Dusty plasmas consist of ions, electrons and charged solid particles, commonly referred to as dust, ranging in size from a few tens of nanometers to several tens of micrometers.  One of the interesting features of dusty plasmas is the ability of the dust particles to “self-organize” into a wide variety of structures, such as dust crystals, liquids, and helical strings.  The dust particles can be treated as proxy atoms, which allows  dusty plasmas to serve as an analogue system for the study of fundamental phenomena in other materials, including melting and crystallization, waves and instabilities, and turbulence.  The benefit of this system is that the individual dust grains can be imaged with a video camera to track their motion.

This project investigated the fundamental physical mechanisms guiding the onset of turbulence in dusty plasma monolayers by applying novel mathematical and numerical techniques to the analysis of dust diffusion. The onset of turbulence is linked to anomalous dust diffusion, by which we mean that the particles can make much greater or shorter displacements in a given time interval than expected for classical diffusion. Anomalous diffusion results from the combination of random processes and long-range interactions, which add complexity to the system. Complex systems exhibiting anomalous diffusion include the Sun’s coronal mass ejections, animals’ migration patterns, molecular transport through cell membranes, and fluctuations of the stock market. Thus, linking the observation of anomalous diffusion to the onset of turbulent instabilities in a complex system is of fundamental importance.

To model anomalous diffusion as a function of random disorder and non-local interactions, we integrated mathematical proofs from spectral theory and fractional calculus.  A one-dimensional numerical model was used to study how the spectrum of energy states available to the dust particles in a monolayer changes as the system transitions from a crystalline to a turbulent liquid state.  Specifically, we calculated the probability for dust transport as a function of increasing spatial scales for input parameters obtained from dusty plasma experiments and molecular dynamics simulations. We developed physical interpretations that allowed us to convert the processes in a dusty plasma into dimensionless parameters in a mathematical operator, called the Hamiltonian, which is used to model how energy propagates through the system. It was established that a dusty plasma monolayer can transition to a turbulent state if the particles are sub-diffusive and the disorder concentration in the system is ~0.1%.

The form, strength, and range of the dust-dust interaction potential and the dynamical instabilities caused by the dust interaction with the plasma environment were found to be important mediators of the resulting diffusion. In particular, it was found that anisotropic interactions among the dust grains can lead to structural states analogous to those observed in liquid crystal (LC) materials. In a smectic LC state, the dust particles align in chains along a preferred direction but form a hexagonal structure in the direction perpendicular to the alignment. This causes energy propagation to be different in the two directions.  Substantial complementary information related to identifying the parameter space where dusty plasma liquids experience instabilities were obtained from work on another project, which was focused on the formation of filamentary dust structures in the microgravity environment of the Plasma-Kristall 4 experiment onboard the International Space Station.

Three graduate students and six undergraduate students contributed to the research undertaken for this project. (One of the graduate students transitioned to a post-doctoral position working on this project.) This project supported two early career PIs, and three of the four original PI/Co-PIs are female.  Four of the nine student participants were female, one is an underrepresented minority. The results of this research were reported through nine published articles, seventeen presentations at national and international conferences, and one Ph.D. dissertation.  The PIs also presented parts of this research in multiple public engagement talks each year.

Last Modified: 11/29/2023
Modified by: Lorin S Matthews