Anti-dynamo theorem
= Anti-dynamo theorem
An anti-dynamo theorem gives a geometric or analytic restriction excluding self-sustained <dynamo action> under stated <magnetic diffusivity>, domain and boundary conditions. It excludes regeneration against resistive decay, not all transient amplification or field induced by an external source. Important restrictions include <Cowling anti-dynamo theorem>, the <toroidal-velocity anti-dynamo theorem>, and the <planar anti-dynamo theorem>. <Backus' necessary condition for dynamo action> instead bounds the stretching required for possible regeneration.