Because of the demand for intense neutron beams for applications in basic and applied sciences, several design concepts have appeared in the literature recently. It is, therefore, appropriate to present a theory that connects the large variety of possible designs in order to individualize the main parameters from the neutronic point of view; the theory is validated with results from numerical analysis that simulate the transport of neutrons in such drastically different systems as spallation and fission sources. The theory is used to present scoping studies for the production of thermal neutron fluxes around and beyond 1020/m2·s.