An important area of magnetospheric research is to understand the dynamics of the magnetopause current layer which is responsive to solar wind-magnetosphere coupling processes. The focus of this study will be on the formation and the stability of the magnetopause current layer using a 2 1/2 dimensional electromagnetic particle simulation model. Previous results obtained from the model revealed that the self-consistent boundary layer between the solar wind and the dipolar magnetic field is unstable with respect to transverse perturbations whose wavelengths were of the order of a solar wind ion gyroradius. The study will extend previous work on the current layer in many directions by using the simulation model and by analytic theory. For example, the anomalous diffusion at the boundary will be studied as well as the formation and stability of the boundary layer.