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The detailed distribution of mass within clusters of galaxies can be used toprobe the nature of dark matter. We show that constraints on the extent of themass distribution around galaxies in the rich cluster Abell 2218 obtained fromcombining strong and weak lensing observations are consistent with thepredictions which assume that the dominant mass component (dark matter) inthese halos is collisionless. A strongly interacting (fluid-like) dark matteris ruled-out at a confidence level of more than 5-sigma.Comment: minor revisions, ApJ Letters in press, matches print versio

Constraints on the Collisional Nature of the Dark Matter from Gravitational Lensing in the Cluster A2218