  Interaction of magnetic moment of point particles with external
electromagnetic fields experiences unresolved theoretical and experimental
discrepancies. In this work we point out several issues within the relativistic
quantum mechanics and the QED and we describe effects related to a new
covariant classical model of magnetic moment dynamics. Using this framework we
explore the invariant acceleration experienced by neutral particles coupled to
an external plane wave field through the magnetic moment: we study the case of
ultra relativistic Dirac neutrinos with magnetic moment in the range of
$10^{-11}$ to $10^{-20}$ $\mu_\mathrm{B}$; and we address the case of slowly
moving neutrons. We explore how critical accelerations for neutrinos can be
experimentally achieved in laser-pulse interactions. The radiation of
accelerated neutrinos can serve as an important test distinguishing between
Majorana and Dirac nature of neutrinos.
