= Cowling anti-dynamo theorem
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= Cowling theorem
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{synonym}
An isolated axisymmetric <magnetic field> cannot be sustained by ordinary resistive <dynamo action> with scalar positive <magnetic diffusivity>. Its <poloidal magnetic flux function> satisfies a homogeneous scalar advection-diffusion equation with no toroidal-to-poloidal source. The maximum principle excludes regeneration of that flux; after it decays the toroidal field has no lasting source either. This constrains the symmetry of the field. An <axisymmetric flow> may still generate a nonaxisymmetric field, and a turbulent mean-field electromotive force is not covered by the unmodified scalar-induction proof.
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