A KINETIC DERIVATION OF A GENERALIZED ZAKHAROV-KUZNETSOV EQUATION FORION-ACOUSTIC TURBULENCE IN A MAGNETIZED PLASMA

The Zakharov-Kuznetsov equation has been derived by a number of author s in the context of a fluid description as well as a kinetic descripti on in a nonmagnetized plasma. We propose, in this short paper, to disc uss the derivation of the equation governing the evolution of ion acou stic waves in a magnetized plasma using kinetic theory. This allows us to introduce Landau damping more specifically, as well as other purel y nonlinear kinetic effects. We first investigate the effects of Landa u damping on the conservation laws, and therefore on the solitary solu tion known to exist in the fluid regime. We also derive a conservation law very much like the one-dimensional case.