  In this work, we compute the structure and composition of the inner crust of
a neutron star in the presence of a strong magnetic field, such as it can be
found in magnetars. To determine the geometry and characteristics of the crust
inhomogeneities, we consider the compressible liquid drop model, where surface
and Coulomb terms are included in the variational equations, and we compare our
results with previous calculations based on more approximate treatments. For
the equation of state (EoS), we consider two non-linear relativistic mean-field
models with different slopes of the symmetry energy, and we show that the
extension of the inhomogeneous region inside the star core due to the magnetic
field strongly depends on the behavior of the symmetry energy in the crustal
EoS. Finally, we argue that the extended spinodal instability observed in
previous calculations can be related to the presence of small amplitude density
fluctuations in the magnetar outer core, rather than to a thicker solid crust.
The compressible liquid drop model formalism, while in overall agreement with
the previous calculations, leads to a systematic suppression of the metastable
solutions, thus allowing a more precise estimation of the crust-core transition
density and pressure, and therefore a better estimation of the crustal radius.
