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We present an investigation of dynamo generation of magnetic fields in the context of accretion disks, which also has relevance to acceleration mechanisms for outflows present in AGN, compact binaries, and YSOs. In this work we improve upon previous treatments of the $\alpha-\omega$ dynamo in accretion disks by including the effects of advection and by adopting known spatial forms for resistivity, shear, and radial drift. In addition we calculate the external fields by employing realistic boundary conditions parameterized to connect to non-zero vacuum or force-free fields. The growth rates for the nonsteady modes are calculated by phase integral approximations and eigenfunction expansions. We find that the fundamental steady quadrupole mode corresponding to a dynamo number of 6.5 has a maximum at the disk surface which is contrary to the usual assumption made. Preliminary results on the theory of MHD winds connecting to dynamo solutions at the disk surface will also be presented.
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