Thermal generation of Alfven waves in oscillatory magnetoconvection

Marginal convection in the form of Alfven waves in an electrically conducti ng Benard layer in the presence of a vertical magnetic field is investigate d analytically using the Boussinesq model for the fluid. Small amplitude so lutions are studied using the linearized magnetoconvection equations. These solutions are represented by double expansions in terms of two small param eters: a dimensionless viscosity and a dimensionless magnetic diffusivity. The leading-order problem corresponds to undamped Alfven waves propagating between the boundaries of the fluid; buoyancy forces appear at higher order and can maintain the Alfven waves against viscous and ohmic damping. The s tructure of the Alfven waves is strongly dependent, even at leading order, on the physical nature of the walls. Four different types of boundary condi tions are considered here: (A) illustrative, i.e. mathematically simple con ditions, (B) solid, perfectly conducting walls, (C) vacuum external to the layer, and (D) solid, perfectly insulating walls. It is shown how in each c ase Alfven waves are excited by a small, but sufficiently strong, thermal b uoyancy but that, because of boundary layers, the solutions for the four se ts of boundary conditions are very different.