Quantum noninvasive three-component beam-spin polarimetry in the Hadron Storage Ring of the Electron-Ion Collider

Abstract

We propose a noninvasive SQUID-based polarimeter for the polarized proton beam in the Electron-Ion Collider (EIC) Hadron Storage Ring (HSR), exploiting the collective magnetic dipole moment of the bunches rather than scattering. The six-snake HSR lattice has synchronous-particle spin tune $ν_s = 1/2$, placing the in-plane spin-precession signal at half the revolution frequency ($\sim$39 kHz), in the DC SQUID band. Three pickup channels (cosine-$θ$ and sine-$θ$ saddle loops for the transverse components, a coaxial axial gradiometer for the longitudinal one) reconstruct the full polarization vector $(P_x, P_y, P_z)$ in two complementary modes. Static mode, the default for continuous noninvasive monitoring, reads all three components: $P_y$ at the revolution frequency and the residual in-plane components at $ν_s f_\mathrm{rev}$, bunch by bunch over an hours-long fill, including $P_z$, inaccessible to single-spin scattering polarimetry by parity conservation. Dynamic mode gives a precise polarization-magnitude measurement: a longitudinal kicker tips a small fraction of the polarization into the horizontal (ring) plane to produce a free-induction-decay (FID) signal, and many phase-locked tip-$π$-echo-restore cycles are summed coherently via a matched filter across all bunches, with $\mathcal{O}(α^2/π^2) \sim 10^{-4}$ loss per cycle, negligible over a full $δP/P = 1\%$ measurement. For tipping angle $α= 30$ mrad, polarization $P = 0.7$, and effective rms spin-tune spread $σ_{ν_s}^\mathrm{eff} = 10^{-3}$ (coherence time $\sim$2 ms), the integration time to reach $δP/P = 1\%$ is about 18 s at injection and 5 min at flattop. The architecture extends to deuteron and $^3$He beams via species-specific spin-magnetic factors, with applications to storage-ring EDM searches.