  The space-space component of the photon polarization operator is calculated
in zero frequency limit for a medium with Bose-Einstein condensate (BEC) of
electrically charged particles. It is found that the polarization operator
tends to a finite value at vanishing photon 3-momentum, as it happens in
superconducting media. It means that magnetic fields are exponentially screened
in such a medium analogously to the Debye screening of electric charges. At
non-zero temperature the screened magnetic field oscillates and contains a
contribution which drops only as a power of distance. This phenomenon is
unknown for superconductors, even in BEC phase and can be potentially
observable.
