Optimization and control of plasma shape and current profile in non-circular cross-section tokamaks

Tokamaks with elongated, non-circular cross-sections are under consideration as fusion reactors because they have the potential for stable operation at high β. Ideal MHD theory, however, predicts that careful current profile control will be required to achieve the potential high-β advantages of non-circular cross-sections. In this paper, high-β equilibria which are stable to all ideal MHD modes are found by optimizing the plasma shape and current profile for doublets, up-down asymmetric dees, and symmetric dees. The ideal MHD stability of these equilibria for low toroidal mode number n is analysed with a global MHD stability code, GATO. The stability to high-n modes is analysed with a localized ballooning code, BLOON. The attainment of high β is facilitated by an automated optimization search on shape and current parameters. The equilibria are calculated with a free-boundary equilibrium code using coils appropriate for the Doublet III experimental device. The optimal equilibria are characterized by broad current profiles with values of βsub(poloidal) approximately equal to 1. Experimental realization of the shapes and current profiles giving the highest β limits is explored with a 1 1/2-D transport code, which simulates the time evolution of the 2-D MHD equilibrium while calculating consistent current profiles from a 1-D transport model. Transport simulations indicate that nearly optimal shapes may be obtained provided that the currents in the field-shaping coils are appropriately programmed and the plasma current profile is sufficiently broad. Obtaining broad current profiles is possible by current ramping, neutral-beam heating, and electron-cyclotron heating. With combinations of these techniques it is possible to approach the optimum β predicted by the MHD theory. (author)