Deuteron Polarization in MEIC Vasiliy Morozov for MEIC Study Group using results of IUCF and COSY SPIN Collaborations led by A.D. Krisch figure-8 concept originally proposed by Ya.S. Derbenev and develop by Yu.N. Filatov, A.M. Kondratenko, and M.A. Kondratenko High Energy Nuclear Physics with Spectator Tagging Old Dominion University, March 10, 2014 F. Lin

Outline Deuteron polarization Spin dynamics and spin resonances Figure-8 concept Summary

Spin Density Matrix Spin-1 state Mathematical expectation of an operator Mathematical expectation for an ensemble of particles where is the fraction of particles in the state. If all beam particles are in the eigenstates then

Vector and Tensor Polarizations Cartesian vector and tensor spin operators Density matrix representation If all particles are in the eigenstates the only non-zero expectation values Rotations

Polarized Ion Source COSY’s polarized ion source Deuterium hyperfine states (in strong magnetic field)

Spin-1 Polarimetry Differential spin-dependent cross-section (using lab-frame polarizations) Polarizations extracted using azimuthal count rate dependence and effective analyzing powers

Spin Resonances 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 RF-induced resonances Coupling and higher-order resonances

RF-Induced Spin Resonance Convenient controllable resonance model for experiments Can be used for spin flipping Experiment using 1.85 GeV/c deuteron beam at COSY

Spin Flipping Sweeping an rf magnet’s frequency through a spin resonance can flip the polarization Spin rotation and Froissart-Stora formula

Siberian Snake Device rotating the spin by some angle about an axis in horizontal plane A “full” Siberian snake rotates the spin by 180 Overcomes all imperfection and most intrinsic resonances Spin tune with a snake Solenoidal snake at low energies Dipole snake at high energies

Figure-8 Concept Figure-8 shape has been chosen for all MEIC rings to achieve high ion (and electron) polarization Spin precession in one arc is exactly cancelled in the other Zero spin tune independent of energy Spin control and stabilization with small solenoids or other compact spin rotators Advantages of the figure-8 scheme for ions Efficient preservation of ion polarization during acceleration Energy-independent spin tune High polarization of all light ions Ease of spin manipulation Any desired polarization orientation at the IP Spin flip A simple way to accommodate polarized deuterons Particles with small anomalous magnetic moment Spin control without affecting the beam dynamics

Pre-Acceleration & Spin Matching Polarization in Booster stabilized and preserved by a single weak solenoid 0.7 Tm at 9 GeV/c d / p = 0.003 / 0.01 Longitudinal polarization in the straight with the solenoid Conventional 9 GeV accelerators require B||L of ~30 Tm for protons and ~110 Tm for deuterons beam from Linac Booster to Collider Ring BIIL

Optical Effect of Solenoid Linear optics without solenoid Linear optics with solenoid Betatron tune shift

Polarization Control in Collider “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) ny control module (constant vertical orbit bump) nz control module 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 Collider 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 Another 3D spin rotator suppresses the zero-integer spin resonance strength 3D Spin Rotator IP Spin-control solenoids Vertical-field dipoles Radial-field dipoles Lattice quadrupoles

Deuteron Polarization Behavior Radial polarization at IP assuming d = 2.510-4, p = 100 GeV/c Vertical polarization at IP Longitudinal polarization at IP nx ny nz

Spin Flipping The universal 3D spin rotator can be used to flip the polarization Consider e.g. longitudinal polarization 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 No resonant depolarization The rate of change of the polarization direction is slow compared to the spin precession rate >0.1 ms for protons and >3 ms for deuterons

Summary Dynamics of the deuteron vector and tensor polarizations in an accelerator are not independent. They are connected through rotations. Preserving the vector polarization also preserves the tensor polarization. Manipulation of the vector and tensor polarizations can be understood in terms of rotations and controlled accordingly. Figure-8 is an elegant solution for preservation and control of the polarization of any particle species: acceleration, orientation, spin flip.