Kinetically modified parametric instabilities of circularly polarized Alfv́n waves: Ion kinetic effects

Parametric instabilities of parallel propagating, circularly polarized, finite amplitude Alfv́n waves in a uniform background plasma is studied, within a framework of one-dimensional Vlasov description for ions and massless electron fluid, so that kinetic perturbations in the longitudinal direction (ion Landau damping) are included. The present formulation also includes the Hall effect. The obtained results agree well with relevant analysis in the past, suggesting that kinetic effects in the longitudinal direction play essential roles in the parametric instabilities of Alfv́n waves when the kinetic effects react "passively." Furthermore, existence of the kinetic parametric instabilities is confirmed for the regime with small-wave-number daughter waves. Growth rates of these instabilities are sensitive to ion temperature. The formulation and results demonstrated here can be applied to Alfv́n waves observed in the solar wind and in the earth's foreshock region.