Stern--Gerlach Spin Sorting and Dynamical Feedback in Relativistic Pair-Plasma Reconnection

We derive a Stern–Gerlach control parameter, $\mathrm{\Xi }$, comparing spin-driven cross-sheet displacement with the relativistic Larmor radius. It places heliospheric plasmas and most astrophysical jets in the negligible regime, some stellar-mass black-hole coronae in a transitional regime, and magnetar sheets in a strong, near-QED regime. Relativistic pair-plasma simulations at fixed ${\gamma }_{\mathrm{t}\mathrm{r}}=2$ show that increasing $\mathrm{\Xi }$ produces, within the coupled SG+${\mathbf{J}}_M$ model, magnetic-moment sorting and magnetization-current feedback that enhance the normalized flux-growth rate through an additional spin-kinetic pathway beyond classical pressure- and geometry-controlled pair-plasma reconnection.