The predictions of gyrokinetic and gyrofluid simulations of ion-temperature-gradient (ITG) instability and turbulence in tokamak plasmas as well as some tokamak plasma thermal transport models, which have been widely used for predicting the performance of the proposed ITER tokamak, are compared. These comparisons provide information on effects of differences in the physics content of the various models and on the fusion-relevant figures of merit of plasma performance predicted by the models. Many of the comparisons are undertaken for a simplified plasma model and geometry which is an idealization of the plasma conditions and geometry in a DIII-D H-mode experiment. Most of the models show good agreements in their predictions and assumptions for the linear growth rates and frequencies. There are some differences associated with different equilibria. However, there are significant differences in the transport levels between the models. The causes of some of the differences are examined in some detail, with particular attention to numerical convergence in the turbulence simulations (with respect to simulation mesh size, system size and, for particle-based simulations, the particle number). The implications for predictions of fusion plasma performance are also discussed.

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One- and two-dimensional simulations and supporting analysis of nonlinear ion acoustic waves as might be associated with the saturation of stimulated Brillouin backscattering (SBBS) are presented. To simulate ion wave phenomena efficiently, while retaining a fully kinetic representation of the ions, a Boltzmann fluid model is used for the electrons, and a particle-in-cell representation is used for the ions. Poisson’s equation is solved in order to retain space-charge effects. We derive a new dispersion relation describing the parametric instability of ion waves, evidence for which is observed in our simulations. One- and two-dimensional simulations of plasma with either initially cold or warm ions (and multi-species ions) exhibit a complex interplay of phenomena that influence the time evolution and relaxation of the amplitude of the excited ion wave: ion trapping, wave steepening, acceleration, heating and tail formation in the ion velocity distribution, parametric decay into longer wavelength ion waves, modulational and filamentation instabilities, and induced scattering by ions. The additional degrees of freedom in two dimensions allow for a more rapid relaxation of the primary ion wave. One-dimensional electrostatic simulations with externally driven ion waves agree qualitatively with electromagnetic simulations in one dimension in which the ponderomotive driving potential is computed self-consistently by solving a Schroedinger-like equation for the electromagnetic waves and calculating the low-frequency ponderomotive force on the electrons.

The nonlinear saturation of the dissipative trapped-ion mode is analyzed. . I The basic mechanism considered is the process whereby energy in long wavelength th unstable modes is nonlinearly coupled via E x B convection to short wavelength modes stabilized by Landau damping due to both circulating and trapped ions. In the usual limit of the mode frequency small relative to the effective electron collision frequency, a one-dimensional nonlinear partial differential equation for the potential can be derived, as first shown by LaQuey, Mahajan, Tang, and Rutherford. The stability and accessibility of the possible equilibria for this equation are examined in detail, both analytically and numerically. The equilibrium emphasized by LaQuey et al. is shown to be unstable. However, a class of nonlinear saturated states which are stable to linear perturbations is found. Included in the analysis are the effects of both ion collisions and dispersion due to finite ion bananawidth effects. Cross-field transport is estimated and the scaling of the results is considered for tokamak parameters (specifically those for the'• Princeton Large Torus). It is concluded that the anomalous• cross-field transport can be much lower than the estimate of Kadomtsev and Pogutse, for relevant parameters.