The burning performance of the self-ignited steady-state plasma is investigated based on a point model. For the ITER-like parameters, the theoretical model scaling law τE, which could explain the characteristics of the L-mode and the high βp-mode fairly well, and the effect of He-ash poisoning are introduced simultaneously. The solutions are obtained by solving the particle and energy balance equations in steady-state conditions, taking account of the effect of radiation loss due to He ash and fuel ions. Typically, there exist four solutions of the plasma current at fixed temperature. The divergence of the temperature, which is predicted by a previous study (Fukuyama et al 1995 Nucl. Fusion 35 1669) for the pure plasma in the high βp-mode, disappears under the influence of He ash. In the low-density limit, the L-mode branches and the high βp-mode branches are well separated on the plane of the current and the temperature. On the other hand, the merging of two branches occurs at higher densities due to the nonlinear effect contained in the scaling law. Examining the constraints imposed on the core plasma (the density limit, the βp limit and so on), we found that the self-ignited state of the high βp-mode operation would be difficult.
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