= Maximum-strain bound on dynamo growth
{title2=$g_B\leq\sup_{x,t}\lambda_{\max}(e(x,t))$}
Under the energy-closed boundary assumptions of <Backus' necessary condition for dynamo action>, the <magnetic energy> equation gives $\dot E_B\leq2s(t)E_B$ after discarding nonnegative resistive dissipation. Integrating gives an upper bound by the time average of the largest spatial <eigenvalue> of the <rate-of-strain tensor>. Thus the field-amplitude exponent is at most its space-time supremum. The exponent of squared energy is twice the field-amplitude exponent.
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