  The space charge limited emission of ions from a target in the focus of an
intense relativistic electron beam is studied analytically for the case of a
spatially varying target density profile. In particular, the emission in the
presence of an under-dense plasma shelf in contact with the solid density
target dramatically differs from the case of an abrupt solid-vacuum boundary.
It is found that an under-dense gradient scale length several times that of the
beam radius at the focus reduces the emission by at least an order of magnitude
over that to be expected from a solid-vacuum boundary.
