  Magnetic fields of strongly magnetized stars can trap conducting matter due
to frozen-in condition. In the force-free regime, the motion of the matter
along the field lines may be considered in the "bead on a wire" approximation.
Such a motion, if gravity and centrifugal forces are taken into account, has
equilibrium points, some of which are stable. In most cases, stability is
possible in about several per cent of the possible locations. Corresponding
oscillation frequencies span the range from zero to $\sqrt{3}$ of the spin
frequency. We suggest that this variability mode may be excited in some X-ray
pulsars during the outbursts and create the peaked broad-band noise component
near the break frequency in the power density spectrum, as well as produce some
of the quasi-periodic oscillation features in this frequency range. Existence
of this variability does not require any changes in mass accretion rate and
involves only a small amount of matter infiltrating from the disc and magnetic
flow due to interchange instabilities.
