  An easily scalable toroidal geometry presents an opportunity for creating
large scale persistent currents in Bose-Einstein condensates, for studies of
the Kibble-Zurek mechanism, and for investigations of toroidally trapped
degenerate Fermi gases. We consider in detail the process of isentropic loading
of a Bose or Fermi gas from a harmonic trap into the scale invariant toroidal
regime that exhibits a high degree of system invariance when increasing the
radius of the toroid. The heating involved in loading a Bose gas is evaluated
analytically and numerically, both above and below the critical temperature.
Our numerical calculations treat interactions within the
Hartree-Fock-Bogoliubov-Popov theory. Minimal change in degeneracy is observed
over a wide range of initial temperatures, and a regime of cooling is
identified. The scale invariant property is further investigated analytically
by studying the density of states of the system, revealing the robust nature of
scale invariance in this trap, for both bosons and fermions. We give analytical
results for a Thomas-Fermi treatment. We calculate the heating due to loading a
spin-polarized Fermi gas and compare with analytical results for high and low
temperature regimes. The Fermi gas is subjected to irreducible heating during
loading, caused by the loss of one degree of freedom for thermalization.
