Excitation of ion-acoustic waves by non-linear finite-amplitude standing Alfv\'en waves

We investigate, using a multi-fluid approach, the main properties of standing ion-acoustic modes driven by nonlinear standing Alfv\'en waves. The standing character of the Alfv\'enic pump is because we study the superposition of two identical circularly polarised counter-propagating waves. We consider parallel propagation along the constant magnetic field and we find that left and right-handed modes generate via ponderomotive forces the second harmonic of standing ion-acoustic waves. We demonstrate that parametric instabilities are not relevant in the present problem and the secondary ion-acoustic waves attenuate by Landau damping in the absence of any other dissipative process. Kinetic effects are included in our model where ions are considered as particles and electrons as a massless fluid, and hybrid simulations are used to complement the theoretical results. Analytical expressions are obtained for the time evolution of the different physical variables in the absence of Landau damping. From the hybrid simulations we find that the attenuation of the generated ion-acoustic waves follows the theoretical predictions even under the presence of a driver Alfv\'enic pump. Due to the nonlinear induced ion-acoustic waves the system develops density cavities and an electric field parallel to the magnetic field. Theoretical expressions for this density and electric field fluctuations are derived. The implications of these results in the context of standing slow mode oscillations in coronal loops is discussed.