  The non-local non-linearity introduced by the dipole-dipole interaction plays
a crucial role in the physics of dipolar Bose-Einstein condensates. In
particular, it may distort significantly the stability of straight vortex lines
due to the rotonization of the Kelvin-wave spectrum. In this paper we analyze
this instability showing that it leads to a second-order-like phase transition
from a straight vortex-line into novel helical or snake-like configurations,
depending on the dipole orientation.
