Fluid moment models for Landau damping with application to the ion-temperature-gradient instability

A closed set of fluid moment equations is developed which represents kinetic Landau damping physics and which takes a simple form in wave-number space. The linear-response function corresponds to a three-pole (or four-pole) approximation to the plasma dispersion function Z. Alternatively, the response is exact for a distribution function which is close to Maxwellian, but which decreases asymptotically as 1/${\mathit{v}}^{4}$ (or 1/${\mathit{v}}^{6}$). Among other applications, these equations should be useful for nonlinear studies of turbulence driven by the ion-temperature-gradient or other drift-wave microinstabilities.