 Quasistatic vertical-field magnetoconvection

When the magnetic field supplies instantaneous damping rather than an evolving magnetic perturbation, the roll amplitudes obey a two-variable linear system with trace $-[s+\sigma (s+Q{\pi }^2/s)]<0$. Its determinant vanishes at the displayed stationary threshold. Therefore its initial instability cannot be a Hopf bifurcation. This reduced model must not be confused with a three-variable magnetoconvection model carrying finite magnetic diffusivity and an additional oscillatory mode.