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The article reviews the physics of fusion alpha particles and energetic neutral beam ions studied in the final phase of TFTR operation, with an emphasis on observations in reversed magnetic shear (RS) and enhanced reversed shear (ERS) DT plasmas. Energy resolved measurements of the radial profiles of confined, trapped alphas in RS plasmas exhibit reduced core alpha density with increasing alpha energy, in contrast to plasmas with normal monotonic shear. The measured profiles are consistent with predictions of increased alpha loss due to stochastic ripple diffusion and increased first orbit loss in RS plasmas. In experiments in which a short tritium beam pulse is injected into a deuterium RS plasma, the measured DT neutron emission is lower than standard predictions assuming first orbit loss and stochastic ripple diffusion of the beam ions. A microwave reflectometer measured the spatial localization of low toroidal mode number (n), alpha driven toroidal Alfven eigenmodes (TAEs) in DT RS discharges. Although the observed ballooning character of the n = 4 mode is consistent with predictions of a kinetic MHD stability code, the observed antiballooning nature of the n = 2 mode is not. Furthermore, the modelling does not show the observed strong dependence of mode frequency on n. These alpha driven TAEs do not cause measurable alpha loss in TFTR. Other Alfven frequency modes with n = 2-4 seen in both DT and DD ERS and RS discharges are localized to the weak magnetic shear region near qmin. In 10-20% of DT discharges, normal low n MHD activity causes alpha loss at levels above the first orbit loss rate.

The deuterium-tritium (D-T) experimental program on the Tokamak Fusion Test Reactor (TFTR) is underway and routine tritium operations have been established. The technology upgrades made to the TFTR facility have been demonstrated to be sufficient for supporting both operations and maintenance for an extended D-T campaign. To date fusion power has been increased to {approximately}9 MW and several physics results of importance to the D-T reactor regime have been obtained: electron temperature, ion temperature, and plasma stored energy all increase substantially in the D-T regime relative to the D-D regime at the same neutral beam power and comparable limiter conditioning; possible alpha electron heating is indicated and energy confinement improvement with average ion mass is observed; and alpha particle losses appear to be classical with no evidence of TAE mode activity up to the P{sub FUS} {approximately}6 MW level. Instability in the TAE mode frequency range has been observed at P{sub FUS} > 7 MW and its effect on performance is under investigation. Preparations are underway to enhance the alpha particle density further by increasing fusion power and by extending the neutral beam pulse length to permit alpha particle effects of relevance to the ITER regime to be more fullymore » explored.« less

Predictions with the 1½-D BALDUR transport code, using recent theory based models for thermal and particle transport, are compared with measured profiles of electron plasma density and electron and ion temperatures for Ohmic, L-mode and supershot discharges on TFTR. The profile consistent drift wave model is found to overestimate the ion temperatures at high heating powers so that a third mode or loss process is needed in addition to drift wave transport (trapped electron mode and ηi mode) and an edge loss model. None of several versions of the local multiple mode models, using the 1989 Carreras-Diamond resistive ballooning mode, gives Te, Ti within 20% for all three TFTR regimes studied.

Linear simulations of plasma microturbulence are used with recent radial profiles of toroidal velocity from similar plasmas to consider nonlinear microturbulence simulations and observed transport analysis on Alcator C-Mod. We focus on internal transport barrier (ITB) formation in fully equilibrated H-mode plasmas with nearly flat velocity profiles. Velocity profile data, transport analysis and linear growth rates are combined to integrate data and simulation, and explore the effects of toroidal velocity on benchmarking simulations. Areas of interest for future nonlinear simulations are identified. A good gyrokinetic benchmark is found in the plasma core, without extensive nonlinear simulations. RF-heated C-Mod H-mode experiments, which exhibit an ITB, have been studied with the massively parallel code GS2 towards validation of gyrokinetic microturbulence models. New, linear, gyrokinetic calculations are reported and discussed in connection with transport analysis near the ITB trigger time of shot No.1001220016.

Ion absorption of the high harmonic fast wave in a spherical torus is of critical importance to assessing the viability of the wave as a means of heating and driving current. Analysis of recent National Spherical Torus Experiment (NSTX) shots has revealed that under some conditions when neutral beam and radio-frequency (RF) power are injected into the plasma simultaneously, a fast ion population with energy above the beam injection energy is sustained by the wave. In agreement with modeling, these experiments find the RF-induced fast ion tail strength and neutron rate at lower B-fields to be less enhanced, likely due to a larger beta profile, which promotes greater off-axis absorption where the fast ion population is small. Ion loss codes find the increased loss fraction with decreased B insufficient to account for the changes in tail strength, providing further evidence that this is an RF interaction effect. Though greater ion absorption is predicted with lower k(sub)||, surprisingly little variation in the tail was observed, along with a small neutron rate enhancement with higher k(sub)||. Data from the neutral particle analyzer, neutron detectors, X-ray crystal spectrometer, and Thomson scattering is presented, along with results from the TRANSP transport analysis code, ray-tracing codes HPRT and CURRAY, full-wave code and AORSA, quasi-linear code CQL3D, and ion loss codes EIGOL and CONBEAM.

The National Spherical Torus Experiment (NSTX) at Princeton is designed to assess the potential of the low-aspect-ratio spherical torus concept for magnetic plasma confinement. The plasma has been heated by up to 5 MW of neutral beam injection, NBI, at an injection energy of 90 keV and up to 6 MW of high harmonic fast wave, HHFW, at 30 MHz. NSTX has achieved beta T of 32%. A variety of MHD phenomena have been observed to limit eta. NSTX has now begun addressing E scaling, eta limits and current drive issues. During the NBI heating experiments, a broad Ti profile with Ti up to 2 keV, Ti > Te and a large toroidal rotation. Transport analysis suggests that the impurity ions have diffusivities approaching neoclassical. For L-Mode plasmas, E is up to two times the ITER-89P L-Mode scaling and exceeds the ITER-98pby2 H-Mode scaling in some cases. Transitions to H-Mode have been observed which result in an approximate doubling of tE. after the transition in some conditions. During HH FW heating, Te > Ti and Te up to 3.5 keV were observed. Current drive has been studied using coaxial helicity injection (CHI), which has produced 390 kA of toroidal current and HHFW, which has produced H-modes with significant bootstrap current fraction at low Ip, high q and high{sub etap}.

The magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), expected to achieve good stability and particle confinement is examined with a method that can lead to estimates of global stability. Making use of fully 3D, ideal-MHD stability codes, the QAS beta is predicted to be limited above 4% by ballooning and high-n kink modes. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space [s, alpha, theta(subscript ''k'')]; s is the edge normalized toroidal flux, alpha is the field line variable, and theta(subscript ''k'') is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, with new types of nonsymmetric, eigenvalue isosurfaces in both the stable and unstable spectrum. The isosurfaces around the most unstable points i n parameter space (well above marginal) are topologically spherical. In such cases, attempts to use ray tracing to construct global ballooning modes lead to a k-space runaway. Introduction of a reflecting cutoff in k(perpendicular) to model numerical truncation or finite Larmor radius (FLR) yields chaotic ray paths ergodically filling the allowed phase space, indicating thatmore » the global spectrum must be described using the language of quantum chaos theory. However, the isosurface for marginal stability in the cases studied are found to have a more complex topology, making estimation of FLR stabilization more difficult.« less

The MHD stability of quasi-axisymmetric compact stellarators is investigated. It is shown that bootstrap current driven external kink modes can be stabilized by a combination of edge magnetic shear and appropriate 3D plasma boundary shaping while maintaining good quasi-axisymmetry. The results demonstrate that there exists a new class of stellarators with quasi-axisymmetry, large bootstrap current, high MHD beta limit, and compact size.

The TRANSP code is used to construct comprehensive, self-consistent models for ITER discharges. Plasma parameters are studied for two discharges from the ITER ``Interim Design`` database producing 1.5 GW fusion power with a plasma current of 21 MA and 20 toroidal field coils generating 5.7 T Steady state profiles for T{sub ion}, T{sub e}, n{sub e}, Z{sub eff}, and P{sub rad} from the database are specified. TRANSP models the full up/down asymmetric plasma boundary within the separatrix. Effects of high-energy neutral beam injection, sawteeth mixing, toroidal field ripple, and helium ash transport are included. Results are given for the fusion rate profiles, and parameters describing effects such as alpha particle slowing down, the heating of electrons and thermal ions, and the thermalization rates. The deposition of 1 MeV neutral beam ions is predicted to peak near the plasma center, and the average beam ion energy is predicted to be half the injected energy. Sawtooth mixing is predicted to broaden the fast alpha profile. The toroidal ripple losses rate of alpha energy is estimated to be 3% before sawtooth crashes and to increase by a factor of three to four immediately following sawtooth crashes. Assumptions for the thermal He transport and the He recycling coefficient at the boundary are discussed. If the ratio of helium and energy confinement times, {tau}*{sub He}/{tau}{sub E} is less than 15, the steady state fusion power is predicted to 1.5 GW or greater. The values of the transport coefficients required for this fusion power depend on the He recycling coefficient at the separatrix. If R{sub rec} is near 1, the required He diffusivity must be much larger than that measured in tokamaks. If R{sub rec} {le} 0.50, and if the inward pinch is small, values comparable to those measured are compatible with 1.5 GW.

Insufficient helium exhaust can seriously degrade the performance of any fusion reactor and has recently been identified as a potentially significant issue for ITER. The effects of variations of the ratios D{sup He}/{chi}i, D{sup He}/D{sup D}, v{sup He}/D{sup He} and of the sawtooth period on helium exhaust in ITER are studied with BALDUR code transport simulations. Recent measurements of D{sup He}/{chi}i, at TFTR, of D{sup He}/D{sup D} at TEXTOR of v{sup He}/D{sup He} at TFTR, TEXTOR, and JT-60 are found compatible with sustained ignition and helium exhaust requirements for ITER. Ignition is found to be critically sensitive to the ratio v{sup He}/D{sup He}, particularly at the plasma edge, and to reduced sawtooth period. These critical dependencies are moderated for reduced helium recycling at the separatrix and for hollow particle diffusivity profiles. 17 refs., 9 figs., 1 tab.

1-{1/2}-d BALDUR transport code predictions using recent theoretically-based models for thermal and particle transport are compared to measured profiles of electron plasma density and electron and ion temperatures for TFTR ohmic, L-mode and supershot discharges. The profile consistent drift wave model is found to overestimate ion temperatures at high heating powers, so that a third mode or loss process is needed in addition to drift wave transport (TEM, {eta}{sub i}) and an edge loss model. None of several versions of local multiple mode models, using the 1989 Carreras-Diamond resistive ballooning model, gives T{sub e}, T{sub i} within 20% for all three TFTR regimes studied. 36 refs., 7 figs., 4 tabs.

The buildup of helium ash in the proposed ITER experiment has been studied in a series of simulations with the BALDUR transport code. Using radially dependent thermal diffusivities which were scaled from JET values, we studied the role of particle transport coefficients and edge recycling on helium poisoning of ignition. A sustained ignition was obtained when the exhaust of helium from the edge plasma was allowed to exceed 10% of the helium flux into the edge plasma from the core plasma, and the ratio of particle (He ion) to thermal diffusivities, D/{chi}, was larger than 1/4. The simulations included the effects of sawtooth oscillations, radiative as well as conductive energy loss channels, and density profile variations. 29 refs., 11 figs.

Line successive over relaxation (LSOR) is an iterative method for solving elliptic differential equations. LSOR takes advantage of the CRAY vector capabilities as compared to the point successive over relaxation (SOR) method, which does not vectorize. The substantial advantages of LSOR on a vectorizing machine are not well-known, except in the field of aerodynamics. By minor modification of the traditional SOR elliptic equation solver, we find that in certain coordinates an increase of a factor of two or greater in convergence time can be realized. As a model problem for comparison of SOR and LSOR, the numerical solution of Poisson's equation will be reviewed in Sec. II. In Sec. III, we discuss the decreased computation time on the National Fusion Energy Computer Center (NMFECC) CRAY computers found with LSOR applied to the iterative solution of plasma equilibria. In Sec. IV, the conditions for which LSOR is most useful are summarized.

The possibility of obtaining ignition in TFTR by means of very centrally peaked density profiles is examined. It is shown that local central alpha heating can be made to exceed local central energy losses (''central ignition'') under global conditions for which Q greater than or equal to 1. Time dependent 1-D transport simulations show that the normal global ignition requirements are substantially relaxed for plasmas with peaked density profiles. 18 refs., 18 figs.

In order to achieve the stated objectives of key future experiments such as CIT, it will be necessary to maintain plasmas with confinement properties significantly improved over those observed in auxiliary-heated L-mode-type tokamak discharges. This underscores the importance of understanding the physics responsible for the favorable trends exhibited, for example, by ''supershot'' discharges in TFTR and by H-mode-type divertor plasmas. In addressing this general issue, the present paper reports results of theoretical investigations dealing with: the onset conditions of the microinstabilities most likely to influence enhanced confinement behavior; gyrokinetic particle simulations and analytic studies of the saturation and transport properties of the most persistent forms of these instabilities; and detailed comparisons of experimental results with predictions from transport codes using appropriate microinstability-based diffusivities and with local diffusivities from various theoretical models. 19 refs., 2 tabs.

This paper reports on results of theoretical studies dealing with: (1) the use of microinstability-based thermal transport models to interpret the anomalous confinement properties observed in key tokamak experiments such as TFTR and (2) the likely consequences of the presence of such instabilities for future ignition devices. Transport code simulations using profile-consistent forms of anomalous thermal diffusivities due to drift-type instabilities have yielded good agreement with the confinement times and temperatures observed in TFTR under a large variety of operating conditions including pellet-fuelling in both ohmic- and neutral-beam-heated discharges. With regard to achieving an optimal ignition margin, the adverse temperature scaling of anomalous losses caused by drift modes leads to the conclusion that it is best to operate at the maximum allowable density while holding the temperature close to the minimum value required for ignition.

Experiments with plasmas having nearly equal concentrations of deuterium and tritium have been carried out on TFTR. To date, the maximum fusion power has been 10.7 MW, using 39.5 MW of neutral-beam heating, in a supershot discharge and 6.7 MW in a high-{beta}{sub p} discharge following a current ramp-down. The fusion power density in the core of the plasma has reached 2.8 MWm{sup {minus}3}, exceeding that expected in the International Thermonuclear Experimental Reactor (ITTER). The energy confinement time, {tau}{sub E}, is observed to increase in D-T, relative to D plasmas, by 20% and the n{sub i}(O){center_dot}{tau}{sub E} product by 55%. The improvement in thermal confinement is caused primarily by a decrease in ion heat conductivity in both supershot and limiter-H-mode discharges. Extensive lithium pellet injection increased the confinement time to 0.27 s and enabled higher current operation in both supershot and high-{beta}{sub p} discharges. First measurements of the confined alpha particles have been performed and found to be in good agreement with TRANSP simulations assuming classical confinement. Measurements of the alpha ash profile have been compared with simulations using particle transport coefficients from helium gas puffing experiments. The loss of energetic alpha particles to a detector at the bottom ofmore » the vessel is well described by the first-orbit loss mechanism. No loss due to alpha-particle-driven instabilities has yet been observed. ICRF heating of a D-T plasma, using the second harmonic of tritium, has been demonstrated. D-T experiments on TFTR will continue both to explore the physics underlying the ITER design and to examine some of the physics issues associated with an advanced tokamak reactor.« less