Theoretical model of ion-acoustic shock wave structure in dusty plasma

Dust is an important component of plasma in multiple environments throughout the solar system, including dust created as comets melt in the vicinity of the Sun or the dust rings that surround massive planets such as Saturn. The effects of dust particles in the structure and propagation of ion-acoustic waves through plasma have been empirically recorded and studied for nearly two decades (see Nakamura et al., 1999, Physical Review Letters, 83, 1602). A Korteweg-de Vries-Burgers (KdVB) PDE involving the electrostatic potential governs the process, and numerical solutions agree well with the overall shock structure. However, the exact form and nature of the dissipation term within this equation is hitherto unknown. Inspired by comments in Nakamura et al. (1999), this research seeks to incorporate ion-dust collisions into the plasma framework in order to obtain an exact form for the dissipation coefficient in terms of experimental quantities. In order to achieve this goal, we assume a simplified (to first order) shielded potential to derive appropriate scattering quantities (e.g. drag and diffusion coefficients) for the Fokker-Plank equation, and then proceed with a Chapman-Enskog expansion, leading to an explicit form of the desired term, among others. With our contribution, we hope to provide a rigorous theoretical foundation for the use of a KdVB equation to describe ion-acoustic shockwave structure (some of which has been done before), and obtain a formula for the dissipation coefficient based on measurable quantities. This will further the understanding of this phenomena, as well as pinpoint certain key parameters that could be adjusted in order to control the wave structure.