to transverse and longitudinal emittance • The coherent part arises due to radial fields from – dipole roll – vertical quadrupole misalignments • V. S. Morozov January 15, 2014 -- 15 --

Compensation of Zero-Harmonic Resonance • In the linear approximation, the zero-harmonic spin resonance strength is determined by two components of the spin perturbation lying in the ring’s plane: and can be compensated by correcting devices whose spin rotation axis lies in the same plane • Spin resonance strength with compensation of the “coherent” component: insertion for spin control insertion for strength compensation V. S. Morozov January 15, 2014 -- 16 --

Conclusions • Schemes were developed for MEIC figure-8 rings that – – – eliminate depolarization problem during acceleration allow control of the beam polarization with small fields without significant orbit perturbation efficiently control the polarization of any particles including deuterons allow adjustment of polarization orientation in either of the two straights allow single-turn as well as multi-turn spin-flipping schemes make possible ultra-high precision experiments with polarized beams • Future plans – – optimization of the developed schemes integration into the ring lattices validation by spin tracking development of spin-flipping techniques V. S. Morozov January 15, 2014 -- 17 --