= Electromagnetic matching for an alpha-Omega interface
{title2=$A=a,\quad A_z=a_z,\quad B=b,\quad\eta B_z=\eta b_z$}
= Interface dynamo matching
{synonym}
For a planar interface, equal permeability and no singular sheet current make all magnetic components continuous. A nonzero horizontal Fourier wavenumber then gives the first three conditions in the title. <Continuity> of the tangential <electric field> supplies the last: continuous mean velocity cancels its advective contribution, and the retained alpha <mean-field electromotive force> is along the toroidal direction, so the other tangential electric component is $-U\partial_xA-\eta\partial_zB$. The given alpha-Omega equations retain only toroidal-to-poloidal alpha generation; adding a full isotropic alpha contribution would alter both the bulk equation and the matching problem.
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