  We generalize to three active flavours a previous two flavour model for the
resonant spin flavour conversion of solar neutrinos to sterile ones, a
mechanism which is added to the well known LMA one. The transition magnetic
moments from the muon and tau neutrinos to the sterile play the dominant role
in fixing the amount of active flavour suppression. We also show, through
numerical integration of the evolution equations, that the data from all solar
neutrino experiments except Borexino exhibit a clear preference for a sizable
magnetic field either in the convection zone or in the core and radiation zone.
This is possibly related to the fact that the data from the first set are
average ones taken during a period of mostly intense solar activity, whereas in
contrast Borexino data were taken during a period of quiet sun. We argue that
the solar neutrino experiments are capable of tracing the possible modulation
of the solar magnetic field. Those monitoring the high energy neutrinos, namely
the $^8 B$ flux, appear to be sensitive to a field modulation either in the
convection zone or in the core and radiation zone. Those monitoring the low
energy fluxes will be sensitive to the second type of solar field profiles
only. In this way Borexino alone may play an essential role, since it examines
both energy sectors, although experimental redundance from other experiments
will be most important.
