The dominant mechanisms of energy flow in a novel magnetic confinement device have been examined. The plasma is contained in the space between two concentric cylinders. There is uniformity in the direction parallel to the curved surfaces of the cylinders, i.e., the toroidal direction, and the confining magnetic field is purely toroidal. The plasma has a rectangular cross section, bounded by a planar electrode at one end and a thermionic emitter at the other, and cylindrical walls inside and outside. There is a modest pressure gradient, i.e., NT ≃ constant. The temperature is high in the core of the plasma, where fusion occurs, but falls to low values near the walls and end-plates. It is hoped that the quasi-isobaric character will eliminate or reduce serious instabilities and that plasma behavior will be near classical The high-N, low-T periphery should reduce damage to the walls from energetic plasma particles. The contributions of alpha-particle slowing down, electron cyclotron radiation transport, atomic processes, bremsstrahlung, conduction, convection, and heat exchange between electrons and ions to the energy balance in the plasma have been evaluated. Radiofrequency heating using waves in the lower hybrid range can balance the differential energy equations for electrons and ions throughout the plasma. For a device producing 125 MW of fusion power, there is a class of magnetohydrodynamic equilibria that is energetically sustainable, with Qdt ≃ 0.3. The inner and outer radii and height of the reactor are 31.4, 38.7, and 7.3 m, respectively. A high magnetic field is required, in the range of 20 to 40 T. The temperature T rises from 200 eV near the walls to 2.7 keV in the fusion core, where Nc ≃ 1.5 × 1014 cm−3. The results obtained here are significantly different from those obtained in an earlier study that assumed a slab geometry. This device may be acceptable as the fusion driver of a fusion-fission hybrid reactor. Major technological developments are necessary before such a device can become viable, but there are also some advantages relative to a tokamak reactor.