A model has been constructed to analyze the gross beam-plasma interaction in a laser solenoid plasma. The model includes a simple solution for a slab plasma response to a given laser beam, and a solution for axial beam size variations in response to arbitrary axial plasma structure. The two solutions are combined to determine the coupled behavior. Trapping of the focused laser beam where it enters the plasma is a significant problem, but can be achieved by a minimum level of imbedded field in the plasma. If the beam is trapped, it first focuses and then defocuses near the front of the bleaching wave (front of the laser heated plasma). In order to avoid divergence of the beam near the front, it is essential to have a pre-formed favorable density profile in the plasma. Such a condition is probably achieved automatically in the early stages of plasma heating. Several techniques are discussed which can be used to avert unfavorable refractive behavior (catastrophic self-focusing and defocusing).