  This paper considers the stability of liquid metal drops subject to a
high-frequency AC magnetic field. An energy variation principle is derived in
terms of the surface integral of the scalar magnetic potential. This principle
is applied to a thin perfectly conducting liquid disk, which is used to model
the drops constrained in a horizontal gap between two parallel insulating
plates. Firstly, the stability of a circular disk is analysed with respect to
small-amplitude harmonic edge perturbations. Analytical solution shows that the
edge deformations with the azimuthal wavenumbers m=2,3,4... start to develop as
the magnetic Bond number exceeds the critical threshold Bm_c=3pi(m+1)/2. The
most unstable is m=2 mode, which corresponds to an elliptical deformation.
Secondly, strongly deformed equilibrium shapes are modelled numerically by
minimising the associated energy in combination with the solution of a surface
integral equation for the scalar magnetic potential on an unstructured
triangular mesh. The edge instability is found to result in the equilibrium
shapes of either two- or threefold rotational symmetry depending on the
magnetic field strength and the initial perturbation. The shapes of higher
rotational symmetries are unstable and fall back to one of these two basic
states. The developed method is both efficient and accurate enough for
modelling of strongly deformed drop shapes.
