Paul R. Garabedian

The NSTAB nonlinear stability code solves differential equations in conservation form, and the TRAN Monte Carlo test particle code tracks guiding center orbits in a fixed background, to provide simulations of equilibrium, stability, and transport in tokamaks and stellarators. These codes are well correlated with experimental observations and have been validated by convergence studies. Bifurcated 3D solutions of the 2D tokamak problem have been calculated that model persistent disruptions, neoclassical tearing modes (NTMs) and edge localized modes (ELMs) occurring in the International Thermonuclear Experimental Reactor (ITER), which does not pass the NSTAB simulation test for nonlinear stability. So we have designed a quasiaxially symmetric (QAS) stellarator with similar proportions as a candidate for the demonstration (DEMO) fusion reactor that does pass the test [1]. The configuration has two field periods and an exceptionally accurate 2D symmetry that furnishes excellent thermal confinement and good control of the prompt loss of alpha particles. Robust coils are found from a filtered form of the Biot-Savart law based on a distribution of current over a control surface for the coils and the current in the plasma defined by the equilibrium calculation. Computational science has addressed the issues of equilibrium, stability, and transport, so it remains to develop an effective plan to construct the coils and build a diverter.

Runs of the NSTAB nonlinear stability code show there are many three-dimensional (3D) solutions of the advanced tokamak problem subject to axially symmetric boundary conditions. These numerical simulations based on mathematical equations in conservation form predict that the ITER international tokamak project will encounter persistent disruptions and edge localized mode (ELMS) crashes. Test particle runs of the TRAN transport code suggest that for quasineutrality to prevail in tokamaks a certain minimum level of 3D asymmetry of the magnetic spectrum is required which is comparable to that found in quasiaxially symmetric (QAS) stellarators. The computational theory suggests that a QAS stellarator with two field periods and proportions like those of ITER is a good candidate for a fusion reactor. For a demonstration reactor (DEMO) we seek an experiment that combines the best features of ITER, with a system of QAS coils providing external rotational transform, which is a measure of the poloidal field. We have discovered a configuration with unusually good quasisymmetry that is ideal for this task.

The NSTAB equilibrium and stability code and the TRAN Monte Carlo transport code furnish a simple but effective numerical simulation of essential features of present tokamak and stellarator experiments. When the mesh size is comparable to the island width, an accurate radial difference scheme in conservation form captures magnetic islands successfully despite a nested surface hypothesis imposed by the mathematics. Three-dimensional asymmetries in bifurcated numerical solutions of the axially symmetric tokamak problem are relevant to the observation of unstable neoclassical tearing modes and edge localized modes in experiments. Islands in compact stellarators with quasiaxial symmetry are easier to control, so these configurations will become good candidates for magnetic fusion if difficulties with safety and stability are encountered in the International Thermonuclear Experimental Reactor (ITER) project.

In a fusion reactor a hot plasma of deuterium and tritium is confined by a strong magnetic field to produce helium ions and release energetic neutrons. The 3D geometry of a stellarator provides configurations for such a device that reduce net toroidal current that might lead to disruptions. We construct smooth coils generating an external magnetic field designed to prevent the plasma from deteriorating.

The study of cavitational flow is formulated as a free boundary problem for the Laplace equation in three dimensions. Constant pressure free streamlines are determined by a variational principle for the virtual mass that can be deduced from a similar result for vortex sheets. Steepest descent applied to minimization of the potential energy suggests a natural iterative scheme to calculate the shape of the cavity bounded by the free streamlines. Numerical methods enable one to estimate the drag and the geometry of the flow. Another version of the variational principle plays an important role in plasma physics and the theory of magnetic fusion. This method has significant applications to stellarators, which are toroidal configurations for confinement of hot plasma whose three-dimensional geometry leads to interesting mathematical problems. Large computer codes implementing the theory play a central role in the design of thermonuclear reactors.

Theory has contributed significantly to recent advances in magnetic fusion research. New configurations have been found for a stellarator experiment by computational methods. Solutions of a free-boundary problem are applied to study the performance of the plasma and look for islands in the magnetic surfaces. Mathematical analysis and numerical calculations have been used to study equilibrium, stability, and transport of optimized fusion reactors.

Three-dimensional computer codes have been used to develop quasisymmetric stellarators with modular coils that are promising candidates for a magnetic fusion reactor. The mathematics of plasma confinement raises serious questions about the numerical calculations. Convergence studies have been performed to assess the best configurations. Comparisons with recent data from large stellarator experiments serve to validate the theory.