Magnetohydrodynamic Model for Plasma Instabilities in the Ion-Kinetic Regime

A magnetized plasma is considered. It is shown that the MHD model provides an adequate description of plasma instabilities in the ion-kinetic regime, where the characteristic scales of the plasma motion fall below the ion Larmor radius. This conclusion is the consequence of the fact that the well known relation between the perturbed plasma density and the perturbed electric potential, which follows from the linearized Vlasov equation (the so-called ion-kinetic response), can be derived with a good accuracy from the MHD model when the Hall effect is taken into account. Moreover, the MHD ion response coincides with a Pade approximation for the ion-kinetic response.