= Strong-field quenching of an isotropic electromotive force
{title2=$\alpha_{\parallel}\propto |B|^{-3}$}
For isotropic monochromatic forcing, the longitudinal coefficient in a <mean-field electromotive force> is proportional to $\int_0^1\mu^2(1+h^2\mu^2)^{-2}d\mu=[\arctan h-h/(1+h^2)]/(2h^3)$, where $h$ is proportional to mean-field strength. This gives generic $|B|^{-3}$ quenching. The natural angular <alpha tensor> is anisotropic in a nonzero mean field: its transverse coefficient instead contains $\int_0^1(1-\mu^2)(1+h^2\mu^2)^{-2}d\mu$ and scales as $|B|^{-1}$. Only the longitudinal contraction enters $\boldsymbol{\mathcal E}=\boldsymbol\alpha\mathbf B$. An effective scalar representation may therefore have every diagonal entry equal to the longitudinal coefficient without being the unique natural response tensor.
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