A simple analytical model of a steady state, resistive magnet tokamak reactor is used to derive an optimized design yielding the minimum cost per watt of electricity. The optimization is performed subject to constraints imposed by plant power balance requirements and first stability region beta scaling laws. In addition, the design is required to satisfy a series of inequalities, derivable from straightforward physics and engineering considerations, which further limit the range of values that reactor parameters can assume. Particular attention is given to the scaling of plant cost per watt with plasma aspect ratio, elongation and safety factor in order to determine the conditions under which raising beta improves reactor performance. Even though the model is idealized, the results agree semi-quantitatively with reactor systems code calculations.
Determination of the tolerable impurity concentrations in a fusion reactor using a consistent set of cooling factors