Preservation and Control of Ion Polarization in MEIC A.M. Kondratenko, M.A. Kondratenko Science and Technique Laboratory Zaryad, Novosibirsk, Russia Yu.N. Filatov Moscow Institute of Physics and Technology, Dolgoprydny, Russia V.S. Morozov, Ya.S. Derbenev, F. Lin, and Y. Zhang Jefferson Lab, Newport News, VA, USA MEIC Collaboration Meeting October 5-7, 2015 F. Lin

Outline Introduction Figure 8 or racetrack? Spin dynamics in a Figure-8 ring Polarization preservation during acceleration Polarization control in the collider ring Spin stability criterion and zero-integer spin resonance Initial spin tracking results Conclusions

Ion Polarization Requirements Major MEIC ion complex components Polarization design requirements High polarization (~80%) of protons and light ions (d, 3He++, and possibly 6Li+++) Both longitudinal and transverse polarization orientations available at all IPs Sufficiently long polarization lifetime Spin flipping to future high-energy collider ring Ion source SRF linac Booster 285 – 7062 MeV (accumulator ring) Medium-energy collider ring 8-100 GeV/c Cooling

Spin Resonances in Conventional Ring Spin tune (number of spin precession per turn) in a conventional ring A spin resonance occurs whenever the spin precession becomes synchronized with the frequency of spin perturbing fields Imperfection resonances due to alignment and field errors Intrinsic resonances due to betatron oscillations Coupling and higher-order resonances

Racetrack Resonances Racetrack booster Ep = 1.22 – 8 GeV, Ed = 2.03 – 8.16 GeV Protons ~13 imperfection resonances ~26 intrinsic resonances require full solenoidal Siberian snake, ~30 Tm Many higher-order resonances Deuterons 0 imperfection resonances 1 or 2 intrinsic resonances can be avoided Higher-order resonances can be accelerated through Racetrack collider ring Ep = 8 – 100 GeV, Ed = 8.16 – 100 GeV ~175 imperfection resonances ~350 intrinsic resonances require two full dipole Siberian snakes, ~50 Tm 7 imperfection resonances can be crossed individually ~12 intrinsic resonances is a problem Many higher-order resonances ruin polarization and polarization lifetime

Figure-8 vs Racetrack Booster Figure-8 booster Same optics for all polarized and unpolarized ion beams Universally good and simple solution for polarization of any particles No restriction on the field ramp rate Additional arc bending angle of 150 Additional integrated dipole field BL = B ~ 70 Tm Extra space for quadrupoles, etc. Racetrack booster Proton & He3 polarization: OK Requires ~10 m long Siberian snake with ~30 Tm longitudinal field integral Snake field must ramp with energy Different optics for each ion species Allows one to shorten circumference by about 10 m Deuteron polarization: OK with fast ramp Can be handled with care Field ramp rate must be >~1 T/s Betatron tune jumps may be needed to cross spin resonances (this technique changes the optics during jumps)

Figure-8 vs Racetrack Collider Ring Figure 8 collider ring Same optics for all polarized and unpolarized ion beams Good for polarization Stable optics during acceleration and spin manipulation Additional arc bending angle of 163.4 Additional integrated dipole field BL ~ 950 Tm Extra space for quadrupoles, etc. Racetrack collider ring Proton polarization: probably OK but challenging Problem with optics stability especially at low energies Requires two full dipole Siberian snakes with a total field integral of ~50 Tm Figure-8 features can be preserved At low energies of ~8 GeV, the snakes introduce a significant tune shift (~0.2), which must be compensated; the tune shift changes nonlinearly with energy ~ -2 Deuteron polarization: realistically NO Cannot be preserved unless the ramp time to 100 GeV/c is less than ~1 s At the present acceleration rate, polarization is lost by ~10 GeV/c Even if polarization is preserved during acceleration, there is no guarantee of sufficient polarization lifetime; in fact, it will most likely be short.

Spin Motion in a Figure-8 Ring Properties of a figure-8 structure Spin precessions in the two arcs are exactly cancelled In an ideal structure (without perturbations) all solutions are periodic The spin tune is zero independent of energy A figure-8 ring provides unique capabilities for polarization control It allows for stabilization and control of the polarization by small field integrals Spin rotators are compact, easily rampable and give no orbit distortion It eliminates depolarization problem during acceleration Spin tune remains constant for all ion species avoiding spin resonance crossing It provides efficient polarization control of any particles including deuterons It is currently the only practical way to accommodate polarized deuterons Electron quantum depolarization is reduced due to energy independent spin tune It makes possible ultra-high precision experiments with polarized beams It allows for a spin flipping system with a spin reversal time of ~1 s

Polarization Control Concept Local spin rotator determines spin tune and local spin direction Polarization is stable if  >> w0 w0 is the zero-integer spin resonance strength B||L of only 3 Tm provides deuteron polarization stability up to 100 GeV A conventional ring at 100 GeV would require B||L of 1200 Tm or BL of 400 Tm

Pre-Acceleration & Spin Matching Polarization in Booster stabilized and preserved by a single weak solenoid 0.6 Tm at 8 GeV/c d / p = 0.003 / 0.01 Longitudinal polarization in the straight with the solenoid Conventional 8 GeV accelerators require B||L of ~30 Tm for protons and ~100 Tm for deuterons beam from Linac Booster to Collider Ring BIIL

Solenoid Matching in Booster Booster lattice without solenoid Booster lattice with solenoid No correction needed solenoid

Polarization Control with 3D Spin Rotator “3D spin rotator” rotates the spin about any chosen direction in 3D and sets the stable polarization orientation nx control module (constant radial orbit bump) z1 =  nx/sin y L 8 m x  1.6 cm By max= 3 T ny control module (constant vertical orbit bump) z2 =  ny/sin x L 8 m y  1.6 cm Bx max= 3 T nz control module z3 =  nz zi, x, y – are the spin rotation angles of solenoid field, radial-field dipole and vertical-field dipole respectively. Control of radial (nx) spin component Control of vertical (ny) spin component Control of longitudinal (nz) spin component IP z x z y

Polarization Control in the Collider Ring Placement of the 3D spin rotator in the collider ring Integration of the 3D spin rotator into the collider ring’s lattice Seamless integration into virtually any lattice Spin-control solenoids Vertical-field dipoles Radial-field dipoles Lattice quadrupoles

Solenoid Strengths Momentum dependence of the solenoid strengths for deuterons, d = 10-4 Momentum dependence of the solenoid strengths for protons, p = 10-2 Radial Vertical Longitudinal Bz1 Bz2 Bz3 Radial Vertical Longitudinal Bz1 Bz2 Bz3

Spin Flipping Necessary for the physics program to reduce systematic uncertainties The universal 3D spin rotator can be used to flip the polarization Consider e.g. multiple polarization reversals at the IP at 100 GeV/c Polarization is flipped by reversing the fields of the solenoids in the radial and longitudinal spin control modules Polarization is preserved if The spin tune is kept constant during spin manipulation The rate of change of the polarization direction is slow compared to the spin precession rate > 0.1 ms for protons and > 10 ms for deuterons Polarization Protons Deuterons Bz2, T Bz3, T Vertical ny = 1 2.19 -1.49 Vertical ny = -1 -2.19 1.49 Longitudinal nz = 1 1.88 -0.06 Longitudinal nz= -1 -1.88 0.06

Zero-Integer Spin Resonance & Spin Stability Criterion The total zero-integer spin resonance strength is composed of coherent part due to closed orbit excursions incoherent part due to transverse and longitudinal emittances Spin stability criterion the spin tune induced by the 3D spin rotator must significantly exceed the strength of the zero-integer spin resonance for proton beam for deuteron beam

Spin Response Function of Collider Ring The coherent part of zero- integer spin resonance induced by perturbing radial field hx() can be calculated using periodical response function F(): F() is calculated from linear optics Perturbing radial fields arise, for example, due to dipole roll errors, vertical quads misalignments, etc. Such perturbing fields result in vertical closed orbit distortion

RMS Vertical Closed Orbit Distortion Assuming certain rms vertical closed orbit distortion, we statistically calculate vertical orbit offset in the quadrupoles and resonance strength rms vertical closed orbit distortion for random misalignment of all quads Assuming that orbit distortion in the arcs < 100 m

Coherent Part of Resonance Strength 2 T  2 m control solenoids allow setting p = 10-2 and d = 10-4 Sufficient for polarization stabilization and control The coherent part of the zero-integer spin resonance strength is determined by closed orbit distortions. Orbit distortion does not exceed 100 m

Incoherent Part of Resonance Strength Effect of higher-order resonances due to incoherent tune spread requires study similarly to the case of two Siberian snakes The incoherent part of the zero-integer spin resonance strength is determined by emittances of betatron and synchrotron oscillations and depends on magnetic lattice In an ideal lattice, the incoherent part is determined primarily by the emittance of vertical betatron oscillations Incoherent part of the resonance strength is determined by the second order and has vertical direction Assuming normalized vertical beam emittance of 0.07 m rad

Spin-Tracking Perfect Figure-8 Ring Spin tracking using Zgoubi in collaboration with F. Meot of BNL MEIC lattice, no errors, 60 GeV/c proton, initial spin nz = 1, reference orbit Proton on one-sigma phase-space trajectories in both x and y

Stabilization against Error Effects One arc dipole rolled by 0.2 mrad, no closed orbit correction After addition of a 1 spin rotator solenoid in the straight (s  310-3)

Acceleration With 0.2 mrad dipole roll, no orbit correction, no spin rotator, 200103 turns After addition of a 5 spin rotator in the straight (s  1.410-2), 300103 turns

Conclusions & Future Plans Schemes have been developed for MEIC based on the figure-8 design that eliminate resonant depolarization problem during acceleration allow polarization control by small fields without orbit perturbation provide for seamless integration of the polarization control into the ring lattice efficiently control the polarization of any particles including deuterons allow adjustment of any polarization at any orbital location allow spin manipulation during experiments make possible ultra-high precision experiments with polarized beams allow for straightforward adjustment of spin dynamics for any experimental needs Initial spin tracking results support the validity of the developed concepts Future work Systematic comparison of figure-8 and racetrack booster options Spin tracking to validate the statistical model and verify developed schemes Development of efficient numerical techniques for spin calculations Optimization of response function at the IP by tuning the lattice Spin flipping development