We consider a mean magnetic induction fieldBevolving in an electrically conducting turbulently convecting fluid sphereV, where gravity acting radially is the only force imposing order. The turbulence is radially stratified and mirror-symmetric about planes through the origin. The only possible mean flow is spherically symmetric and radial. For small-scale turbulence, a large-scale mean field emf is generated that to a good approximation is linear inBandVB.This emf comprises the spherically symmetric #x3B2;1, #x3B2;2, #x3B3;1and #x3B4;r1effects of R#xE4;dler (1980). In combination with the molecular magnetic diffusivity #x3B7;m, these effects produce anisotropic diffusion, different for poloidalSand toroidalTmagnetic fields, and characterised by generalised diffusion coefficients #x3B7;i(i= 0, 1, 2). The #x3B3;1and #x3B4;r1effects also produce field generation similar to induction by a radial compressible laminar flow or equivalent (e.g. thermomagnetic) effect. Reasoning that usually #x3B7;i 0, we prove decay of the norms maxr2Br and T/r1,v. For each of these norms, we give a bounding function that decays exponentially with a prescribed decay rate. Furthermore, the decay of each norm is strictly monotonic, regardless of time variations in the generation or diffusion terms. We infer that a self-exciting mean field dynamo cannot persist unless some mechanism, such as rotation, is present to break either the spherical or mirror symmetry of the turbulence. For low conductivity (large #x3B7;m) or strong turbulence (large #x3B2;1), and relatively weak anisotropy (smaller #x3B2;2, #x3B4;r1) the decay occurs on the total diffusion time-scale determined by #x3B7;m+ #x3B2;1In stars where #x3B2;1probably dominates, the decay is therefore very fast on the molecular diffusion time-scale. In such cases rotation is an obvious choice for symmetry-breaker, and possible field maintenance.
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