Modelling and Linear Stability Analysis for Dilute Plasma Jets with Ion-Neutral Collisions

Recent work is reported on modelling of dilute plasma jets with ion-neutral elastic momentum-exchange collisions, ionization, flow field gradients, and magnetic fields. A total of 9 equations are considered, including continuity and three momentum equations for neutrals and ions, respectively, and the Poisson equation for electric potentials. Several models and assumptions are adopted to simplify the corresponding mathematical governing equations, and the jet flows are modelled as one dimensional. Linear temporal stability analysis is further performed on this model, to identify possible wave behaviors inside those jets. General expressions for small perturbations are derived. This study focuses on long waves with small wave numbers along the plasma jet centerline. With proper assumptions, the nine relations are simplified and decouple into two groups. A software package with symbolic computation capabilities is utilized to find the corresponding eigenvalues. Eight harmonic wave modes are obtained. The basic mode is stable and the group velocity is an average of ions’ and neutrals’ speeds. Elastic momentum exchange collisions can lead to damping waves and flowfield velocity gradients and ionization can result in either damping or growing waves. Very strong magnetic fields can affect the wave frequencies. This theoretical analysis is general and extendable for more comprehensive experimental and numerical studies in the future.