Subcritical magnetoconvection

Subcritical magnetoconvection means finite-amplitude convection on the stable side of the linear conductive-state threshold. At large magnetic Reynolds number, flux expulsion can reduce interior magnetic inhibition enough to sustain a nonlinear convective cell even when infinitesimal disturbances decay in the unredistributed imposed field. Stable subcritical states can produce hysteresis and magnetic flux separation. A schematic saturated amplitude equation $\dot{A}=\mu A+c|A{|}^{2}A-d|A{|}^{4}A$, $c,d>0$, has an unstable lower branch and stable upper radial branch for $-c^2/(4d)<\mu <0$, coexisting with stable $A=0$. This illustrates bistability; it is not a derivation of coefficients for all magnetoconvection geometries.