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For disturbances varying only along the imposed magnetic field, set $k=0$ and $x=m^2>0$. The steady horizontal-field magnetoconvection dispersion relation becomesExpand it in powers of $x$:Its derivative and second derivative areBecause $R$ diverges as $x\to 0$ and $x\to \infty$, the unique minimum is determined byFor large Chandrasekhar number, this equation first gives $x\sim {\pi }^3{Q}^{-1/2}$ and hence the requested strong-field steady magnetoconvection varying along the field selection law:

For the threshold through order unity, the leading $Qx+{\pi }^6/x$ contribution at its optimum is $2{\pi }^3\sqrt{Q}$. More precisely, the stationary equation givesThe correction to $Qx+{\pi }^6/x$ has no first-order contribution because that expression is already stationary at its leading minimizer. Also $3{\pi }^{2}x=O(Q^{-1/2})$ and $x^2=O(Q^{-1})$. ThereforeThe constant term $3{\pi }^4$ must be retained. This restricted family bends magnetic field lines, so its large stationary threshold is compatible with the unrestricted field-aligned minimum in the preceding part.