Search

The global confinement and the local transport properties of improved core confinement plasmas in JT-60U were studied in connection with E_r shear formation. In the improved core confinement mode with internal transport barriers (ITBs), these are roughly classified into `parabolic type' ITBs and `box type' ITBs. The parabolic type ITB has a reduced thermal diffusivity χ in the core region; however, the E_r shear, dE_r/dr, is not as strong. The box type ITB has a very strong E_r shear at the thin ITB layer and χ decreases to the level of neoclassical transport there. The estimated E × B shearing rate, ω_{E × B}, becomes almost the same as the linear growth rate of the drift microinstability, γ_L, at the ITB layer in the box type ITB. Experiments with hot ion mode plasmas during the repetitive L-H-L transition showed that the thermal diffusivity clearly depends on the E_r shear and the strong E_r shear contributes to the reduced thermal diffusivity.

A study of the MHD stability properties of bean-shaped tokamak plasmas is presented. For ballooning modes, while increased indentation gives larger stable-beta configurations, the existence and accessibility of the second stable region are sensitive to the pressure and safety factor profiles. The second stable region appears at lower beta values for large aspect ratio and moderately high q-values. Finite-Larmor-radius kinetic effects can significantly improve the stability properties. For low-q (1) operation, long-wavelength (n ~ 2, 3) internal-pressure-driven modes occur at modest ?pvalues and accessibility to higher beta operation is unlikely. Indentation modifies the nature of the usually vertical axisymmetric instability, but the mode can be passively stabilized by placing highly conducting plates near the tips of the plasma bean. At constant q, indentation has a stabilizing effect on tearing modes.

A comprehensive analysis of the stability properties of the appropriate kinetically generalized form of MHD ballooning modes, together with the usual trapped-particle drift modes, is presented. The calculations are fully electromagnetic and include the complete dynamics associated with compressional ion acoustic waves. Trapped-particle effects, together with all forms of collisionless dissipation, are taken into account without approximations. The influence of collisions is estimated with a model Krook operator. Results from the application of this analysis to realistic tokamak operating conditions indicate that unstable short-wavelength modes with significant growth rates can extend from ? = 0 to values above the upper ideal-MHD critical beta associated with the 'second stability regime'. Since the maximum growth rates of the relevant modes appear to vary gradually with beta, these results support a 'soft' beta-limit picture involving a continuous (rather than abrupt or 'hard') modification of anomalous transport already present in low-beta tokamaks. However, at higher beta the increasing dominance of the electromagnetic component of the perturbations indicated by these calculations could also imply significantly different transport scaling properties.

It has recently been proposed that the presence of high-energy ions from neutral-beam injection can have a strong stabilizing effect on kinetically modified ideal-MHD ballooning modes in tokamaks. To assess realistically the importance of such effects, a comprehensive kinetic stability analysis, which takes into account the integral equation nature of the basic problem, has been applied to this investigation. In the collisionless limit, the effect of adding small fractions of hot beam ions is indeed found to be strongly stabilizing. On the other hand, for somewhat larger fractions of hot ions, a different, beam-driven root of the mode equations is found to occur with a growth rate comparable in magnitude to the growth rate of the usual MHD ballooning mode in the absence of hot ions. This implies that there should be an optimal density of hot particles which minimizes the strength of the relevant instabilities. Employing non-Maxwellian equilibrium distribution functions to model the beam species makes a quantitative, but not qualitative, difference in the results. Adding collisions to the calculation tends to reduce considerably the stabilizing effect of the hot ions.

The finite-Larmor-radius modification of the Suydam criterion involves a competition between stabilizing finite-Larmor-radius effects and destabilizing curvature. In the case of the toroidal calculation, corresponding to the Mercier criterion, ballooning effects from regions of unfavourable curvature must be taken into account. In the case of a model equilibrium, valid near the magnetic axis, a complete solution is obtained. Results indicate that the amount of finite-Larmor-radius stabilization needed to overcome the effects of unfavourable average curvature increases as a function of the toroidal ballooning parameter.

For high density Ohmic discharges in the TEXT tokamak, a distinct ion mode (i.e. density fluctuations propagating in the ion diamagnetic drift direction) is observed in the microturbulence spectra. The magnitude and spectral characteristics of the mode are identified. A microinstability based transport model is used for the purpose of interpreting anomalous confinement properties. Onset of the ion feature occurs at plasma densities where a clear saturation is evident in the global energy confinement time ?E. When the ion feature in the fluctuation spectra is strongest, agreement between predictions from the transport model and experimentally measured values of the global energy confinement time is realized if anomalous ion effects due to the ion pressure gradient driven (?i) instability are included. By injecting pellets, a high density plasma is created in which the density profile is sharply peaked. Under these conditions the ion feature in the fluctuation spectra is suppressed. A possible connection between this experimentally observed ion mode and the theoretically predicted properties of the ?iinstability is explored.

Significant investigations in the area of tokamak microinstability theory are reviewed. Special attention is focused on low-frequency electrostatic drift-type modes, which are generally believed to be the dominant tokamak microinstabilities under normal operating conditions. The basic linear formalism including electromagnetic (finite-beta) modifications is presented along with a general survey of the numerous papers investigating specific linear and non-linear effects on these modes. Estimates of the associated anomalous transport and confinement times are discussed, and a summary of relevant experimental results is given. Studies of the non-electrostatic and high-frequency instabilities associated with the presence of high-energy ions from neutral-beam injection (or with the presence of alpha-particles from fusion reactions) are also surveyed.

The influence of enhanced ('anomalous') thermal transport on the neoclassical picture for confinement near the separatrix of a divertor tokamak is investigated. When such transport is taken into account, it is found that the beneficial effects associated with single-null configurations, where the ion grad-B drift direction is towards the x-point, can still persist under realistic conditions.

The paper deals with the formulation of microinstability-based thermal transport coefficients (?j) for the purpose of modelling anomalous energy confinement properties in tokamak plasmas. Attention is primarily focused on ohmically heated discharges and the associated anomalous electron thermal transport. An appropriate expression for ?eis developed which is consistent with reasonable global constraints on the current and electron temperature profiles as well as with the key properties of the kinetic instabilities most likely to be present. Comparisons of confinement scaling trends predicted by this model with the empirical Ohmic database indicate quite favourable agreement. The subject of anomalous ion thermal transport and its implications for high density Ohmic discharges and for auxiliary heated plasmas is also treated.

A model is proposed for explaining the behaviour of the gross energy confinement time in ohmically heated tokamak plasmas. The analysis takes into account the effect of the anomalous thermal conductivity due to small scale turbulence and the effect of the macroscopic MHD behaviour which provides some constraints on the temperature profile. The results indicate that the thermal conductivity associated with the dissipative trapped-electron mode can account for Neo-Alcator scaling and the thermal conductivity associated with the ion temperature gradient mode can account for the saturation of the energy confinement time with density. Comparisons with experimental results show reasonable agreement.

A study of the possible non-linear saturation by mode coupling of the dissipative trappedion mode is presented in which both radial and poloidal variations are considered. The saturation mechanism consists of, the non-linear coupling via convection of energy from linearly unstable modes to stable modes. Stabilization is provided at short poloidal wavelengths by Landau damping from trapped and circulating ions for ?i? d ln(Ti)/d ln(n0) < 2/3, at short radial wavelengths by effects associated with the finite ion banana excursions and at long wavelengths by ion collisions. The authors' analysis applies only to the case ?i< 2/3. A one-dimensional, non-linear partial differential equation for the electrostatic potential derived in earlier work is extended to two dimensions and to third order in amplitude. Included approximately in a systematic way are kinetic effects, e.g. Landau damping and its spatial dependence due to magnetic shear. The stability and accessibility of equilibria are considered for cases far from as well as close to marginal stability. In the first case, three-wave interactions are found to be important when the spectrum of unstable modes is sufficiently narrow. In the latter case, it is found that, for a single unstable mode, a four-wave self-interaction can provide a saturation mechanism. Accessibility of equilibria is determined in both cases. In the case where three-wave interactions are dominant, the stability analysis is inconclusive. However, plasma parameters are found for which equilibria established by means of the four-wave self-interaction are stable to linear perturbation. Cross-field transport is calculated, and the scaling of results is considered for tokamak parameters.

Aspects of the stability of the toroidal field ripple-assisted neutral beam injection scheme proposed by Jassby and Goldston are considered. It is found that beams sufficiently peaked in perpendicular energy are unstable to the generation of loss-cone modes - specifically, lower hybrid waves propagating nearly perpendicular to the magnetic field and driven unstable by the perpendicular velocity space anisotropy-free energy. In the infinite-medium theory, the beam density threshold is intolerably small. However, radial convection of energy provides an important additional source of damping. The resulting threshold may be tolerable if the beam temperature is sufficiently high. Even if the linear stability condition is violated, it is shown that quasilinear diffusion will produce broadening quite rapidly (several e-foldings), with small saturated field amplitudes.