= Strong-field wavenumber selection in magnetoconvection
{title2=$k_*\propto Q^{1/6}$}
Both steady and oscillatory neutral curves have the form $R=C(k^2+p)^3/k^2+DQp(k^2+p)/k^2$, with $p=\pi^2$. Their exact minimizing condition is $x^2(2x+3p)=p^3+(D/C)Qp^2$, where $x=k^2$. For fixed positive coefficients and large <Chandrasekhar number>, $x\sim[Dp^2Q/(2C)]^{1/3}$ and $R_{\rm min}=DpQ+3C^{1/3}(Dp^2Q/2)^{2/3}+O(Q^{1/3})$. The optimum balances transverse diffusion against the magnetic penalty, leading to increasingly narrow rolls.
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