Modeling of anomalous transport in stellarators

Solutions are found to the time-independent transport equations (equations of diffusion and thermal conductivity) for the plasma density N(r); the electron and ion temperatures, T-e(r) and T-i(r); and the ambipolar electric field E(r). These equations account for both neoclassical and anomalous losses. The neoclassical transport includes a complete matrix of transport coefficients (including nondiagonal terms), which were previously derived theoretically, and anomalous losses, which were treated phenomenologically. In particular, the anomalous transport coefficients were chosen to be proportional to C(B, r) X T-e(s-1)(r)/N(r), where the parameter s equals 1.5 or 0.33, and the coefficient C(B, r) can depend on the magnetic field B and the minor radius r. In order to determine the adjustable parameters s and C(B, r), the results of calculations were compared with experimental data from the W7-A and L-2 stellarators. The best agreement between calculated and experimental values was obtained for s = 0.33. In this case, the coefficient C(B, r) can be assumed to be independent of the magnetic field and radial coordinate. For these values of s and C, plasma parameters were calculated for certain experiments in the ATF, Heliotron-E, CHS, L-2M stellarators, and the LHD stellarator, which is under construction. The energy lifetime tau(E) obtained in our model is shown to agree well with that obtained from the LHD scaling. Also, the influence of a biased probe and auxiliary peripheral heating on the magnitude and radial distribution of the ambipolar electric field and the effect of near-wall turbulence on the energy lifetime are studied.