A point model of particle densities and temperatures within a CTR is formulated, and equilibrium solutions are obtained for different plausible operating regimes of a D-T reactor of commercial interest. The stability of these equilibrium points against excursions in the overall particle densities and temperatures is determined by linear analysis and confirmed by dynamic simulation – certain regimes are found to be unstable. Control of a CTR about an unstable equilibrium point by varying the injected ion intensity and D-T mixture is investigated and found to be difficult when the ion containment time is not large with respect to the delay time between consecutive changes in the injected ion beam.