Relativistic Scaling and Magnetization-Current Feedback in Stern Gerlach-Modified Pair-Plasma Reconnection: SpinPIC2D Validation and Nonlinear Regimes

We investigate the relativistic scaling and electromagnetic feedback of Stern–Gerlach (SG) force driven spin transport in pair-plasma reconnection with SpinPIC2D. The model advances relativistic proper momentum and magnetic BMT spin precession, applies the SG force, deposits spin magnetization, and includes ${\mathbf{J}}_M=\mathrm{\nabla }\times \mathbf{M}$ in Ampere’s law. In a weak-seed scan at fixed ${\gamma }_{\mathrm{t}\mathrm{r}}=2$, the normalized global magnetic flux-growth remains near the classical control-run for $\mathrm{\Xi }\le 0.1$, is $0.016$ at $\mathrm{\Xi }=0.4$, and reaches approximately $0.12$ and $0.25$ at $\mathrm{\Xi }=0.7$ and 1, respectively over $3\le t\mathrm{/}{\tau }_{\mathrm{s}\mathrm{p}}\le 7$. Because $\mathrm{\partial }\mathrm{/}\mathrm{\partial }y=0$ in the 2.5-D geometry, the direct $y$-directed SG term vanishes and the enhancement is indirect: sheet-normal SG sorting restructures branch-resolved electron and positron velocity distributions which results in changes in pressure moments and generates a layered magnetization current. Along a fixed-${\chi }_{\mathrm{s}\mathrm{i}\mathrm{m}}$ family, increasing ${\gamma }_{\mathrm{t}\mathrm{r}}$ reduces $\mathrm{\Xi }$ and suppresses branch sorting, whereas the matched-control flux-growth enhancement remains positive for ${\gamma }_{\mathrm{t}\mathrm{r}}=2,3,5$. Retuning ${\chi }_{\mathrm{s}\mathrm{i}\mathrm{m}}$ to hold $\mathrm{\Xi }=1$ does not preserve nonlinear similarity: both the coupling and $J_{M,y}$ increase with ${\gamma }_{\mathrm{t}\mathrm{r}}$, and the ${\gamma }_{\mathrm{t}\mathrm{r}}=5$ case develops a multi-X-line state. Thus $\mathrm{\Xi }$ orders the onset of SG-modified reconnection, while the nonlinear response also depends on the absolute spin coupling and magnetization-current amplitude.