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

Abstract

In this paper, the concept of a generalized ignition contour map, 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. The generalized saddle point 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, the authors 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.