Field-reversed configurations (FRCs) have extremely attractive reactor attributes because of their singly connected geometry. They have been created in theta-pinch devices, but being compact toroids and lacking a center hole, their toroidal current cannot be sustained by transformer action as in other toroidal configurations. A new device, the Translation, Confinement, and Sustainment (TCS) facility has been constructed to use rotating magnetic fields (RMFs) to build up and sustain the flux of hot FRCs formed by the normal theta-pinch method. RMF formation and sustainment of similar, but cold, pure poloidal field configurations have been demonstrated in devices called rotamaks, and RMF formation, but not sustainment, has been achieved in a smaller FRC facility called the Star Thrust Experiment (STX). Initial formation and sustainment have now been achieved in TCS, albeit still with cold (Te ~ 50 eV) plasmas. Both the formation and final steady-state conditions are found to agree with newly developed analytic and numerical models for RMF flux buildup and sustainment inside a standard cylindrical flux conserver. The required plasma conditions (mainly resistivity but also density) can now be determined for the planned hot FRC, RMF flux buildup experiments and for eventual reactor conditions.