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Solar prominences are subject to both field-aligned (longitudinal) andtransverse oscillatory motions, as evidenced by an increasing number ofobservations. Large-amplitude longitudinal motions provide valuable informationon the geometry of the filament-channel magnetic structure that supports thecool prominence plasma against gravity. Our pendulum model, in which therestoring force is the gravity projected along the dipped field lines of themagnetic structure, best explains these oscillations. However, several factorscan influence the longitudinal oscillations, potentially invalidating thependulum model. The aim of this work is to study the influence of large-scalevariations in the magnetic field strength along the field lines, i.e.,variations of the cross-sectional area along the flux tubes supportingprominence threads. We studied the normal modes of several flux tubeconfigurations, using linear perturbation analysis, to assess the influence ofdifferent geometrical parameters on the oscillation properties. We found thatthe influence of the symmetric and asymmetric expansion factors on longitudinaloscillations is small.}{We conclude that the longitudinal oscillations are notsignificantly influenced by variations of the cross-section of the flux tubes,validating the pendulum model in this context.

The effects of magnetic-field geometry on longitudinal oscillations of solar prominences: Cross-sectional area variation for thin tubes