Abstract
An analysis of thermomagnetic convection in a thin horizontal layer of magnetic fluid constrained
horizontally by impermeable layers and subjected to a spatially and symmetrically modulated magnetic field is
presented. The magnetic field as well as the temperature gradient are oriented vertically. For any nonzero magnetic
field the base state is a convective one formed by a double vortex which reflects the symmetrical modulation. For
long wave modulations the linear stability analysis reveals that the critical Rayleigh number Rac for the stability
of the base state against small disturbances increases with increasing magnetic driving force. An analytical
expression for Rac is derived which shows the characteristic feature of sudden jumps of Rac at particular values
of the magnetic driving force.
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