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The neutrino chirality-flip process under the conditions of the supernovacore is investigated in detail with the plasma polarization effects in thephoton propagator taken into account in a more complete form than in earlierpublications. It is shown in part that the contribution of the proton fractionof plasma is essential. New upper bounds on the neutrino magnetic moment areobtained: mu_nu < (0.5 - 1.1) 10^{-12} mu_B from the limit on the supernovacore luminosity for nu_R emission, and mu_nu < (0.4 - 0.6) 10^{-12} mu_B fromthe limit on the averaged time of the left-handed neutrino washing out. Thebest upper bound on the neutrino magnetic moment from SN1987A is improved bythe factor of 3 to 7.

Plasma induced neutrino spin-flip in a supernova and new bounds on the neutrino magnetic moment