Neutrino Spin Flavour Precession in Fluctuating Solar Magnetic Fields

The effect of a random magnetic field in the convective zone of the Sun on resonant neutrino spin oscillations, i.e. transitions of the type $\nu_{eL}\to\tilde\nu_{\mu R}$, is considered. The average survival probability and the expected experimental signals in the existing solar neutrino experiments are computed as a function of the level of the noise and magnitude of a constant magnetic field in the convective zone. From comparison with observed detection rates we conclude that the RSFP solutions to the SNP with negligible mixing angle are stable under the presence of low or moderate levels of noise. Detection rates, specially in the Homestake experiment, are however sensitive to large levels of noise. As a consequence, an upper limit on small scale magnetic fluctuations is obtained from the combined solar data: $\surd\langle B^2\rangle< 140-200$ kG for the scale $L_0\sim 1000$ km and transition moment $\mu=10^{-11} \mu_B$.