The thermomagnetic flux-jump instability of the Bean critical state is
considered, which may occur during flux penetration in thin films of
type-II superconductors in a perpendicular magnetic field. We calculat
e the applied field B-j at which this instability occurs and its depen
dence on the ramp rate B-a, on the nonlinear current-voltage curve, an
d on the thermal resistance between the film and the substrate. As exa
mples we consider the thermomagnetic flux-jump instability at the stra
ight edge of a superconducting film and of the same edge containing a
small indentation of semicircular shape. The presence of a small inden
tation drastically reduces the field or ramp rate at which the thermom
agnetic instability occurs.