  Using analytic calculations, the effects of the edge flux surface shape and
the toroidal current profile on the penetration of flux surface shaping are
investigated in a tokamak. It is shown that the penetration of shaping is
determined by the poloidal variation of the poloidal magnetic field on the
surface. This fact is used to investigate how different flux surface shapes
penetrate from the edge. Then, a technique to separate the effects of magnetic
pressure and tension in the Grad-Shafranov equation is presented and used to
calculate radial profiles of strong elongation for nearly constant current
profiles. Lastly, it is shown that more hollow toroidal current profiles are
significantly better at conveying shaping from the edge to the core.
