  The design of any large stellarator requires a plan for the removal of the
particles and heat that are exhausted across the plasma edge. This is called
the divertor problem, for the particle exhaust must be diverted into pumping
chambers. Although the physics of diverted plasmas has many subtleties, the
magnetic field configuration between the plasma edge and the surrounding
chamber walls is the foundation upon which divertor design is based. The
properties of this magnetic configuration has both practical constraints and
mathematical constraints from magnetic field lines obeying a 1~1/2 degree of
freedom Hamiltonian. Constraints from plasma physics will also be discussed;
they need to be integrated with the constraints from from Hamiltonian mechanics
in conceptual designs of stellarator divertors.
