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Given a compact 3-manifold $Y$ and a $\mathbb Z_2$-harmonic spinor $(\mathcalZ_0, A_0,\Phi_0)$ with singular set $\mathcal Z_0$, this article constructs afamily of local solutions to the two-spinor Seiberg-Witten equationsparameterized by $\epsilon \in (0,\epsilon_0)$ on tubular neighborhoods of$\mathcal Z_0$. These solutions concentrate in the sense that the $L^2$-norm ofthe curvature near $\mathcal Z_0$ diverges as $\epsilon\to 0$, and afterrenormalization they converge locally to the original $\mathbb Z_2$-harmonicspinor. In a sequel to this article, these model solutions are used in a gluingconstruction showing that any $\mathbb Z_2$-harmonic spinor satisfying somemild assumptions arises as the limit of a family of two-spinor Seiberg-Wittensolutions on $Y$.

Concentrating Local Solutions of the Two-Spinor Seiberg-Witten Equations on 3-Manifolds