SOLAR INTERFACE DYNAMOS .1. LINEAR, KINEMATIC MODELS IN CARTESIAN GEOMETRY

We describe a simple, kinematic model for a dynamo operating in the vi cinity of the interface between the convective and radiative portions of the solar interior. The model dynamo resides within a Cartesian dom ain, partioned into an upper, convective half and lower, radiative hal f, with the magnetic diffusivity eta of the former region (eta(2)) ass umed to exceed that of the latter (eta(1)) The fluid motions that cons titute the alpha-effect are confined to a thin, horizontal layer locat ed entirely within the convective half of the domain; the vertical she ar is nonzero only within a second, nonoverlapping layer contained ins ide the radiative half of the domain. We derive and solve a dispersion relation that describes horizontally propagating dynamo waves. For su fficiently large values of a parameter analogous to the dynamo number of conventional models, growing modes can be found for any ratio of th e upper and lower magnetic diffusivities. However, unlike kinematic mo dels in which the shear and alpha-effect are uniformly distributed thr oughout the same volume, the present model has wavelike solutions that grow in time only for a finite range of horizontal wavenumbers. An ad ditional consequence of the assumed dynamo spatial structure is that t he strength of the azimuthal magnetic field at the location of the alp ha-effect layer is reduced relative to the azimuthal field strength at the shear layer. When the jump in eta occurs close to the alpha-effec t layer, it is found that over one period of the dynamo's operation, t he ratio of the maximum strengths of the azimuthal fields at these two positions can vary as the ratio (eta(1)/eta(2)) of the magnetic diffu sivities.