  The neutrino helicity-flip process under the conditions of the supernova core
is reinvestigated. Instead of the uniform ball model for the SN core used in
previous analyses, realistic models for radial distributions and time evolution
of physical parameters in the SN core are considered. A new upper bound on the
Dirac neutrino magnetic moment is obtained from the limit on the supernova core
luminosity for nu_R emission.
