# Ionization equation of state for the dusty plasma including the effect of ion--atom collisions

## TL;DR

This paper develops an ionization equation of state for dusty plasma that incorporates ion-atom collisions, improving the accuracy of dust particle charge predictions and explaining experimental observations under microgravity conditions.

## Contribution

It introduces a modified IEOS model that accounts for ion-atom collisions, enhancing the understanding of dust particle charging and density in dusty plasmas without fitting parameters.

## Key findings

- Decreased particle charge compared to previous models.
- Reproduction of experimental dust density and pressure dependence.
- Derived threshold conditions for lane formation in binary dusty plasmas.

## Abstract

The ionization equation of state (IEOS) for a cloud of the dust particles in the low-pressure gas discharge under microgravity conditions is proposed. IEOS relates pairs of the parameters specific for the charged components of dusty plasma. It is based on the modified collision enhance collection model adapted for the Wigner--Seitz cell model of the dust cloud. This model takes into account the effect of ion--atom collisions on the ion current to the dust particles and assumes that the screening length for the ion--particle interaction is of the same order of magnitude as the radius of the Wigner--Seitz cell. Included effect leads to a noticeable decrease of the particle charge as compared to the previously developed IEOS based on the orbital motion limited model. Assuming that the Havnes parameter of the dusty plasma is moderate one can reproduce the dust particle number density measured in experiments and, in particular, its dependence on the gas pressure. Although IEOS includes no fitting parameters, it can ensure a satisfactory precision in a wide range of dusty plasma parameters. Based on the developed IEOS, the threshold relation between the dusty plasma parameters for onset of the lane formation in binary dusty plasmas is deduced.