  We study the properties of a magnetic dipolar Bose-Einstein condensate (BEC)
in an elongated (cigar shaped) confining potential in the beyond
quasi-one-dimensional (quasi-1D) regime. In this system the dipole-dipole
interactions (DDIs) develop a momentum-dependence related to the transverse
confinement and the polarization direction of the dipoles. This leads to
density fluctuations being enhanced or suppressed at a length scale related to
the transverse confinement length, with local atom number measurements being a
practical method to observe these effects in experiments. We use meanfield
theory to describe the ground state, excitations and the local number
fluctuations. Quantitative predictions are presented based on full numerical
solutions and a simplified variational approach that we develop. In addition to
the well-known roton excitation, occurring when the dipoles are polarized along
a tightly confined direction, we find an "anti-roton" effect for the case of
dipoles polarized along the long axis: a nearly non-interacting ground state
that experiences strongly repulsive interactions with excitations of
sufficiently short wavelength.
