  We show that the moduli space of regular affine vortices, which are solutions
of the symplectic vortex equation over the complex plane, has the structure of
a smooth manifold. The construction uses Ziltener's Fredholm theory results
[31]. We also extend the result to the case of affine vortices over the upper
half plane. These results are necessary ingredients in defining the "open
quantum Kirwan map" proposed by Woodward [24].
