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 representation. On this map, the height of (with Pht the total heating power density and τE 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 ; the value of 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 by (fα is the fraction of the alpha particle heating Pα causing confinement degradation, ηα is the fraction of the alpha heating power trapped in the plasma). The saddle point becomes higher and shifts to a larger nτE regime by this alpha degradation effect.