Gyro-Landau fluid models for toroidal geometry

Gyro-Landau fluid model equations provide first-order time advancement for a limited number of moments of the gyrokinetic equation, while approximately preserving the effects of the gyroradius averaging and Landau damping. This paper extends the work of Hammett and Perkins [Phys. Rev. Lett. 64, 3019 (1990)] for electrostatic motion parallel to the magnetic field and E×B motion to include the gyroaveraging linearly and the curvature drift motion. The equations are tested by comparing the ion-temperature-gradient mode linear growth rates for the model equations with those of the exact gyrokinetic theory over a full range of parameters.