Generalized Saddle Point Condition for Ignition in a Tokamak Reactor with Temperature and Density Profiles

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Abstract
The concept of a generalized ignition contour map, showing , nτE, and T, is extended to the realistic case of a plasma with temperature and density profiles in order to study access to ignition in a tokamak reactor ( is the average total auxiliary heating power density). The “generalized” saddle point, which corresponds to the minimum height of , is found to lie between the Lawson and ignition conditions. If the height of the operation path with Goldston L-mode scaling is higher than the generalized saddle point, a reactor can reach ignition with this scaling for the case with no confinement degradation effect due to alpha-particle heating. In this sense, the saddle point given in a general form is a new criterion for reaching ignition. Peaking the profiles for the plasma temperature and density can lower the height of the generalized saddle point and help a reactor to reach ignition. With this in mind, we can judge whether next-generation tokamaks, such as Compact Ignition Tokamak, Tokamak Ignition/Burn Experimental Reactor, Next European Torus, Fusion Experimental Reactor, International Tokamak Reactor, and AC Tokamak Reactor, can reach ignition with realistic profile parameters and an L-mode scaling law. We can also obtain the required confinement enhancement factor with respect to L-mode scaling for reaching ignition. The confinement degradation effects on the operation path due to alpha heating are also considered.