  We examine analytically equilibrium conformations of elastic chains of
paramagnetic beads in the presence of a precessing magnetic field.
Conformations of these filaments are determined by minimizing their total
energy, given in the harmonic approximation by the sum of the bending energy,
quadratic in its curvature, and the magnetic dipolar interaction energy,
quadratic in the projection of the vector tangent to the filament onto the
precession axis. In particular, we analyze two families of open filaments with
their ends aligned along the precession axis and described by segments of
planar curves and helices. These configurations are characterized in terms of
two parameters encoding their features such as their length, separation between
their ends, as well as their bending and magnetic moduli, the latter being
proportional to the magnitude and precession angle of the magnetic field. Based
on energetic arguments, we present the set of parameter values for which each
of these families of curves is probable to occur.
