Spin-orbital dynamics in the B-phase of superfluid helium-3

We report numerical calculations on the spin-orbital dynamics of He-3-B within the formalism of Poisson brackets with the two-fluid model by Leggett and Takagi. We incorporate an additional orbital term in the equations,for the spin-orbit dynamics which plays an important role at very low temperatures, when the damping of orbit dynamics is small. We also find that, under the relevant experimental conditions, the Brinkman-Smith mode is strong v modified by the orbital dynamics. The orbital momentum does not relax completely to the direction of magnetic field, but remains significantly deflected, particularly at very low temperatures, and precesses at the dipole-dipole frequency and nutate at the NMR frequency. We report numerical calculations of the spin-orbit dynamics in the spatially inhomogeneous case. We solved for the mode of precession near the walls of the experimental cell, which significantly deviates from that, obtained in theoretical calculations in previous publications. We also identified the mechanism of instability of homogeneous precession at very low temperatures, the exponential growth of textural-spin waves of the longitudinal mode of NMR.