The paper presents a method for determining the potential of a reactor design to reach ignition conditions. The method makes use of a 'generalized' contour map with a three-dimensional (P h ,T|, nr E , T) representation. On this map, the height of P h j\ (with P hl the total heating power density and T E the energy confinement time) at the saddle point provides a criterion for reaching ignition. By a combination of this map with Goldston's L-mode scaling law, it is found that the operating point of the tokamak moves along a line of constant P h ,T|; the value of P h ,r| for H-mode scaling can be increased with auxiliary heating power so that the saddle point can be reached. Confinement degradation effects due to alpha particle heating can be treated by replacing P h I r| by (P h , + f a i) a P a )T| (f o is the fraction of the alpha particle heating P a causing confinement degradation, rj a is the fraction of the alpha heating power trapped in the plasma).The saddle point becomes higher and shifts to a larger nr E regime by this alpha degradation effect.