Neutrino Spin-Flavor Conversions and Electron Antineutrino emission from the Sun with Random Magnetic Field

The magnetic field in the solar convective zone has a random small-scale component with the r.m.s. value substancially exceeding the strength of a regular large-scale field. For two Majorana neutrino flavors and two helicities in the presence of a neutrino transition magnetic moment and nonzero neutrino mixing we analize the displacement of the allowed (Delta m^2 - sin^2 2theta)-parameter region reconciled for all Underground experiments with solar neutrinos in dependence on the r.m.s. magnetic field value b. In contrary with the RSFP scenario with a regular large-scale magnetic field, we find an effective production of electron antineutrinos in the Sun even for small neutrino mixing through the cascade conversions like nu_eL -> \bar{nu}_muR -> \bar{nu}_eR. It was found that usual SMA and LMA MSW parameter regions maybe forbidden while opening LOW MSW as the allowed one from the non-observation of \bar{nu}_eR in the SK experiment if random magnetic fields have strengths b > 100 kG and correlation lengths shorter than L_0 < 1000 km.