Kinetically modified parametric instabilities of circularly-polarized   Alfven waves: Ion kinetic effects
  Parametric instabilities of parallel propagating, circularly polarized finite amplitude Alfven 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 Alfven 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 Alfven waves observed in the solar wind and in the earth's foreshock region. 
Yasuhiro Nariyuki, Tohru Hada