Drift wave model tokamak ignition projections with a zero-dimensional transport code

A zero-dimensional transport code formulated with theoretical drift wave models having an ad hoc q-dependence is used to estimate ignition conditions for the proposed Compact Ignition Tokamak (CIT). The theoretical models are normalized to tokamak confinement time data over a wide range of density, field and size (ISX, TFTR, DIII, DIII-D, JET) for L- and H-modes. The fit coefficient for the dissipative trapped electron (DTE) mode is fixed by low density Ohmic discharges and the coefficient for the ion temperature gradient (ITG) mode is fixed by beam heated discharges. While the theoretical models are almost indistinguishable from the standard (Kaye-Goldston) empirical model in fitting the available data, they have significant quantitative and qualitative differences on projection to ignition. The empirical model fails to account for the unfavourable temperature scaling of the DTE mode masked in Ohmic heating and the favourable density scaling of the ITG mode masked by beam penetration and impurity line radiation effects in the present experiments. The ignition conditions are analysed with explicit formulas for the minimum required auxiliary power P m and a figure of merit F M given essentially by the radio of β MHD to the minimum beta on the ignition curve B M [F M = B M 5/6 , Q M = 5 F M /(1 - F M )] Both P m and B M have strong favourable scaling with size (a) and field (B) and depend sensitively on the normalization of confinement time within the scatter of the data, f = τ exp /τ model : B M −1 ≅ (B M DTE ) −1 + (B M ITG ) −1 where B M DTE = 1.47 (a/55 cm) 2 (B/100 kG) 3 f OH 1.2 and B M ITG = 1.14 (a/55 cm) 4 × (B/100 kG) 5 f aux 2.5 ( /2.5) 2.5 for the standard CIT broad density profile case parameters, = τ H /τ L corresponds to the factor 2.5 improvement in H over L confinement time. Clearly, when ITG dominates, B M J ∼ O(10) B M L . The minimum ignition densities n m are typically in excess of Ohmic density limits scaling with current density, but it is demonstrated that sufficient auxiliary power can burn out line radiation, allowing operation at higher densities.