Transport survey calculations using the spectral collocation method

A novel transport survey code has been developed and is being used to study the sensitivity of stellarator reactor performance to various transport assumptions. Instead of following one of the usual approaches (0-D model or 1-D time-dependent solution to the energy transport equations), the steady-state transport equations are solved in integral form using the spectral collocation method. This approach effectively combines the computational efficiency of global models with the general nature of 1-D solutions. A compact torsatron reactor test case was used to study the convergence properties and flexibility of the new method. The heat transport model combined Shaing's model for ripple-induced neoclassical transport, the Chang-Hinton model for axisymmetric neo-classical transport, and neoalcator scaling for anomalous electron heat flux. Alpha particle heating, radiation losses, classical electron-ion heat flow, and external heating were included. For the test problem, the method exhibited some remarkable convergence properties. As the number of basis functions was increased, the maximum pointwise error in the integrated power balance decayed exponentially until the numerical noise level was reached (approx. = 25 basis functions). Better than 10% accuracy in the globally-averaged quantities was achieved with only 5 basis functions; better than 1% accuracy was achieved with 10 basis functions. The numerical method was also found to be very general. Extreme temperature gradients at the plasma edge which sometimes arise from the neoclassical models and are difficult to resolve with finite-difference methods were easily resolved. Constraints on the temperature gradients were also introduced without causing any numerical instabilities. (author). 8 refs, 6 figs