We de-cribe here a numerical model of a free boundary axisymmetric tokaraak plasma and its associated control systems.The plasma is modeled v>ith a hybrid method using two-dimensional velocity and flux functions with surface-averaged MHO equations describing the evolution of the adiabatic invariants. Equations are solved for the external circuits and for the effects of eddy currents in nearby conductors. The method is verified by application to several test problems and used to simulate the formation of a bean-shaped plasma in the PBX experiment.

This paper reviews the nonlinear interaction calculations for the internal gravity wave field in the deep ocean. The nonlinear interactions are a principal part of the dynamics of internal waves and are an important link in the overall energy cascade from large to small scales. Four approaches have been taken for their analysis: the evaluation of the transfer integral describing weakly and resonantly interacting waves, the application of closure hypotheses from turbulence theories to more strongly interacting waves, the integration of the eikonal or ray equations describing the propagation of small‐scale internal waves in a background of large‐scale internal waves, and the direct numerical simulation of the basic hydrodynamic equations of motion. The weak resonant interaction calculations have provided most of the conventional wisdom. Specific interaction processes and their role in shaping the internal wave spectrum have been unveiled and a comprehensive inertial range theory developed. The range of validity of the resonant interaction approximation, however, is not known and must be seriously doubted for high‐wave number, high‐frequency waves. The turbulence closure calculations and the direct numerical modeling are not yet in a state to be directly applicable to the oceanic internal wave field. The closure models are too complex and rest on conjectures that are not demonstrably justified. Numerical modeling can treat strongly interacting waves and buoyant turbulence, but is severely limited by finite computer resolutions. Extensive suites of experiments have only been carried out for two‐dimensional flows. The eikonal calculations provide an efficient and versatile tool to study the interaction of small‐scale internal waves, but it is not clear to what extent the scale‐separated interactions with larger‐scale internal waves compete with and might be overwhelmed by interactions among like scales. The major shortcoming of all four approaches is that they neglect the interaction with the vortical (=potential vorticity carrying) mode of motion that must be expected to exist in addition to internal waves at small scales. This interaction is intrinsically neglected in all Lagrangian‐based studies and in the non‐rotating two‐dimensional simulations. The most promising approach for the future that can handle both arbitrarily strong interactions and the interaction with the vortical mode is numerical modeling once the resolution problem is overcome.

The National Spherical Torus Experiment (NSTX) is being built at PPPL to test the fusion physics principles for the ST concept at the MA level. The NSTX nominal plasma parameters are R 0 = 85 cm, a = 67 cm, R/a ³ 1.26, B T = 3 kG, I p = 1 MA, q 95 = 14, elongation k £ 2.2, triangularity d £ 0.5, and plasma pulse length of up to 5 sec. The plasma heating / current drive (CD) tools are High Harmonic Fast Wave (HHFW) (6 MW, 5 sec), Neutral Beam Injection (NBI) (5 MW, 80 keV, 5 sec), and Coaxial Helicity Injection (CHI). Theoretical calculations predict that NSTX should provide exciting possibilities for exploring a number of important new physics regimes including very high plasma beta, naturally high plasma elongation, high bootstrap current fraction, absolute magnetic well, and high pressure driven sheared flow. In addition, the NSTX program plans to explore fully noninductive plasma start-up as well as a dispersive scrape-off layer for heat and particle flux handling. MotivationA broad range of encouraging advances has been made in the exploration of the Spherical Torus (ST) concept. 1 Such advances include promising experimental data from pioneering experiments, theoretical predictions, near-term fusion energy development projections such as the Volume Neutron Source 2 , and future applications such as power plant studies 3 . Recently, the START device has achieved a very high toroidal beta b T » 40% regime with b N » 5.0 at low q 95 » 3. 4 The National Spherical Torus Experiment (NSTX) is being built at PPPL to test the fusion physics principles for the ST concept at the MA level. 5 The NSTX device/plasma configuration allows the plasma shaping factor, I p q 95 / a B , to reach as high as 80 an order of magnitude greater than that achieved in conventional high aspect ratio tokamaks. The key physics objective of NSTX is to attain an advanced ST regime; i.e., simultaneous ultra high beta (b), high confinement, and high bootstrap current fraction (f bs ). 6 This regime is considered to be essential for the development of an economical ST power-plant because it minimizes the recirculating power and power plant core size. Other NSTX mission elements crucial for ST power plant development are the demonstration at the MA level of fully noninductive operation and the development of acceptable power and particle handling concepts. NSTX Facility Design Capability and Technology ChallengesThe NSTX facility is designed to achieve the NSTX mission with the following capabilities: ¥ I p = 1 MA for low collisionality at relevant densities, ¥ R/a ³ 1.26, including OH solenoid and coaxial helicity injection 7 (CHI) for startup,