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,

Compact optimized stellarators offer novel solutions for confining high-β plasmas and developing magnetic confinement fusion. The three-dimensional plasma shape can be designed to enhance the magnetohydrodynamic (MHD) stability without feedback or nearby conducting structures and provide driftorbit confinement similar to tokamaks. These configurations offer the possibility of combining the steady-state low-recirculating power, external control, and disruption resilience of previous stellarators with the low aspect ratio, high β limit, and good confinement of advanced tokamaks. Quasiaxisymmetric equilibria have been developed for the proposed National Compact Stellarator Experiment (NCSX) with average aspect ratio 4-4.4 and average elongation ∼1.8. Even with bootstrap-current consistent profiles, they are passively stable to the ballooning, kink, vertical, Mercier, and neoclassicaltearing modes for β > 4%, without the need for external feedback or conducting walls. The bootstrap current generates only 1/4 of the magnetic rotational transform at β = 4% (the rest is from the coils); thus the equilibrium is much less non-linear and is more controllable than similar advanced tokamaks. The enhanced stability is a result of 'reversed' global shear, the spatial distribution of local shear, and the large fraction of externally generated transform. Transport simulations show adequate fast-ion confinement and thermal neoclassical transport similar to equivalent tokamaks. Modular coils have been designed which reproduce the physics properties, provide good flux surfaces, and allow flexible variation of the plasma shape to control the predicted MHD stability and transport properties.

In this paper a laboratory investigation is made on magnetic reconnection in high-temperature Tokamak Fusion Test Reactor (TFTR) plasmas [Plasma Physics and Controlled Nuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 51]. The motional Stark effect (MSE) diagnostic is employed to measure the pitch angle profile of magnetic field lines, and hence the q profile. An analytical expression that relates pitch angle to q profile is presented for a toroidal plasma with circular cross section. During the crash phase of sawtooth oscillations in plasma discharges, the ECE (electron cyclotron emission) diagnostic measures a fast flattening of the two-dimensional (2-D) electron temperature profile in a poloidal plane, an observation consistent with the Kadomtsev reconnection theory. On the other hand, the MSE measurements indicate that central q values do not relax to unity after the crash, but increase only by 5%–15%, typically from 0.7 to 0.8. The latter result is in contradiction with the 2-D models of Kadomtsev and/or Wesson. In the present study this puzzle is addressed by a simultaneous analysis of electron temperature and q profile evolutions. Based on a heuristic model for magnetic reconnection during the sawtooth crash, the small change of q, i.e., partial reconnection, is attributed to the precipitous drop of pressure gradients that drive the instability and the reconnection process, as well as flux conserving plasma dynamics.

The role of shear in determining the ideal MHD stability properties of tokamaks is discussed.In particular, we assess the effects of low shear within the plasma upon pressure-driven modes. The standard ballooning theory is shown to break down, as the shear ia reduced and the growth rate is shown to be an oscillatory function of n f the toroidal mode number, treated as a continuous parameter. The oscillations are shown to depend on both the pressure and safety-factor profiles. When the 3hear is sufficiently weak, the oscillations can result in bands of unstable n values which are present even when the standard ballooning theory predicts complete stability. These instabilities are named "infernal modes." The occurrence of. these Instabilities at integer n is shown to be a sensitive function of q-axis, raising the possibility of a sharp onset AS plasma parameters evolve. DISCLArMER ' 2^~H^X£X«£™ * -M-"-•*« a*.employe. malcs m y warram J££ °™ "• «.,, agency .hereof, no, a n y orilKir M.l» for the curacy, completeness, or 2^? "*• ^ ^^ m «P™* ence herein to any specific commercial D ra*Ki ™Z 8 n < C « Sari * ««« « reflect tno5e J% £' y " r DISTRIBUTION OF THIS OUCUrilEM !S UKCWITEB

The Tokamak Simulation Code (TSC) has been used to model the time dependence of several ohmic discharges in the TFTR experiment. We have refined the semi-I empirical thermal conductivity model and the sawtooth model in TSC so that good agreement is obtained between the simulation and the experiment in electron and ion temperature profiles, and in the current profiles for the entire duration of the discharges. Neoclassical resistivity gives good agreement with the measured surface voltages and rate of poloidal flux consumotion.

Recently, various schemes for controlling the resistive wall mode have been proposed. Here, the problem of resistive wall mode feedback control is formulated utilizing concepts from electrical circuit theory. Each of the coupled elements (the perturbed plasma current, the poloidal passive shell system and the active coil system) is considered as lumped parameter electrical circuits obeying the usual laws of linear circuit theory. A dispersion relation is derived using different schemes for the feedback logic. The various schemes differ in the choice of sensor signal, which is determined by some combination of the three independent circuit currents. Feedback schemes are discussed which can, ideally, completely stabilize the kink mode. These schemes depend, for their success, on a suitable choice for the location of the sensors. A feedback scheme based on sensing the passive shell eddy current is discussed which seeks to drive the feedback system response to a point of marginal stability. For realizable feedback gain factors, this feedback system can suppress the kink mode amplitude for times that are very long compared with the L/R time-scale of the passive shell system. The circuit equation approach discussed provides a useful means for comparing various control strategies for n ⩾ 1 kink mode control, and allows useful analogies to be drawn between kink mode control and the control of n = 0 vertical position instabilities.