The method of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] to model Landau damping has been recently applied to the moments of the gyrokinetic equation with curvature drift by Waltz, Dominguez, and Hammett [Phys. Fluids B 4, 3138 (1992)]. The higher moments are truncated in terms of the lower moments (density, parallel velocity, and parallel and perpendicular pressure) by modeling the deviation from a perturbed Maxwellian to fit the kinetic response function at all values of the kinetic parameters: k∥vth/ω, b=(k⊥ρ)2/2, and ωD/ω. Here the resulting gyro-Landau fluid equations are applied to the simulation of ion temperature gradient (ITG) mode turbulence in toroidal geometry using a novel three-dimensional (3-D) nonlinear ballooning mode representation. The representation is a Fourier transform of a field line following basis (ky′,kx′,z′) with periodicity in toroidal and poloidal angles. Particular emphasis is given to the role of nonlinearly generated n=0 (ky′ = 0, kx′ ≠ 0) ‘‘radial modes’’ in stabilizing the transport from the finite-n ITG ballooning modes. Detailing the parametric dependence of toroidal ITG turbulence is a key result.

The performance of a targets designed for the National Ignition Facility ͑NIF͒ are simulated in three dimensions using the HYDRA multiphysics radiation hydrodynamics code. ͓M. Marinak et al., Phys. Plasmas 5, 1125 ͑1998͔͒ In simulations of a cylindrical NIF hohlraum that include an imploding capsule, all relevant hohlraum features and the detailed laser illumination pattern, the motion of the wall material inside the hohlraum shows a high degree of axisymmetry. Laser light is able to propagate through the entrance hole for the required duration of the pulse. Gross hohlraum energetics mirror the results from an axisymmetric simulation. A NIF capsule simulation resolved the full spectrum of the most dangerous modes that grow from surface roughness. Hydrodynamic instabilities evolve into the weakly nonlinear regime. There is no evidence of anomalous low mode growth driven by nonlinear mode coupling.

The gyro-Landau fluid (GLF) model equations for toroidal geometry [R.E. Waltz, R.R. Dominguez, and G.W. Hammett, Phys. Fluids B 4, (1992) 3 1381 have been recently applied to the study ion temperature gradient (ITG) mode turbulence using the 3D nonlinear ballooning mode representation (BMR) outlined in [R.E. Waltz, G.D. Kerbel, and J. Milovich, Phys. Plasmas 1, 2229 (1994)l. The present paper extends this work by treating some unresolved issues concerning ITG turbulence with adiabatic electrons. Although eddies are highly elongated in the radial direction long time radial correlation lengths are short and comparable to poloidal lengths. Although transport at vanishing shear is not particularly large, transport at reverse global shear, is significantly less. Electrostatic transport at moderate shear is not much effected by inclusion of local shear and average favorable curvature. Transport is suppressed when critical ExB rotational shear is comparable to the maximum linear growth rate with only a weak dependence on magnetic shear. Self consistent turbulent transport of toroidal momentum can result in a transport bifurcation at suffciently large r/(Rq). However the main thrust of the new formulation in the paper deals with advances in the development of finite beta GLF models with trapped electron and BMR numerical methods for treating the fast parallel field motion of the untrapped electrons. ...

A description of a bounce-averaged Fokker–Planck quasilinear model for the kinetic description of tokamak plasmas is presented. The nonlinear collision and quasilinear resonant diffusion operators are represented in a form conducive to numerical solution with specific attention to the treatment of the boundary layer separating trapped and passing orbit regions of velocity space. The numerical techniques employed are detailed insofar as they constitute significant departure from those used in the conventional uniform magnetic field case. Examples are given to illustrate the combined effects of collisional and resonant diffusion.