  An important issue in the dynamics of neutron star binaries is whether tidal
interaction can cause the individual stars to collapse into black holes during
inspiral. To understand this issue better, we study the dynamics of a cluster
of collisionless particles orbiting a non-rotating black hole, which is part of
a widely separated circular binary. The companion body's electric- and
magnetic-type tidal fields distort the black hole and perturb the cluster,
eventually causing the cluster to collapse into the hole as the companion
spirals in under the influence of gravitational radiation reaction. We find
that magnetic-type tidal forces do not significantly influence the evolution of
the cluster as a whole. However, individual orbits can be strongly affected by
these forces. For example, some orbits are destabilized due to the addition of
magnetic-type tidal forces. We find that the most stable orbits are close to
the companion's orbital plane and retrograde with respect to the companion's
orbit.
