Do solar neutrinos constrain the electromagnetic properties of the neutrino?

It is of great interest whether the recent KamLAND bound on the flux of electron antineutrinos from the Sun constrains the electromagnetic properties of the neutrino. We examine the efficiency of the electron antineutrino production in the solar magnetic fields, assuming the neutrinos are Majorana particles with a relatively large transition moment. We consider fields both in the radiative and convective zones of the Sun, with physically plausible strengths, and take into account the recently established values of the oscillation parameters. Our analysis shows that the production rate in question is presently unobservable. In the radiative zone, it is suppressed by the large measured value of the flavor mixing angle which eliminates the resonant level crossing. A corresponding general resonance condition, valid for large as well as small values of the mixing angle, is derived. Likewise, in the convective zone, the strength of the small-scale magnetic field is likely insufficient. Thus, no useful bound on the neutrino transition moment can be derived from the published KamLAND bound. KamLAND may be, however, on the edge of probing an ``optimistic'' scenario, making further improvements of its sensitivity desirable.