= Strong-field steady magnetoconvection varying along the field
{title2=$m_c^4\sim\pi^6/Q,\quad R_c=\pi^2Q+2\pi^3\sqrt Q+3\pi^4+o(1)$}
Restrict the <horizontal-field magnetoconvection dispersion relation> to $k=0$, $x=m^2>0$. The steady neutral curve becomes $R=\pi^2Q+(Q+3\pi^2)x+x^2+3\pi^4+\pi^6/x$. Its unique minimum satisfies $x^2(Q+3\pi^2+2x)=\pi^6$, since $R''(x)=2+2\pi^6/x^3>0$. Expanding at large <Chandrasekhar number> gives $x\sim\pi^3Q^{-1/2}$ and the stated <asymptotic expansion>. Unlike field-aligned rolls, these disturbances bend the field, and their stationary threshold grows with field strength.
// Target: fluid-mechanics.bigb
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