  The screening of impurities in plasma with Bose-Einstein condensate of electrically charged bosons is considered. It is shown that the screened potential is drastically different from the usual Debye one. The polarization operator of photons in plasma acquires infrared singular terms at small photon momentum and the screened potential drops down as a power of distance and even has an oscillating behavior, similar to the Friedel oscillations in plasma with degenerate fermions. The magnetic properties of the cosmological plasma with condensed W-bosons are also discussed. It is shown that W-bosons condense in the ferromagnetic state. It could lead to spontaneous magnetization of the primeval plasma. The created magnetic fields may seed galactic and intergalactic magnetic fields observed in the present-day universe. 
Condensation of charged bosons in plasma physics and cosmology