The conditions for the operation of a tokamak fusion reactor are studied considering a fiducial operating state and analyze variations about this state. We use a volume averaged 0-D two-temperature model and consider the case of a fusion thermonuclear reactor of the ITER type which will operate with a burning plasma at an energy gain factor of Q=10. The possible operation states are represented in POPCON plots of density n versus electron temperature Te by varying parameters such as the fusion power, the energy gain and the auxiliary heating power, but keeping the ratio (T_e - T_i)/T_e fixed, in order to determine the optimal operation point. Then, the thermonuclear instability of the burning plasma around this point is studied with a linear analysis. It is found that this instability cannot be excited, due to the fact that the plasma is far from ignition.
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