= Localization condition for the fastest orthogonal-field interface mode
{title2=$K_*H=(B_-^2-B_+^2)/(4B_+^2)\gg1$}
For the density jump of a <magnetic pressure discontinuity in an isothermal atmosphere>, with $0<|B_+|<|B_-|$, the fastest <Rayleigh-Taylor instability> has $m=0$ and $|k|=K_*=(B_-^2-B_+^2)/(4B_+^2H)$. Its vertical decay length is $K_*^{-1}$. Hence localization relative to both common <scale heights> requires $4B_+^2\ll B_-^2-B_+^2$. This also makes its growth speed small compared with the isothermal sound speed. If $B_+=0$, the ideal sharp-interface <dispersion relation> instead has unbounded growth as $|k|\to\infty$: there is no finite maximizing mode.
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