It has been recognized both by NASA (2018 Strategic Plan) and the National Academy of Sciences (2019 Search for Life report) that the future of space exploration will require challenging missions to nearby planets and moons. Such missions will involve high-speed aircraft atmospheric entries, which become increasingly technical in thick atmospheres, such as the atmospheres of gas giants, due to the resulting extreme heating of the spacecraft. This motivates the desire to develop and test the next generation of heat shields that can protect spacecrafts during such ambitious entries. To address this problem of high significance to the U.S. goals in space exploration, we collaborate with Dr. Dmitri Orlov and Dr. Igor Bykov from University of California San Diego in a project where we study what happens to aircraft heat shield materials when exposed to extreme conditions.

We aim to reproduce the processes occurring during spacecraft atmospheric entries by exposing material targets to the plasma environment of the DIII-D National Fusion Facility in San Diego and the IPG6-B inductive plasma generator in the CASPER lab (figure on the left). DIII-D experiments can reproduce the high heat environments encountered in some of the most ambitious missions ever attempted, such as the Galileo probe, which entered Jupiter’s atmosphere with a speed of almost 50 km/s. Instead of accelerating test materials to such extreme speeds, we recognized that the DIII-D tokamak plasma itself rotates with comparable speed, which means that any object launched radially from the wall of the tokamak incurs motion relative to the plasma which is comparable to the entry speed of Galileo.

Fig. 1. a) Non-interacting particles move randomly (normal diffusion.) b) Correlated particles can make huge jumps in space (anomalous diffusion.)

In a famous 1972 publication, Philip Anderson argued that the behavior of complex systems cannot be reduced to the interactions of elementary entities. Instead, at each level of complexity entirely new properties emerge due to the many-body correlations involved. Simply put, more is different. While non-interacting particles move in a random fashion, called normal diffusion, correlated particles move in a less random way, called anomalous diffusion. Anomalous diffusion is so common in the natural world that scientists often conclude: anomalous is normal. The marriage between increasing complexity and anomalous transport often results in turbulent dynamics of the many-body system. Dusty plasmas are ideal media for the investigation of these phenomena.
In this project we study turbulence in a dusty plasma by computing the spectrum of energies available to the dust particles as a function of random disorder and properties of nonlocal interactions mediated by the plasma. We argue that at critical scales within the system, anomalous dust diffusion, guided by nonlocal interactions, leads to enhancement of energy transport and increased probability for turbulent dynamics. These theoretical predictions are compared against results from many-body simulations and dusty plasma experiments conducted on board the International Space Station.

This research is funded by NSF-1903450, NSF- 1707215, NASA- 1571701, DE-SC0021284

All authors acknowledge the joint ESA / Roscosmos “Experiment Plasmakristall-4” onboard the International Space Station.

Check out a video talk on this subject:

It is often pointed out that plasma is the most abundant form of visible matter throughout the universe, which makes it not surprising that a large class of plasma-related phenomena have practical applications in various fields of science and industry. However, the vast majority of plasma research studies are hardly thorough without understanding how plasma interacts with other forms of matter. From the investigation of star and planet formation to the cutting-edge research in fusion technology, materials science, and low temperature plasma physics, scientists cannot ignore the presence of small solid or liquid particles (also called dust) existing within plasmas. Most environments containing plasma are also likely to contain dust due to both plasma-surface interactions and dust particle chemical growth. The physics of these dusty plasmas has naturally evolved as a cross-disciplinary research field encompassing a wide range of topics relevant to both fundamental science and technological development (Fig. 1)

Fig. 1. (a) Topics of interest in dusty plasma physics. (b) Dust particle growth in reactive plasma.

Complex (dusty) plasmas form a special class of plasmas where millimeter (10⁻³m) to nanometer (10⁻⁹m) sized particles are levitated within a plasma gas. Dust grains immersed in plasma become negatively charged and are subject to ion drag forces and collective plasma interactions. The presence of a dust component is characteristic of plasmas with various spatial, temporal, and density scales found in both laboratory conditions and astrophysical environments (Fig. 2).

Fig. 2. Dusty plasma parameter space.

An interesting aspect of dusty plasmas is their ability to self-organize into dust liquids, 2D and 3D dust lattices, and 1D filamentary structures. This feature provides researchers the ability to examine classical collective phenomena on time and length scales allowing for direct observation (at the kinetic level) of fundamental microscopic and macroscopic processes across a wide range of coupling regimes. Thus, in addition to its direct relevance to numerous topics in the field of plasma physics, dusty plasmas can also play an important role as analogue systems for the investigation of complex cross-disciplinary phenomena predicted in theoretical physics and mathematics. Figure 3 provides an overview of recent studies employing dusty plasma analogues.

Fig. 3. Dusty plasma analogues: (a) nonlinear waves and (b), (c) shocks (Merlino et al., 2012), (d) dust grid pattern in external magnetic field (Thomas et al., 2015), (e) 2D honeycomb monolayer (Max Planck Institute), f) electrorheological dusty plasma (PK-4 lab), (g) folding of filamentary structures (Hyde et al., 2013).

Note that the images used on this page are adapted from a white paper submitted by the CASPER lab as a contribution to the Decadal Assessment of Plasma Science

A common issue in the study of laboratory plasma is the perturbative nature of electric probes, such as the Langmuir probe, commonly used to obtain the discharge characteristics. Dusty plasma systems offer an alternative approach, where the dynamical processes within the plasma can be studied by optically tracking the motion of individual dust grains suspended in the discharge. Due to their mesoscopic size, the dust particles are less perturbative than a typical probe and more sensitive to changes in the plasma environment. Therefore, dusty plasmas provide a powerful diagnostics tool for the investigation of various phenomena, including plasma-material interactions, electric field mapping, plasma sheath characteristics, etc.

The goal of this research project is to develop a set of dust diagnostics techniques, which will be employed in the characterization of new discharge devices, such as CASPER Cell 3 shown below.

Cell 3 is a capacitively-coupled radio frequency (RF) discharge located in the CASPER lab.

This is a series of research projects that aims to incorporate newly-developed mathematical techniques in the study of exotic transport phenomena in physical systems characterized by disorder, non-local interactions, and correlated effects. Specifically, we focus on the application of spectral theory and fractional calculus to important phenomena, such as turbulence, streaming instability, and conductivity in low-dimensional materials. Our work is a generalization of the famous theory of Anderson localization introduced in 1958 by Philip Anderson, for which he received the Nobel Prize in Physics in 1977. While the original question addressed by Anderson was focused on localization due to disorder, our work aims to identify the physical systems where delocalization can exist, despite the presence of disorder. Anderson ended his Nobel Prize speech with a reference from Lewis Carroll, emphasizing how complex, yet fascinating a simple transport question can be.

“Now, here, you see, it takes all the running you can do, to keep in the same place.” ~ Lewis Carroll, Alice Through the Looking Glass

The spectral approach developed by our collaborator, Dr. Conni Liaw, is a mathematical technique which determines the existence of a continuous component in the spectrum of the system’s Hamiltonian. In our previous work, we have provided a physical interpretation of the spectral method and applied to the study of conductivity in two-dimensional (2D) materials of various geometry and the investigation of waves in 2D dusty plasma crystals. A significant outcome of this work was theoretically confirming the existence of a metal-to-insulator transition in honeycomb lattices with substitutional disorder, such as graphene doped with hydrogen. In the present study, we combine the spectral approach with a fractional Laplacian technique that models anomalous diffusion in correlated media. Since the combined mathematical model is applicable to the study of transport in complex systems (including multiphase flows, strongly coupled systems, and plasmas), it can open the door to a wonderland of scientific discoveries.

The self-organization and stability of macroscopic astronomical objects, such as stars and galaxies throughout the universe, is dominated by the force of gravity. In contrast, when the structures are microscopic, such as systems of atomic and subatomic particles, the same processes are guided by nuclear forces and quantum effects. As one follows the growth of an astronomical body from the subatomic level up, a natural question emerges: What fundamental mechanisms dictate self-organization and stability in the transitional (mesoscopic) range, where the spatial scale is neither small nor large?

A few decades ago, the international complex plasma community recognized that the fundamental questions of  mesoscopic physics can be explored using a series of dusty plasma experiments in space. Currently, the most effective way of achieving microgravity conditions is to perform these experiments on board the International Space Station (ISS). In February 2001, the dusty plasma experiment PKE Nefedov became the first natural science experiment installed on board the ISS. Since then, dusty plasma research on the ISS has revealed that the mesoscopic structures can exhibit a variety of condensed and soft matter phenomena including, crystallization and melting, wave instabilities and mode coupling, formation of vortices and self-excited turbulences, and electrorheology. The current dusty plasma lab installed on the ISS, Plasma Kristall-4 (PK-4) , is the first project of this kind with direct involvement of US research groups, one of which is the CASPER group.

The International Space Station., Astronomy Picture of the Day on April 6, 2009

The PK-4 laboratory is a successor of the PKE-Nefedov and PK-3 Plus facilities that investigated complex plasma liquids and solids in uncompressed, homogeneous plasma created by a parallel-plate capacitively coupled RF discharge. In contrast, the PK-4 consists of an elongated Π-shaped glass chamber in which the plasma can be ignited either by cylindrical DC electrodes or by RF coils (as shown below). Thus, the apparatus allows for experiments in pure DC, pure inductive RF, or combined DC-RF discharge. The PK-4 design makes it ideal for the investigation of various fluid phenomena. In my research related to this project, I am interested in studying the physical mechanisms which can trigger the onset of dusty plasma waves and instabilities. Specifically, my goal is to establish connections between anomalous dust particle diffusion and the onset of a ion-dust streaming instability. The streaming instability is considered a possible mechanism for dust coagulation in protoplanetary disks. However, it has not been thoroughly investigated and understood in charged multi-component flows under microgravity conditions. The results from this project can considerably improve our understanding of the dust-plasma dynamics in astrophysical systems.

Sketch of the PK-4 experimental setup. The Π-shaped glass chamber consists of three glass tubes welded together, each with 30 mm inner diameter. A working area of about 200 mm (occupying the middle of the main tube) is illuminated by a laser sheet and observed by the two (micro)particle observation cameras (marked as C1 and C2). Dust particles of various size can be injected from both sides of the glass tube and manipulated with several manipulation devices. Those include: stationary and movable rf coils, thermal manipulator, manipulation laser, electric manipulation (EM) electrode.