  An exact analytic representation of the critical state of a current-carrying
type-II superconductor strip located inside a cylindrical magnetic cavity of
high permeability is derived. The obtained results show that, when the cavity
radius is small, penetration of magnetic flux fronts is strongly reduced as
compared to the situation in an isolated strip. From our generic representation
it is possible to establish current profiles in closed cavities of various
other geometries too by means of conformal mapping of the basic configuration
addressed.
