Thermal stability of a thermonuclear plasma for a temperature dependent confinement time and application of the model to the Kaye-Goldston scaling

The thermal stability of the ignition operation is investigated using a simple zero-dimensional model for a temperature dependent energy confinement time (tausub(E) varies as to 1/Tsup(γ)). The stability limit in the (ntausub(E), T) plane is calculated for a plasma with external heating. The degradation of the confinement time with increasing temperature is found to be favourable for the divergence temperature and for the minimum temperature for stable ignition. This degradation also decreases the external power per unit volume necessary to reach divergence. However, the degradation is extremely unfavourable for the ntausub(E) required for divergence and ignition. Detailed results are given for the special case of the Kaye-Goldston scaling (γ = 1.38). The very pessimistic numerical results obtained are discussed and some effects are mentioned which may have a favourable influence but which have not been included in the present model. (author)