Limits to sympathetic evaporative cooling of a two-component Fermi gas

We find a limit cycle in a quasiequilibrium model of evaporative cooling of a two-component trapped fermion gas. The existence of such a limit cycle represents an obstruction to reaching the quantum ground state evaporatively. We show that evaporatively beta mu similar to O(1). We speculate that one may be able to cool an atomic Fermi gas further by photoassociating dimers near the bottom of the Fermi sea.