Linear Waves in Partially Ionized Plasmas in Ionization Non-equilibrium

We aim to investigate the properties of linear Alfv\'en and slow magnetoacoustic waves in a partially ionised plasma in ionisation non-equilibrium. The propagation characteristics of these waves are studied within the framework of a two-fluid plasma in terms of the collisional strength between heavy particles for different degrees of ionisation. In the ionisation non-equilibrium state the rates of ionisation and recombinations are not equal. For analytical progress we assume a background that is ionisation equilibrium, the non-equilibrium is driven by perturbations in the system, {\bf therefore, non-equilibrium effects are related to the perturbed state of the plasma}. Using simple analytical methods, we show that ionisation non-equilibrium can provide an additional coupling between ions and neutrals (implicitly a secondary damping mechanism in the collisionless limit) and this process is able to keep the neutrals in the system even in the collisionless limit. Due to the coupling between different species waves become dispersive. The present study improves our understanding of the complexity of dynamical processes partially ionised plasma in the lower solar atmosphere and solar prominences. Our results clearly show that the problem of partial ionisation and non-equilibrium ionisation introduce new aspects of plasma dynamics with consequences on the evolution waves and their dissipation.