Ionization instability and dusty plasma structurization

In the presence of ionization processes, a homogeneous equilibrium dust distribution often appears as a balance between plasma generation by ionization and plasma absorption by dust particles. It is shown that such equilibrium, often present in laboratory plasmas, is generally unstable against the formation of dust clumps separated by dust-free regions (dust voids). The driving force that separates an initially homogeneous dusty plasma into dust clumps and dust voids is the drag force produced by ions flowing out from the regions with reduced dust density. The lower the dust density, the lower the electron absorption by dust particles and the larger the ionization rate proportional to the electron density. An increase in the ion drag force leads to a further decrease in the dust density and, thus, drives the instability. In the nonlinear stage, the instability creates structures—dust clouds separated by dust voids. The dependence of the instability growth rate on the wavenumber (or, in other words, on the size of the dust-free and dust-containing regions) is investigated. It is shown that, for sufficiently small wavenumbers, a homogeneous distribution is always unstable. An analogy with a gravitational-like instability related to shadowing of the plasma flux by dust particles is pointed out. This effect, which is due to collective shadowing of the plasma flux, dominates the shadowing by individual dust particles discussed previously. Similar to the usual gravitational instability, perturbations with the largest scales are always unstable. Contrary to the usual gravitational instability, the largest growth rate corresponds not to the largest possible scale but to the size close to the mean free path of plasma particles colliding with dust particles. A special investigation is undertaken to determine the influence of the ion-neutral collisions on the growth rate of the instability.