References - Bogoliubov Laboratory of Theoretical Physics - JINR

SPIN-MANIPULATING POLARIZED DEUTERONS AND PROTONS
M.A. Leonova † for SPIN@COSY Collaboration
Spin Physics Center, University of Michigan, Ann Arbor, MI 48109-1040, USA
† E-mail: leonova@umich.edu
Abstract
We made the first systematic study of the spin resonance strengths induced by rf
dipoles and solenoids using 2.1 GeV/c polarized protons and 1.85 GeV/c polarized
deuterons stored in COSY. We found huge disagreements between the strengths
measured in Froissart-Stora sweeps and the theoretical values calculated using the
well-known formulae. These data resulted in correction of these formulae. We also
tested Chao’s matrix formalism for describing the spin dynamics near and inside
a spin resonance, which allows analytic calculations of the beam polarization’s behavior.
Our measurements agreed precisely with the Chao formalism’s predicted
oscillations. We also tested Kondratenko’s proposal to overcome depolarizing resonances
by ramping through them with a crossing pattern that forces the depolarizing
contributions to cancel themselves. Our tests with an rf bunched deuteron beam
gave an ∼ 20-fold reduction in the depolarization. We recently used an rf solenoid to
study rf spin resonances with both unbunched and bunched polarized beams of both
protons and deuterons. We found narrowing of the bunched deuteron resonance, indicating
that the beam’s polarization behaved as if there was no momentum spread.
However, we found widening of the proton resonance due to bunching.
Polarized scattering experiments require frequent spin-direction reversals to reduce
systematic errors; one must overcome many spin resonances to maintain the polarization.
In flat circular rings, each beam particle’s spin precesses around the vertical fields of the
ring’s bending magnets. The spin tune νs (the number of spin precessions during one turn
around the ring) is given by νs = Gγ, where G is the particle’s gyromagnetic anomaly
and γ is its Lorentz energy factor. The vertical polarization can be perturbed by any
horizontal magnetic field. RF fields can induce an rf spin resonance when fr = fc(k ± νs),
where fr is the resonance frequency, fc is the circulation frequency and k is an integer.
Ramping an rf magnet’s frequency through fr can flip each particle’s spin. The
Froissart-Stora (FS) equation [1] relates the beam’s final polarization after crossing the
resonance Pf, to its initial polarization Pi
Pf = Pi
�
2exp
�
−(π εFS fc) 2 �
Δf/Δt
�
− 1 ; (1)
εFS is the spin resonance strength, Δf and Δt are the rf frequency’s ramp range and
ramp time. For a flat ring, with a short rf magnet causing the only spin perturbation,
εBdl due to rf solenoid’s or an rf dipole’s B-field was thought to be given by [2]
RF solenoid (longitudinal B): εBdl = 1
π2 √ 2
415
e(1 + G) �
Brmsdl, (2)
p