Previous Vlasov theories of the plane magnetopause have yielded nonunique solutions because particle distribution functions were assigned arbitrarily in different regions of phase space. We show that consideration of particle accessibility removes this nonuniqueness. In a restricted model consisting of a collisionless, steady state, plane model with no normal magnetic field component, particles are trapped at the magnetopause. Therefore these restrictions must be relaxed in order to allow for particle access to the magnetopause via drifts from source region. The first adiabatic invariant for particle motion can be defined in such a way that it is preserved in regions of large field gradients, provided that the gradients are in a direction primarily perpendicular to the particle drifts. This generalized invariant provides an adiabatically conserved quantity that can be used to characterize particles as they move from a source region, through the drift region, and into the magnetopause itself, and therefore can e used to help resolve the accessibilty question. We show how to obtain magnetopause structure based on location of the particle guiding points and give some preliminary results. However, a complete solution will probably require a time-dependent determination of the particle drift paths.