MHD model including small-scale perturbations in a plasma with temperature variations

The possibility is studied of using a hydrodynamic model to describe a magnetized plasma with density and temperature variations on scales that are arbitrary with respect to the ion Larmor radius. It is shown that the inertial component of the transverse ion thermal flux should be taken into account. This component is found from the collisionless kinetic equation. It can also be obtained from the equations of the Grad type. A set of two-dimensional hydrodynamic equations for ions is obtained with this component taken into account. These equations are used to derive model hydrodynamic expressions for the density and temperature variations. It is shown that, for large-scale perturbations (when the wavelengths are longer than the ion Larmor radius), the expressions derived coincide with the corresponding kinetic expressions and, for perturbations on sub-larmor scales (when the wavelengths are shorter than the Larmor radius), they agree qualitatively. Hydrodynamic dispersion relations are derived for several types of drift waves with arbitrary wavenumbers. The range of applicability of the MHD model is determined from a comparison of these dispersion relations with the kinetic ones. It is noted that, on the basis of the results obtained, drift effects can be included in numerical MHD codes for studying plasma instabilities in high-temperature regimes in tokamaks.