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 ${\nu }_s=1/2$, placing the in-plane spin-precession signal at half the revolution frequency ($\sim$39 kHz), in the DC SQUID band. Three pickup channels (cosine-$\theta$ and sine-$\theta$ 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 ${\nu }_s{f}_{\mathrm{rev}}$, 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-$\pi$-echo-restore cycles are summed coherently via a matched filter across all bunches, with $\mathcal{O}({\alpha }^2/{\pi }^2)\sim 10^{-4}$ loss per cycle, negligible over a full $\delta P/P=1\%$ measurement. For tipping angle $\alpha =30$ mrad, polarization $P=0.7$, and effective rms spin-tune spread ${\sigma }_{{\nu }_s}^{\mathrm{eff}}=10^{-3}$ (coherence time $\sim$2 ms), the integration time to reach $\delta P/P=1\%$ 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.

67 pages, 18 figures, 10 tables