  A dipolar condensate confined in a toroidal trap constitutes a self-induced
Josepshon junction when the dipoles are oriented perpendicularly to the trap
symmetry axis and the s-wave scattering length is small enough. The ring-shaped
double-well potential coming from the anisotropic character of the mean-field
dipolar interaction is robust enough to sustain self-trapping dynamics, which
takes place when the initial population imbalance between the two wells is
large. We show that in this system the self-trapping regime is directly related
to a vortex-induced phase-slip dynamics. A vortex and antivortex are
spontaneously nucleated in the low density regions, before a minimum of the
population imbalance is reached, and then cross the toroidal section in
opposite directions through the junctions.This vortex dynamics yields a phase
slip between the two weakly linked condensates causing an inversion of the
particle flux.
