Dusty plasmas are electrically quasi-neutral media that, along with electrons, ions, neutral gas, radiation, and electric and/or magnetic fields, also contain solid or liquid particles with sizes ranging from a few nanometers to a few micrometers. These media can be found in many natural environments as well as in various laboratory setups and industrial applications. As a separate branch of plasma physics, the field of dusty plasma physics was born in the beginning of 1990s at the intersection of the interests of the communities investigating astrophysical and technological plasmas. An additional boost to the development of the field was given by the discovery of plasma crystals leading to a series of microgravity experiments of which the purpose was to investigate generic phenomena in condensed matter physics using strongly coupled complex (dusty) plasmas as model systems. Finally, the field has gained an increasing amount of attention due to its inevitable connection to the development of novel applications ranging from the synthesis of functional nanoparticles to nuclear fusion and from particle sensing and diagnostics to nano-contamination control. The purpose of the present perspectives paper is to identify promising new developments and research directions for the field. As such, dusty plasmas are considered in their entire variety: from classical low-pressure noble-gas dusty discharges to atmospheric pressure plasmas with aerosols and from rarefied astrophysical plasmas to dense plasmas in nuclear fusion devices. Both fundamental and application aspects are covered.

With this Perspectives paper, the dusty plasma community for the first time identifies promising future directions for its development. It was prepared by 34 leading experts in the field, representing ten countries. The intention of this paper is to highlight the current state-of-the-art and challenges in the field of dusty plasma physics and its technological applications, thereby serving as a guideline to colleagues in the field and fields connected to it. Moreover, the Perspectives discussed may give a direction to policymakers and (inter-)national funding agencies in terms of allocating resources. The paper consists of 14 topical sections. Each of them is coauthored by two to three experts who present their personal views on the state-of-the-art of the topic as well as on its perspectives. The authors are listed in alphabetic order.

Dusty plasmas are electrically quasi-neutral media that, along with electrons, ions, neutral gas, radiation, and electric and/or magnetic fields, also contain solid or liquid particles with sizes ranging from a few nanometers to a few micrometers. Once immersed in an ionized medium, dust particles unavoidably get charged due to incoming fluxes of electrons and ions on their surfaces. Therefore, the charge (as well as the surface temperature) of the dust is self-consistently coupled not only to electron and ion temperatures and densities but also to parameters, such as collisionality, magnetization, dust density, dust shape, and surface conditions.

Under laboratory and microgravity conditions, dusty plasmas are usually investigated in low-pressure gas discharges in which the dust particles are either grown by chemical reactions or externally injected. The presence of dust in a plasma leads not only to quantitative changes of plasma parameters but also to the appearance of new dust-induced phenomena like void formation and low-frequency instabilities. In general, the modeling of dusty gas discharges is considerably more complicated with respect to the modeling of dust-free discharges due to the very slow dynamics of dust compared to that of electrons and ions present in the plasma. Also, classical plasma diagnostic techniques need to be modified to take into account the presence of dust. Moreover, new diagnostic methods have been developed in recent years in order to measure typical dust parameters, such as temporal and spatial distributions of dust size and/or number density and the charge that dust particles obtain in the plasma.

Micrometer-sized dust particles arrange themselves toward typical inter-particle distances of the order of fractions of millimeters in low-pressure discharges. This makes their suspensions accessible for observation at the level of single dust particles. In addition to that, the strong coupling of the dust particles due to their Coulomb interaction often leads to the crystallization of their sub-system. This makes dusty plasmas interesting model systems for studying generic condensed matter phenomena at the level of atomistic dynamics, such as phase transitions, lattice formation, and density waves. Two-dimensional systems can be created, for instance, in the sheath of a radio frequency (RF) discharge. Three-dimensional systems are studied in different discharge configurations and under microgravity conditions.

As mentioned above, dust particles can grow in low-pressure reactive discharges. Controlling this process allows one to grow semiconductor particles of nm-size (i.e., so-called quantum dots), which have many applications in biological labeling or sensing. At the moment, they are mainly produced in wet chemistry processes, which have certain disadvantages compared to plasma synthesis. Similarly, there are attempts to grow semiconductor nanoparticles in atmospheric pressure microdischarges either from gas phase or from aerosol precursors.

In spite of certain similarites between atmospheric pressure plasmas (APPs) containing aerosols and dusty plasmas, both areas of research have mainly been developing separately from each other. Nevertheless, following the suggestion expressed in the dusty plasma section of the recent low-temperature plasma roadmap,1 it was decided to bring the two fields together in this Perspectives paper in order to promote possible collaborative efforts. Atmospheric pressure plasmas containing aerosols are important not only for the synthesis of functional nanoparticles but also as reactive media for nitrogen fixation or, e.g., for deactivation of pathogens in bio-aerosols.

The oldest topic associated with the applications of dusty plasmas, dust contamination control of plasma processes, has recently got a new impulse due to the emergence of extreme ultraviolet lithography and other high-tech ultra-clean industrial processes. In such processes, the possible presence of pulsed plasma (either induced by inherent photoionization or by remote plasma sources) may provide charges on the particles and electric fields transporting them to (optical) elements, which are highly vulnerable to contamination.

Recently, several dusty plasma setups with magnetic field in the Tesla range have been introduced. These setups allow us to study basic processes in dusty plasmas of different degrees of magnetization. Those investigations are of importance in the scope of magnetic confinement fusion research where dust, emerging in the plasma volume due to different mechanisms, has long been recognized as a considerable problem.

Ionospheric and space dusty plasmas also represent a traditional branch of dusty plasma research. Many of the current, as well as planned, space missions have investigation of dust in different regions of the Solar system as one of their major goals. The scope of this space dusty plasma research has been considerably broadened to, e.g., the heliosphere, space-debris-related problems, or planetary debris disks of stars.

In spite of the diversity of the topics, the dusty plasma community will definitely benefit from more intense collaborations between experts performing experimental gas-discharge-based laboratory and large-scale-facility research (fusion, long-term microgravity laboratories, space missions, etc.), theory, and modeling. Also, collaborations between groups conducting basic and application-oriented research should allow the former to better streamline their efforts and the latter to better understand the physical mechanisms underlying their applications. Establishing such frameworks would enable the community to tackle more efficiently the scientific and societal challenges ahead.

Throughout this Perspectives paper, we will use the terminology similar to that of Ref. 2. Namely, in cases when the dust component of the plasma consists of industrially manufactured particles of regular shape and definite chemical composition, we will term the dust component as “microparticles.” In vast majority of other cases, we will apply the terms “dust,” “dust grains,” or “dust particles” to the dust component. We will also apply the most general term “dusty plasmas” to all plasmas containing dust. Only in cases when the system of microparticles in plasmas is specifically designed for the purpose of modeling the generic phenomena of condensed matter, we will apply a more specific term “complex plasmas.” Established physical terms like, e.g., “dust component” or “dust acoustic wave” will be used irrespective of the source and nature of dust immersed in plasmas. Some sections use specific terminology. For example, in Sec. IV, the term “nanodusty plasma” is used to emphasize the nanometer size of dust particles. In the fusion community (see Sec. VIII), the terms dust and “powder” are used equivalently. Section XI introduces the terminology associated with atmospheric plasmas with aeorsols. Terms applied to astro- or geophysical media (e.g., “meteoric smoke” or “noctilucent clouds”) imply the presence of dusty plasmas (Sec. XIII).

Dust charging dictates single grain dynamics and collective effects.3,4 The relevant spatial scales are the dust size r d , Debye length λ D , plasma gyroradii ρ α , collision mean free paths λ c α , and mean intergrain distance d. For isolated spherical dust, the orbital motion (OM) theory applies in the non-emissive, collisionless, unmagnetized limit, i.e., r d , λ D ρ α , λ c α .5–8 It is based on energy and angular momentum conservation, expressed in a non-linear Poisson equation supplemented by the floating potential condition. The orbital motion limited (OML) approach is an OM approximation that neglects effective potential barriers to plasma collection.9 Remarkably, in OML, the dust potential relative to the plasma potential is determined only by the floating potential condition, thus circumventing Poisson's equation fully. The dust charge is computed without plasma screening, with a vacuum capacitance, limiting OML validity to r d λ D . Unparalleled simplicity is the reason behind OML's wide utility. The effect of ion–neutral collisions was addressed early.10–13 Semi-empirical formulas exist in the full ion collisionality range,14–16 tested against experiments.17–19 In discharge plasmas, the contribution of ion–neutral collisions to charging becomes significant already for λ n , i 10 λ D .14 

Plasma screening of the dust charge dictates the dust–dust interaction potential: the key quantity for the description of collective effects in dusty plasmas within the one-component assumption. Even for isotropic plasmas, the Debye–Hückel (Yukawa) form20 is valid for weak ion–grain coupling as well as in the absence of collisions with neutrals and plasma sources/sinks.21 In the collisionless case, exact potential profiles can be obtained by solving the non-linear Poisson equation with the charge density derived from the stationary Vlasov equation.22,23 The Yukawa form persists at short-to-intermediate distances provided that an effective screening length is utilized that depends on the ion non-linearity parameter.24–26 In the collisional case, an asymptotic theory5,27,28 together with the linearization of a BGK-type ion kinetic equation with point-sinks29,30 or the drift-diffusion approximation31,32 have quantified non-Yukawa aspects. In the presence of electron emission8,33 or source/sink competition,34–37 the formation of attractive potential wells has been reported.

The ion drag force, due to scattering of drifting ions, has been known to drive dust dynamics in discharges, tokamaks, and space. In collisionless subthermal flowing plasmas, the binary collision approach of classical scattering theory has been employed for Yukawa interactions and arbitrary ion–grain coupling with shifted Maxwellian or more accurate ion distribution functions.38–41 For ion–neutral collisions and arbitrary Mach numbers, the linear response approach has been employed with self-consistent ion distributions within the weak coupling limit.42,43 The complementarity of these approaches was exploited in a more general hybrid approach.44 Particle-in-cell (PIC) simulations provided invaluable benchmark data, bridged the gap between the formalisms, and yielded accurate analytical correction factors at arbitrary collisionality and non-linearity in the practical Mach number range.45–47 

A problem has been pointed out in the original formulation of OML that did not allow incorporation of plasma screening due to an error in the ion density.23,48 A revised OML theory has been formulated.22,23 A comparison with PIC simulations revealed that accuracy is retained up to r d λ D and that screening effects on the dust charge can be significant.49 The extension to positively charged dust has also been reported.50 

Recent studies have been driven by tokamak dust,51–55 where effects beyond OML can become important. First-principles simulations have revealed that OML can become very inaccurate in the emission-dominated space-charge-limited regime due to a potential well formed by the slow emitted electrons being attracted back to the positively-charged dust.8,33,56 The potential well can alter the plasma electron collection and substantially decrease electron heating.56 A correction to the OML has been proposed, dubbed as OML+, shown to be in good agreement with simulations. Other OML modifications have been proposed57,58 for direct use in transport codes. Initial work combining electron emission and electron magnetization59 identified how the emitted electron flux can be reduced by prompt redeposition via gyro-motion, strongly affecting charging. However, more sophisticated charging/heating models60 accounting for the collisional magnetized presheath suggest a weaker heat flux dependence on the dust charge than in OML, rendering a very accurate description of electron emission less important.

Much attention has been paid to dust charge screening in the presence of ion flows. The shifted Maxwellian ion distribution used in early studies61,62 has been proven to grossly misrepresent the exact state of affairs.63 In fact, self-consistent distributions that include neutral collisions and electric field acceleration are asymmetric and much broader. Exact Monte Carlo (MC) results have been compared with kinetic theory for constant cross sections or constant collision frequencies (BGK).63 Self-consistent distributions were employed for the calculation of the potential profile with a linear response theory.64,65 PIC simulations of dust pairs helped to elucidate non-linear wake aspects, shadowing in the absorption-induced ion drag force, downstream grain decharging, the importance of ion drag perturbation, and the downstream grain electric force approximation based on the potential structure of the upstream grain alone.66–69 Experimental studies of wake formation should also be mentioned.70–72 

The non-reciprocity of dust–dust interactions in flowing plasmas, known from early works,73,74 has also received scrutiny.75 Action–reaction symmetry is broken, since interactions are mediated by a non-equilibrium medium. Failure to comply with Newton's third law has some important statistical mechanics consequences. Simple idealized models that decompose the interaction to reciprocal and non-reciprocal parts can capture the main physics and have been employed in simulation studies.76,77 Non-reciprocal effective forces have been directly measured.78 

1. Dust in magnetized plasmas

There is an imperative need for semi-empirical analytical expressions that accurately describe the collected plasma fluxes, ion drag force, and dust interaction potential. Indicative of the difficulties are the (doubly) broken spherical symmetry, the addition of the plasma gyroradii to the characteristic length scales, the complexity of the magnetized plasma susceptibilities, and the extended collisional pre-sheath including a cross-field transport mechanism for depleted flux tube replenishment. Linear response theory calculations,79–81 molecular dynamics (MD) simulations,82,83 MC simulations with ad hoc screened potentials,84 and self-consistent PIC simulations85–88 have been reported. Interpolation between analytical limits is advisable. Many lessons can be learnt from the tokamak probe theory.60,89

2. Simultaneous OML violations

In some scenarios, more than one OML applicability condition can be violated. For dust in fusion devices, thin sheath effects are important for ion collection and electron collection can be magnetized, ρ e , λ D r d ρ i .60 Moreover, when considering hot dust embedded in magnetized plasmas, thermionic emission is strongly suppressed by prompt return to the surface in the course of the first Larmor gyration.59,90,91 Furthermore, multiple electron emission mechanisms can be simultaneously active, such as thermionic and potential ion-induced emission or photoelectric and secondary electron emission. A general theory of particle collection is certainly hard, but many quantitative characteristics can be understood by examining the large size limit, for which respective studies are typically available.92–95 

3. Effect of closely packed grains

High dust densities have been known to reduce the dust charge.96,97 Charge cannibalism is mainly not only due to global electron depletion, which can be accounted for via the quasi-neutrality condition, but also due to the sharing of particle fluxes when the mean interparticle distances are smaller than the plasma Debye length.98–100 Even in the absence of plasma flows, the latter close packing effects on the dust–dust interaction potential have only been studied in an overly simplifying manner.101,102 In the presence of ionic flows, PIC simulations of multiple grains have confirmed the decharging of downstream grains due to ion focusing and revealed the dependence of the charge on the specific arrangement.103 Close packing effects should become severe in two frontier topics:104 magnetized dusty plasmas due to elongated collection areas for the magnetized species and binary dusty plasmas due to pure geometrical considerations.

4. Sheath-within-a-sheath

Theory and simulation efforts to study charge and momentum exchange between isolated grains and flowing plasmas generally assume a homogeneous plasma background. However, in nature or in laboratories, dust is often confined in strongly inhomogeneous plasma regions formed near electrodes, containing walls or large objects. Strong modifications are expected when the plasma inhomogeneity length(s) is comparable to the dust shielding length. This has been confirmed in a work that combined an electrostatic sheath theory with a linear response theory in the point charge approximation.105 Self-consistent PIC modeling of dust charging and potential screening, including finite size effects, is highly desirable for many sheath-within-a-sheath scenarios, such as dust levitation in rf discharge sheaths,106,107 dust dynamics in lunar photoelectron dominated sheaths,108–110 dust release in the magnetized sheaths of tokamaks,111,112 and dust measurements by spacecraft.113,114 It is worth to emphasize the particular problem of the detachment of dust residing on the surface of plasma-wetted objects, see, for instance, dust remobilization in tokamaks115,116 or electrostatic dust lofting on the moon117 (see Secs. VIII and XIII, respectively), where the large intervening surface prohibits the electrostatic lensing of plasma particles (with strong consequences on the potential profile and ion drag force) and where adhesive forces are important (typically weakened van der Waals interactions due to the unavoidable surface roughness).118–122 

5. Plasma–dust interface microphysics

A standard dusty plasma idealization concerns the dust interface acting as a perfect absorber. In reality, bound electrons are constantly emitted after electron impact (secondary electron emission),123 ion/neutral impact (kinetic emission),124 or ion neutralization (potential emission),125 while plasma electrons can be inelastically backscattered from the bulk or quasi-elastically reflected from the surface barrier.123 Moreover, plasma ions are continuously backscattered after recombining,126 and the material is chemically or physically sputtered as neutrals.127 Plasma simulation tools model microphysical processes via electron emission or sputtering yields as well as energy/angular distributions of the emitted species.54,128–130 Parameters are externally adopted from reliable experiments or dedicated MC simulations of particle transport in matter.131,132 Such plasma–dust simulations are not truly coupled, since they do not consider the effect of plasma on the dust internal structure with the yields adopted from ultrahigh vacuum experiments or modeling in vacuo. However, particle induced emission is known to be extremely sensitive to surface conditions133 and the plasma-induced dust surface charge layers can modify the yields. Progress in the modeling of electron reflection with the invariant embedding approach has confirmed such expectations.134–136 Energy exchange aspects should be even more sensitive to interface descriptions.137 The future use of semi-classical (MD, MC), quantum Boltzmann, and ab initio (density functional theory, non-equilibrium Green functions) approaches for interface simulations has been discussed,138 but concrete applications are scarce.139 Fully integrated plasma–interface–dust modeling remains an ambition.

6. Non-spherical shape and magneto-dielectric properties

Non-spherical dust studies have been reported.140–144 Non-sphericity gives access to rotational degrees of freedom, which have been argued to be important in various scenarios.145–149 PIC codes able to conform to objects of arbitrary shape can be used for self-consistent modeling.150,151 The impact of electric152 and magnetic moments153 also remains poorly understood.

Modeling dusty discharges is challenging because of the wide range of space and time scales that must be resolved. Given the ratio of the masses of the electrons and a typical 1 μ m diameter dust grain, the difference in time scales is about seven orders of magnitude, covering the dynamics of electrons on the nanosecond timescale to the dust particle dynamics on the millisecond timescale. The charging and interactions of dust grains require the resolution of spatial scales as small as the grain radius on the micrometer or nanometer scale and as large as the size of a centimeter-scale gas discharge. The difference in spatial scales ranges over four to five orders of magnitude. Current methods are being developed to bridge these time and length scales.

Laboratory dusty plasma experiments are often conducted at low pressure conditions in direct current (DC) or radio frequency (RF) discharges, where electron transport is generally non-local in nature. Kinetic plasma modeling, e.g., by solving the Boltzmann equation in a continuum model or tracing individual particle trajectories and collisions with particle-in-cell simulations combined with Monte Carlo treatment of collisions (PIC/MCC), is required to achieve physical accuracy.

DC discharges consist of two spatial regimes. Electrons and ions are accelerated in the large sheath electric field near the cathode, resulting in gas-phase ionization and ion-induced secondary electron emission, driving plasma generation. In the positive column regime, a relatively small electric field drives just enough ionization to compensate for recombination losses occurring at the discharge tube walls. The non-local transport in the cathode region can be modeled using a Monte Carlo simulation of the electrons coupled to a fluid-type model for the ions and combined with the electrostatic field solver154,155 or by solving the two-term Boltzmann equation.156 

As the positive column increases in length, it is likely that instabilities (ionization waves and striations) will develop.157 Hybrid simulations are able to reproduce the experimental observations,158 even in the presence of dust.159,160 The PIC/MCC method161 has been successfully used in more recent studies162 to self-consistently model the whole DC discharge, even in the case of complex gas mixtures.163 

Low-pressure RF discharge plasma or capacitively coupled plasmas (CCPs) drive the ionization of the background gas by the alternating cycles of collapse and expansion of the RF sheaths at both electrodes; the sheath motion periodically accelerates electrons toward the plasma bulk. At high RF power (>100 W) and high driving frequencies (>100 MHz), electromagnetic effects, such as standing waves and the skin effect, can significantly influence the plasma distribution, but in typical dusty plasma experimental systems (13.56 MHz, 1–100 W), the electrostatic approximation is well justified.

Low-pressure CCPs are self-consistently described by advanced fluid models,164–166 solutions of the Boltzmann equation for electron kinetics,167 hybrid schemes,168 and PIC/MCC simulations.169–171 The limitations and the optimization of the PIC/MCC method have also been discussed.172–174 

The charging currents to the dust surface are usually calculated through an orbit motion limited (OML) theory.175,176 The currents are a function of the grain surface potential and plasma parameters, including plasma density and temperature. In regions of a plasma where electric fields are present, the net flow (drift) of ions due to electric fields not only changes the ion current to the grain surface177 but also increases the ion density in a region downstream of the grain. The ion wake is a positive space-charge region that can exert an attractive force on downstream particles,178–180 contributing to the stability of dust structures.181–183 PIC codes have been used to determine the structure of the ion wakefield downstream of a dust grain and to compute the resulting non-linear grain–grain interactions.67,68,184,185 The characteristics of the ion wakefield behind charged dust grains have also been studied using molecular dynamics (MD) simulations of the ions in the plasma flow, treating the electrons as a Boltzmann fluid.82,178,179,183,186 A simplification of the wake structure is to represent the ion wakefield as a point-like region of positive space charge (the wakefield focus) located a fixed distance downstream of the grain.187–189 

Sub-micrometer particles may have a charge of only tens or hundreds of electrons, and the charge fluctuations due to the discrete additions of charge can be a significant fraction of the equilibrium charge.190 The characteristic time scale for these charge fluctuations can be comparable to those of the dynamic processes affecting the dust,191,192 with an asymmetry in the charging and discharging times since electrons (which charge a grain) move on shorter timescales than ions (which discharge a grain).191,193,194

Non-spherical grains have a varying surface potential, complicating the calculation of the equilibrium grain charge and affecting dust dynamics. The distribution of charge over the surface can be modeled by dividing the surface into discrete patches.195–197 Charge collects at the extremities of the surface and aggregate grains tends to collect more charge than a spherical grain due to their increased surface area.196 The non-symmetric charge arrangement can be modeled in dynamics simulations as a monopole plus dipole or more accurately by treating the charge distribution as a set of point charges.198 

To date, no single numerical scheme has been implemented that covers all relevant time and distance scales. Currently, three different regimes are treated by models: resolving electron and ion dynamics to model the gas discharge plasma on timescales up to a microsecond with picosecond resolution; resolving ion and dust motion to model the charging and ion wake on timescales up to a few seconds; and modeling the evolution of an ensemble of dust grains in the plasma on timescales of tens to hundreds of seconds. In the strongly coupled regime, long time scales are needed to capture the dynamics of collective phenomena, such as wave propagation, phase transitions, and instabilities. The loop must be closed to calculate the back reaction of the dust on the plasma. To some extent, this can be done by treating the dust as a fluid,199 although in this case the interaction with ion wakes is not included and the information on self-assembled dust structures is lost. Until now, some kind of simplified approach has been necessary, focusing on a specific phenomenon while being approximate at other scales. Consequently, we identify here three main directions of development in the near future. These are (i) the improvement of gas discharge modeling by implementing realistic gas phase and surface processes and geometries, (ii) the realization of self-consistent multi-scale models by including feedback loops between the individual modules, and (iii) the use of modern techniques, such as machine learning (ML) algorithms and massively parallel computing architectures.

Recent modeling efforts have used a hybrid approach in which the global plasma properties are modeled using a PIC/MCC approach, and the results are used to provide boundary conditions for an MD simulation of particles within a small region of the discharge where dust resides.72,183,200 Extending such models to the timescales necessary to resolve the dust motion remains a challenge, especially for cases where the plasma exhibits instabilities or fluctuations.

Models of low-temperature discharges can be improved by including additional chemical and physical processes. The influence of long-lived (metastable) excited states (in the case of noble gas discharges) and reactive radicals (in molecular gases) on the gas-phase ionization and electron emission at the surfaces is known to be significant, but a self-consistent implementation of the interaction between numerous excited states in discharge simulations is computationally demanding. Collisional-radiative models require the density of ground state species and electrons and the electron energy distribution function as input parameters to compute the distribution of excited states and the transition rates between them.195,201

Models that focus on dust and ion dynamics, treating the electrons as a Boltzmann fluid, can be adapted for discharge conditions with both hot electrons and Maxwellian cold electrons. The presence of hot electrons has a major effect on the dust charge.202,203 However, treating electrons as a Boltzmann fluid misses the important back-reaction of the dust on the electrons. Dust clouds in Plasmakristall-4 (PK-4) facility204 (see also Sec. IX) are dense enough that the electron density can be reduced by a factor of two.160 This electron density reduction becomes very important in understanding the nature of instabilities in the plasma or rapidly changing plasma conditions, such as ionization waves. Dynamic charging and ion wakes are particularly important for studying the waves and instabilities present in a complex plasma.205,206

In laboratory discharges, there are several effects that require modification of the OML currents, such as ion–neutral collisions, ion flow, discrete charging, and irregular grains (see Sec. II). The dust charge can vary significantly depending on where the dust is located in the discharge, whether it is due to variations of the plasma in space (such as the bulk or sheath region),207 or in time (afterglow).208,209

The most fundamental property governing the dynamics of dust in plasma is the dynamical screening of the negative dust grains by the positive ions in the plasma. The ion flow causes the shielding length to vary with position, and in most cases the ion wake is not well represented by a point charge. A goal of current research is to develop a simplified model of the interaction potential between dust grains that accounts for the position-dependent ion wake, which changes in both magnitude and direction as the grains interact with each other (Fig. 1). Both the dust charge and the ion flux, which together determine the wake structure, are functions of plasma parameters, such as neutral gas pressure, electron temperature, and degree of ionization. The gas pressure plays a more important role in determining the dust charge and wake characteristics than the power delivered to the discharge.210 The shape of the grain also influences the wake characteristics.211 

FIG. 1.

Changing ion wake structure in the vicinity of two charged dust grains (white circles). Darker shades indicate higher ion density. The dashed lines mark the contours where the ion density ni is 1.4 times greater than the background ion density n i 0 . Figure produced using the DRIAD code.178 

FIG. 1.

Changing ion wake structure in the vicinity of two charged dust grains (white circles). Darker shades indicate higher ion density. The dashed lines mark the contours where the ion density ni is 1.4 times greater than the background ion density n i 0 . Figure produced using the DRIAD code.178 

Close modal

More complex models require more efficient algorithms and full utilization of computing resources. Over the past decade, the evolution of computer architectures has shifted from accelerating sequential code to implementing parallel execution capabilities. Modern CPUs provide tens of independent execution units, while graphics processors (GPUs) provide thousands of cores for general-purpose computing. Recent efforts in dusty plasma modeling have taken advantage of GPU-accelerated computing to create MD models that can be easily adapted to a range of boundary conditions and plasma states (MAD-BORIS, SARKAS, DRIAD, and OpenDust).82,178,212,213 By covering a large parameter space, the results can be analyzed using ML techniques to develop heuristic models of the detailed microphysics that can be incorporated into the simulation of macroscopic systems.

The application of ML techniques, mostly based on neural network models, is in its infant stage in relation to gas discharge and dusty plasma modeling. Current studies include the non-linear response analysis for dust particles to determine the equation of motion and, thus, the effective grain–grain interaction,214 and the improvement of dust particle detection in noisy environments.215 Certainly, with the rapid advancement of this technique, it bears a great potential for the prediction of various plasma properties.

Before turning to the topic addressed in the title, it is necessary to clarify its meaning since the term “diagnostics of dusty gas discharge” may be understood in different ways.

The first meaning of diagnostics of dusty gas discharges relates to the measurement of parameters, such as, e.g., electron density or electron temperature in plasmas containing nanoparticles. In this context, the question arises to what extent the presence of nanoparticles affects the performance or interpretation of standard diagnostics, such as Langmuir probes216,217 or laser absorption spectrometry (LAS).218 Such methods will probably work the common way as long as the dust concentration in the plasma is low. The Havnes parameter219, P is an appropriate order parameter for this decision. P 1 describes a “dust in plasma” situation where the dust component has almost no global impact on the plasma, whereas P > 1 is a dusty plasma situation, where a strong electron depletion ( n e < n i ) is in effect (see Ref. 220 for details).

The second meaning of diagnostics of dusty gas discharges concerns the use or development of diagnostic methods that can be used in plasmas in general, but which are of particular interest for the understanding or the control of phenomena occurring in particle-containing plasmas. One example here is the measurement of negative ions, which are believed to play an important role in the formation of nanoparticles in discharges operated with organic monomers.221,222 As most of the dusty plasmas which have technological relevancy are nanodusty plasmas, which contain particles from 100 nm down to a few nanometers, the particle properties (as size, refractive index, crystalinity, etc.) are a priori not known since the particles are produced inside of the plasma.

This leads us to the third meaning of diagnostics of dusty gas discharges. It refers to the diagnostics of the particles themselves, as the detailed knowledge of the particle size, shape, and density are the key parameters for the diagnostic of dusty plasmas. The characterization of the particles will be the focus of this paper. In this context, the term diagnostics covers a variety of different techniques and methods, each of which is used to investigate different particle properties. One further remark that should be briefly made concerns the fact that the diagnostics that will be mentioned here will mostly be in situ diagnostics applied to particles that are inside the plasma.

In principle, different particle diagnostics can be—for the sake of simplicity—divided into two main categories: indirect and direct diagnostics.

1. Indirect measurements

The indirect detection methods are based on the fact that the presence of dust particles in a plasma induces changes in the plasma characteristics. This response of the plasma to the formation of particles can be used as a simple and sensitive kind of global diagnostic that delivers information about the existence of particles in the discharge. Several effects can be used here for diagnostic purpose: the change in light emitted by the discharge, the reduction in electron density caused by the attachment of electrons to the particles, and the change in ion currents. Other examples concern the change in “electrical properties” that occur in some RF discharges, such as the DC bias voltage,223,224 the phase angle between voltage and current, or the anharmonicity of the wave-forms of RF current and voltage.225 

2. Direct measurements

Most of the direct measurements are based on the interaction of nanoparticles with electromagnetic radiation where the latter can range from the x-ray region to the (far) infrared. Depending on the particle properties to be investigated, there are different types of diagnostics, e.g.,

Laser scattering imaging:226 The video analysis of dust ensembles is the working horse of dusty plasma physics with micrometer sized dust particles. The basis of this technique is a 2d laser stripe which enables the video analysis of 2d cross sections of 3D dust clouds.

  • Computed tomography:227,228 The 3D dust distribution of arbitrarily shaped dust clouds is determined by a combination of 2d extinction measurements and computed tomography.

Information about the particle size (and depending on the method, also about the refraction index of the particles) can be obtained by

  • Light extinction spectrometry229 

  • White light scattering230 

  • Kinetic Mie polarimetry without231,232 and with imaging properties233 

  • Laser-induced incandescence (LII).234 

Information about the elemental composition of particles, respectively, their bonding situation can be acquired by

  • Laser induced particle explosive evaporation235 

  • Infrared absorption spectroscopy236–238 

  • X-ray scattering techniques.239 

Information about particle charge can be gained by

  • Infrared phonon resonance shift (IRPRS)240 

  • Laser-induced electron detachment.241 

Absolute densities of precursor molecules inside of the nanodusty plasma are measured with

  • Frequency modulation spectroscopy.242,243

Again, this list including the cited literature is not exhaustive, and it must be emphasized that these diagnostic methods (in contrast to the aforementioned indirect techniques) were not developed specifically for the study of dusty plasmas, but are more general tools often used in fields, such as aerosol research. (In the literature cited here, we limit ourselves to cases in which these diagnostics were used in the study of dusty plasmas.) There are some important in situ diagnostics that are not based on the interaction of light with nanoparticles:

  • Mass spectrometry244 

  • Multi-mode microwave cavity resonance spectroscopy245 

  • Dust density wave diagnostic (DDW-D).220,246

Of course, the current knowledge about the physics of dusty plasmas relies on the interplay of experimental investigation, modeling, and simulation. Simulations are challenging, however, because the dust has a highly variable charge. Even for particles with a radius of 100 nm, the charge can vary from zero to more than 1000 elementary charges at a given time within the same discharge system. Simulations and consequently the diagnostic of such plasmas247,248 have to take into account the coupled physics of the plasma discharge, the plasma chemistry,249 the “aerosol” physics of the charged dust, and the plasma related details of particle growth processes.180 

The question of which diagnostics should be developed further or deserve more attention depends heavily on the intended applications or the specific research one is aiming for. In the field of complex plasma research, particles with known properties are very often injected into the discharge and it is studied, for example, how individual particles or collections of particles form certain time-dependent structures. In this area of research, there is obviously no need for diagnostics that provide information about the properties of the particles. Instead, tomographic methods are needed that provide precise, time-resolved information about the locations of a large number of individual particles.

In research areas dealing with the formation of particles, which are particularly important for applications, the situation is quite different. The diagnostic challenges are clear from Fig. 2, which provides a simple illustration of nanoparticle formation in (reactive) plasmas. The figure shows the different phases of the particle growth chain from molecular precursors to micrometer-sized particles and the transitions between the different phases. Regardless of the exact details of this process, which may vary depending on the precursors used (e.g., acetylene, methane, silane, HMDSO, and other gases or vapors), the simple schematic illustrates the need for diagnostics that can detect different types of species: from molecules to macromolecules to clusters (charged and neutral) and finally to particles at the nanometer or micrometer scale.

FIG. 2.

Growth chain of nanoparticles in a low-pressure discharge in argon with acetylene admixture. The different phases of particle growth are strongly related to the specific conditions of the plasma and its interaction with the precursors, clusters, and nanoparticles (based on Ref. 250). The lower graph shows the angle-dependent light scattering of red, green, and blue light of a spherical particle with a refractive index of N = 1.84 + 0.07 i (typical refractive index of a:C–H particles) at radii of 0.17, 1, 50, and 100 nm. The intensity for each radius is normalized to its maximum intensity. The Mie-code from Bohren and Huffman251 in Mätzlers implementation252 was used.

FIG. 2.

Growth chain of nanoparticles in a low-pressure discharge in argon with acetylene admixture. The different phases of particle growth are strongly related to the specific conditions of the plasma and its interaction with the precursors, clusters, and nanoparticles (based on Ref. 250). The lower graph shows the angle-dependent light scattering of red, green, and blue light of a spherical particle with a refractive index of N = 1.84 + 0.07 i (typical refractive index of a:C–H particles) at radii of 0.17, 1, 50, and 100 nm. The intensity for each radius is normalized to its maximum intensity. The Mie-code from Bohren and Huffman251 in Mätzlers implementation252 was used.

Close modal

In addition to these requirements, the diagnostics used to monitor particle formation must be able to detect processes that can involve time scales ranging from less than a millisecond to several hours. The need for time-resolved diagnostics arises not only from the different time scales inherent in the process but also from the large technological potential of pulsed discharges,253 which automatically involve new and often small time scales. In addition, information about the spatial distribution of particles is of great importance, especially for technical processes where, for example, the contamination of certain components must be avoided. This underscores the need to develop imaging techniques that can directly provide such detailed spatial information.

It is unlikely that any single diagnostic will be able to fulfill this task. The future task, therefore, is rather to employ several different (in situ) diagnostics in such a way that their combination can help to provide a more complete picture of the entire process. One of the biggest challenges (and one of the biggest needs) here is certainly the spatially and temporally resolved detection of clusters in the sub-nanometer to the nanometer range. Therefore, adapting existing techniques, such as coherent Rayleigh–Brillouin scattering,254 to technically relevant plasma environments is a high priority for the future.

Another important parameter that has to be addressed in more detail in the future is time dependent surface temperature of growing nanoparticles (see also Sec. VII). In particular, for processes, such as, e.g., the deposition of ultra-thin films or the fabrication of nano-composite materials, it is also highly desirable to obtain information on the surfaces exposed to the species flows emerging from the plasma. Especially the contribution of large (potentially charged) macromolecules or clusters to the growth of such systems is of great interest in this context. Only the combination of in situ (surface) diagnostics such as GISAX255 and TEM, plasma diagnostics such as mass spectrometry (that measures the flux of species), and diagnostics that provide information on the growth of clusters in the plasma volume will provide sufficient information to understand the whole process. However, the simultaneous use of different types of diagnostics is extremely time-consuming and both labor- and cost-intensive. Therefore, it is of great importance in the future to offer simpler alternatives, especially for mere users of dusty plasmas. These alternatives may not be able to draw a complete picture of the entire process but allow easy process control and optimization.

The aforementioned indirect diagnostics may offer such an alternative since they are easy to employ and relatively cheap. However, they initially provide only quite limited information about the complicated processes in dusty plasmas. The combination of sophisticated diagnostics and new modeling efforts may resolve this dilemma. Such an effort could lead to new insight that would allow a better interpretation of the signals resulting from indirect measurements. This is, in particular, important for the control of particle growth in reactive plasmas. Simultaneous time-resolved measurements of multiple quantities, such as (total) light emission or DC self-bias, could help to monitor the different phases of particle growth (see Fig. 2) with relatively simple diagnostic tools and greater accuracy. The use of diagnostics that provide (time resolved) signals with a high signal-to-noise ratio would facilitate the extraction of useful information from the acquired data.

However, the collection of large amounts of data associated with such measurements presents new challenges and opportunities. A concerted effort of experimental and theoretical investigations in combination with new techniques such as ML may help to understand, control, and especially predict the basic processes of the dust growth across all phases shown in Fig. 1. This is important for processes where the formation of particles needs to be suppressed as well as for processes where one wants to “harvest” nanoparticles or nanoclusters with a certain size.

Dust immersed in gas-discharge plasmas or grown in gas-discharge plasmas modifies the plasma properties.2 This modification is the result of four different physical mechanisms: Dust particles (i) absorb the fluxes of plasma species on their surfaces; (ii) non-negligibly contribute to the formation of electric fields; (iii) are sensitive to fluxes and temperature gradients in charged as well as neutral components of the plasma; and (iv) due to their low charge-to-mass ratio, exhibit significantly slower dynamics compared to those of other plasma components. Presence of dust, therefore, leads, in many cases, to the appearance of “new” dust-induced phenomena that do not exist in dust-free plasmas and, moreover, disturb its calmness and uniformity which is desired for technological applications and microgravity experiments. In the following, we will present the current status of understanding of these phenomena and highlight the possible future directions of their investigation and control.

Dust acoustic wave (DAW) or dust-density wave instability revealing itself as a compressional wave pattern propagating along the local electric field is one of the most ubiquitous instabilities in dusty plasmas. It was observed in practically all types of discharges, dc,256,257 inductively coupled rf,258,259 and capacitively coupled rf,260 under laboratory261 and microgravity262,263 conditions, with injected microparticles264 and grown dust.265 Lots of works are devoted to the details of its theory.258,260,266–274 This instability is understood as a streaming instability, caused by ions drifting through the dust suspension confined in a plasma. It was shown to cause coagulation of dust particles.275,276 It is also used for diagnostics of electric field and dust charge in nanodusty plasmas.246,277

Different instabilities were observed during growth of dust particles in reactive rf discharges of different chemistry. For example, when growing dust by sputtering graphite278,279 or plastic microspheres lying on the bottom electrode of the discharge,280–283 the electrical and optical characteristics of the discharge started to exhibit instabilities which stopped only when dust particle size reached fractions of a micrometer. During the first dust growth in silane chemistry,284,285 the instability was associated with the agglomeration of the very first nanoclusters. However, in the further dust growth cycles with uninterrupted silane supply,286 the instability became continuous as in the case of sputtering experiments. Other plasma instabilities triggered by the growth of dust particles cause the appearance of numerous regions of bright plasma emission of spheroidal shape (of mm sizes) which appear in the close vicinity of the electrodes287 and sometimes rotate288 as in the carousel instability.289 In fully developed instabilities, these spheroids are also present in the bulk plasma where they can merge or split.290 The nature of these spheroids is not clear but they could be small dust-free regions where an enhanced emission takes place.

Operation of PK-4 facility on the International Space Station204 (see also Sec. IX) revealed three specific dust-induced instabilities in the dc discharge: “dust-induced stratification,”2,160 “transverse instability,”291 and “partitioning of the dust suspension.”2,292 The last two instabilities observed in the polarity-switched discharge (which represents the main working regime of PK-4) significantly limited the parameter range in which calm and uniform dust suspensions could exist. No reliable explanation proven by systematic experiments exists for both instabilities.

The problem of void, usually an eye-shaped (sometimes more complicated shapes are observed293–295) dust-free region in the center of a discharge,278,296,297 seemed to be closed for rf plasmas since the microgravity experiments on void closure in PK-3 Plus laboratory298 and numerous simulations.299–304 The void was supposed to occur due to the mechanical balance of ion drag force (due to the outward drift of ions) and electrostatic force exerted by the ambipolar electric field confining the dust in the plasma. However, comparison of experimental and simulated plasma emission patterns and dust distributions305 as well as very recent discovery of dim and bright void regimes306 (Fig. 3) have questioned the universality of that simple and widely accepted concept. Earlier observations of void size increase on the increase in dust particle size in reactive plasmas307 also suggest dim-to-bright-void transition during dust growth.

FIG. 3.

Dim-to-bright void transition on the increase in the RF discharge power. Reproduced with permission from Pikalev et al., Plasma Sources Sci. Technol. 30, 035014 (2021). Copyright 2021 IOP Publishing Ltd.

FIG. 3.

Dim-to-bright void transition on the increase in the RF discharge power. Reproduced with permission from Pikalev et al., Plasma Sources Sci. Technol. 30, 035014 (2021). Copyright 2021 IOP Publishing Ltd.

Close modal

Closely related to the void problem is the problem of the so-called “heartbeat” instability.308–316 It appears in dusty rf discharges as periodic contraction of the void with (sometimes very) low frequency. A bright flash of plasma emission precedes the contraction of the void.312 Careful investigations313 have shown that the heartbeat instability is a mixed-mode oscillation in which rare catastrophic void contractions are mixed with small breathing oscillations of the void boundary.316 Not only dust component, but the entire plasma exhibits this mixed-mode behavior. At a fixed amount of dust in the discharge, the instability was shown to occur in a certain range of discharge power and neutral gas pressures.315 Discovery of dim and bright void regimes led to the hypothesis that the heartbeat instability is nothing but a self-excited oscillation between these two regimes. This hypothesis, however, still leaves many open questions on the mechanisms that could lead to such an oscillation.

Dust-induced phenomena in gas discharges are rarely so local that they can be explained by local effects of dust only.2 Usually, the entire discharge including its optical and electrical characteristics is modified by presence of dust. Therefore, progress in understanding the dust-induced phenomena in gas discharges can only be achieved with the improvement of basic understanding of the physics of dusty gas discharges.

Generalization of scattered experimental and simulation results led to the formulation of a heuristic concept of the formation of dusty discharges which connects mechanical balance of dust particles with the ionization balance in the plasma. According to this concept, in the presence of only ion drag and electrostatic forces acting on dust particles, there are two principles according to which the dusty discharges form: (i) At relatively low discharge powers, the ion densities are so small that the mechanical balance can only be achieved if local ambipolar electric field vanishes; the ionization balance then localizes due to the absorption of plasma species on the surface of dust particles; (ii) at relatively high discharge powers, the mechanical balance of dust particles can be achieved at a finite value of the ambipolar electric field, and the ionization balance then stays non-local as in a dust-free discharge.

Systematic theoretical and simulation work is required not only to give this concept more solid grounds but rather to understand how the transition between the two formation principles occurs. Nowadays, dim and bright void regimes as well as the heartbeat instability are supposed to represent manifestations of these two principles and of a dynamic transition between them, respectively.2,306,316 More detailed understanding of the connection between the mechanical and ionization balance in dusty plasmas could lead to further progress in understanding of other dust-induced phenomena.317–320 In addition to this, on the experimental side, improvement of plasma diagnostics is required. In particular, optical measurements of electric fields in the range of 0.1 1  V cm−1 would make the observation of the above mentioned transition possible. Such measurements are usually performed at low neutral gas pressures ( 0.1  Pa) using laser-induced fluorescence (LIF) technique321,322 on ions. Extension of this technique to higher neutral gas pressures could help to improve the understanding of the connection between mechanical balance of dust particles and ionization balance.

Very recently, experiments in the PK-4 facility revealed an abnormally fast compressional wave mode in dusty plasmas.323 This mode was treated as an ionization wave in dusty plasmas where the ionization balance is localized due to absorption of plasma species on the surfaces of dust particles.323,324 Although, it is still unclear whether the ionization effects play a role in this particular case,325,326 their role in the propagation of compressional waves in dusty plasmas should be clarified.

First-principles simulations of dusty gas discharges represent a difficult problem due to the enormously large difference in the charge-to-mass ratio between electrons and dust particles (see Sec. III). New approaches have to be sought to either speed-up the calculations or to simplify the models while keeping all the essential physics inside. For complicated phenomena (like, e.g., heartbeat instability), development of phenomenological mathematical models or adaptation of such models from other fields would already represent a large step forward.313 

Real-time diagnostics capable of measuring temporal evolution of dust particle density and size at a nanometer scale233 (see Sec. IV) have to be further developed in order to describe the coupling between dust particle properties and the plasma behavior. This improvement would lead to progress in understanding the particle-growth instabilities.

It would be also very interesting to implement the feedback control of the instabilities in dusty plasmas in analogy to what is done for, e.g., instabilities in electronegative plasmas.327 It is a promising method for limiting the impact of instabilities on plasma processing or basic plasma experiments requiring calm conditions.

Apart from purely academic importance, the issues described above are vital for the improvement of the design of (quite expensive) microgravity complex plasma experiments as well as for the improvement of the quality of interpretation of their results. Knowledge gained about the dust-induced phenomena in gas discharges should be used to design the experimental hardware in such a way that the dust suspensions remain uniform and calm in the widest possible parameter range. This is especially important for project COMPACT328 (Sec. IX) which is at the moment in the feasibility study phase.

Laboratory complex plasmas containing injected well-characterized spherical micro-particles amenable for optical tracking are an ideal experimental test system to analyze correlation effects in macroscopic or mesoscopic many-particle systems.329–331 The attractive feature of complex plasmas is the mesoscopic size of the suspended dust grains and the comparatively large inter-particle distances (of the order of 100 μ m), which enables direct optical imaging of crystal or fluid-like states of grain collective behavior. In addition, the dynamical time scales associated with the dust grains, of the order of tens of milliseconds, allow the accurate resolution of the dynamics of a system of particles with the use of fairly unsophisticated high speed video cameras. Direct visual tracking is not possible in other strongly correlated systems, such as electrons in solids or nuclear matter. Complex plasmas are complementary to other experimental model systems used in soft matter physics, such as colloids and granular media.332 

Complex plasmas are an ideal test bed for understanding strong coupling phenomena. Indeed, complex plasma experiments allow the detailed kinematic resolution of elementary collision processes at mesoscopic ( r 10 μ m to mm) length scales that mimic the atomic level of ordinary matter in a purely classical context. With nominal dust particle charge magnitudes in the range Z p 10 2 e , , 10 4 e , where e is the elementary charge, the Coulombic interaction between highly charged microparticles decaying as r 1 ensures a strong coupling (as measured by the coupling parameter Γ Z p 2 e 2 / ( 4 π ϵ 0 n p 1 / 3 m p v p 2 / 2 ) at experimentally easily attainable dust grain concentrations ( n p 10 4 , , 10 6  cm−3) and nominal mean microparticle kinetic energies ( m p v p 2 / 2 ) / k B 10 2 , , 10 3  K. This is a major advantage compared to other strongly coupled systems, such as ion or electron one-component plasmas (OCPs), which attain strong coupling behavior only at extremely high number densities (in that case, Zp = 1, and densities exceeding solid state density) or ultracold temperatures ( 1 mK, , 10  K).330 Thus, complex plasmas are ideal model systems to analyze strong coupling effects in classical OCPs. However, unlike ion/electron OCPs, microparticle motion in a strongly coupled complex plasma is under-damped due to dissipative dust–neutral collisions.333,334 Collisions can also non-trivially modify the microparticle charge.14,17,25,335–337 Flows of ions can also induce an ion drag force on the microparticles.25,38,45,46,260 Finally, due to the presence of the background plasma, interactions are not purely Coulomb but, in a first approximation, follow a screened-Coulomb (Yukawa) interaction with a typical screening length given by the plasma Debye length.338–340 Other forces can also act on the microparticles depending on specific experiments (thermophoresis, laser forces, etc.).340 In a microparticle suspension trapped in a gas discharge, the microparticles gain kinetic energy through electrostatic interactions. This energy is dissipated by the neutral gas medium, effectively cooling down the microparticle suspension and allowing for strong coupling between the particles.341,342 The gas pressure is, therefore, an important control parameter in complex plasma experiments for studying strongly coupled system behavior in under-damped regimes with particle level kinematic resolution.

A phase diagram of complex plasma states of matter in two dimensions343 and three dimensions344 allowed to identify the coupling regime of the different phases resolved experimentally on the single-particle level: the Coulombic gas ( Γ 1 ), liquid complex plasma ( 1 < Γ < Γ m , Γ m is the melting/freezing point in Γ-space; Γ 1 being a measure of grain kinetic temperature), and solid phases ( Γ > Γ m ). Strongly coupled systems of microparticles have allowed the study of collective phenomena, such as waves,259,345–348 phase transitions,342,349–351 energy transport,349 viscous352 and visco-elastic353 dissipation, and crystal lattices,347,354–357 behaving as classical analogues of real matter. Complex plasmas also offer the possibility of studying pseudo-attractive interaction of like-charged microparticles. When the microparticles are located in regions of ion flow in the plasma, ion wakes are formed downstream of each particle,358–360 leading to non-reciprocal attractive forces between dust particles. In two-dimensional complex plasma crystals, these ion wakes, under specific conditions, can trigger the mode coupling instability during which energy is transferred from the ion flow to the microparticle monolayer.181,206,361 Such systems can be used as model system to study flame propagation in 2D solids362 and impulsive spot heating in ordinary reactive matter.363 

Laboratory studies of complex plasmas can also be used to study the action of very strong magnetic fields on charged particles,364–366 which is particularly important to understand the dynamics of dust particles, for example, in nuclear fusion devices367 (Sec. VIII) and astrophysical environments368 (Sec. XIII). A key question relevant to both, the dusty/complex plasma and the fusion plasma communities, is the effect of magnetic field on the dynamics of the plasma and the dust. However, the sensitivity of charged particles to magnetic fields is low due to the very low charge-to-mass ratio of dust particles. While electrons and ions are considered to be magnetized for relatively low magnetic fields ( 5 and 100 mT, respectively), very strong magnetic fields (>1 T) are needed to magnetize the dust particles. However, at high magnetic fields, the gas discharge plasma in which the experiments are performed (typically capacitively coupled radio frequency discharges) can become inhomogeneous (due to phenomena such as filamentation364,369) consequently destroying the dust particle cloud homogeneity as well or even imposing circulation patterns.370 The plasma filamentation phenomenon is generally observed at low pressures ( 20  Pa), such as studies of propagating waves. In addition, in most reported experiments, to date, the applied magnetic field was not large enough to magnetize the dust component but only the background ions and electrons.366 These experiments have, nevertheless, allowed one to improve our understanding of the dust charging process,371,372 ion wake formation,373,374 dust density waves, etc.375,376 However, even if experiments with real magnetic fields are limited to a few Tesla,364–366 a quasi-magnetic field can be produced by setting a microparticle suspension in a plasma in rotation and using the formal equivalence of the Coriolis force to the Lorentz force as proposed by Kählert et al.377,378 It allows one to reach effective magnetic fields of up to 3000 T for the microparticles (whereas electrons and ions are almost unaffected) and successfully demonstrated to accurately reproduce the collective modes379 and transport properties, such as diffusion coefficient in magnetized plasmas380 otherwise inaccessible in standard experiments using real magnetic fields.

Complex plasmas offer opportunities for foundational discoveries both at the level of a single microparticle (particle level) and at the length scale of the microparticles as a population (particle phase level).

1. Particle level transport processes

A complex plasma can be viewed as a collection of microparticles that are exchanging mass, momentum, energy, and in some cases, chemical species with the plasma that consists of ions, electrons, neutral gas molecules, photons, and electric fields. Coupled transport processes that take place on the surface of a single microparticle, such as charging, ion drag, heating, aggregation, or radiation (see Sec. II), are of interest to the fusion community in understanding plasma–wall interactions.55 The same processes are also of interest to the materials synthesis and processing communities381 (see Sec. VII). Especially, the contribution of dust to the overall energy balance in fusion reactors is important to understand and ensure that it does not significantly hinder energy production. For instance, a reliable technique to infer the particle's surface temperature is not available at the moment (see Sec. IV) even though many studies have discovered that the particle temperature can far exceed that of the background gas,382 being still well below the electron temperature. On the other hand, particles can also be used as probes to understand the local plasma conditions. Their dynamics, a result of the charge and net force exerted by the local environment, can be used as a diagnostic.186 Further work is necessary in this area to develop reliable diagnostic tools of microparticle parameters, such as surface temperature, charge, and surface reaction rates, to name a few to understand local plasma conditions. Finally, light scattering can also be used to infer local discharge properties.383–386 Scattering by both single microparticles and their suspensions can be done by varying the wavelength of the incident light to extract structure factors that contain information about the particle's local geometry that scatters light. Finally, superconducting grains levitating in superfluid helium can be used as a sensitive probe for collective quantum effects in and out of equilibrium.387 

2. Particle phase level behavior

The ability to resolve single particle dynamics when combined with advanced machine learning and deep learning algorithms388 can potentially unravel the interactions between microparticles that have remained an open question for long due to difficulties in completely characterizing the gas discharge conditions using probe as well as non-invasive measurements. Specifically, the effect of ion wakes, ion flows, and the effect of externally applied magnetic fields can be holistically approached by taking advantage of the particle-level resolution offered by complex plasmas. The key challenge is that the recorded microparticle trajectories are the result of physics intrinsic to the plasma itself as well as the physics that one is trying to understand by deliberately introduced perturbations. While the kinetic resolution of particle motion is certainly exciting, it becomes expensive to obtain large system sizes (number of microparticles) that can realistically mimic the behavior of continuous media. Recent developments that use large electrodes (for instance, 85 cm diameter electrodes as part of the large diameter RF complex plasma device at DLR389) and the ability to engineer dust–dust and dust–ion potential interactions by adjusting the gas discharge parameters are some of the approaches taken to use complex plasmas for studying important condensed matter effects. The most challenging aspect is the isolation of specific plasma effects from the collective phenomenon being studied. Wherever that is not trivial, modeling must be used to deconvolute the two efforts to draw inferences about strong coupling phenomena.

Chemically reactive non-thermal plasmas have a propensity to nucleate and grow nanoparticles. While this was first identified as a contamination problem in semiconductor processing by Selwyn and co-workers,390,391 more recently non-thermal dusty plasmas have gained significant attention for the growth of functional nanoparticles.381 For nanoparticle synthesis, several attributes uniquely differentiate dusty plasmas from other synthetic routes, such as colloidal solutions or flames.

Nanoparticle charge

As in other dusty plasma situations, nanoparticles in plasmas are generally negatively charged, even though their charge may fluctuate and particles may temporarily become neutral for very small particles with only a few nanometers in diameter.392 Due to their unipolar negative charge, nanoparticles mutually repel each other, which strongly suppresses or eliminates particle agglomeration,393 that is, a problem for other gas phase syntheses.

Nanoparticle heating

Nanoparticles in plasmas experience intense exothermic surface reactions, such as electron–ion recombination, reaction with chemical radicals, or recombination of hydrogen atoms and other species. These reactions can release large amounts of energy that, on a per atom basis, significantly exceed the atomic kinetic energy at the gas temperature. Accordingly, nanoparticles in plasmas can temporarily reach temperatures that exceed the gas temperature by several hundreds of Kelvin, which explains the capability of non-thermal dusty plasmas to create crystalline nanoparticles of materials with very high melting points, such as silicon,394 titanium nitride,395 graphite/graphene, and alumina.396 

Size control

Non-thermal dusty plasmas offer excellent size control for the nanoparticles grown. In most cases, the nanoparticle size is linearly correlated with the residence time of particles in the plasma.

Green chemistry

Non-thermal plasmas, already considered a green technology in some countries when operated with renewable electricity, can be a fully carbon-free synthesis that does not require solvents or wet chemical processes, thus potentially reducing toxicity and waste.

Interest in the use of non-thermal dusty plasmas for the synthesis of functional nanocrystals initially focused on silicon for use in novel electronic and optical devices.397,398 Effective dusty plasma synthesis techniques were developed both at low pressure394 and atmospheric pressure.399 In subsequent years, dusty plasma synthesis of nanoparticles was extended to a wide range of materials, including carbon based materials, metal oxides, sulfides, nitrides, and elemental metals as well as alloys. The state of the art until about 2016 has been summarized in several review papers.381,400

Since then, important progress has been made in multiple areas. Doping of semiconductor nanocrystals had long been a challenge.401 Hence, the successful synthesis of doped silicon nanocrystals demonstrated this exciting capability of dusty plasmas402,403 and opened the door to new device applications, such as thermoelectric materials. It is believed that the non-equilibrium nature of a dusty plasma may favor kinetic control of nanoparticle growth and may enable structures that deviate from thermodynamic equilibrium. For example, hyperdoping of silicon beyond the thermodynamic solid solubility limit was demonstrated with dusty plasma synthesis.404 These hyperdoped nanocrystals exhibited exciting new properties, such as near-infrared plasmomic resonances.405 Moreover, co-doping with both boron acceptors and phosphorous donors enabled near-infrared emission.406 

Nanoparticles in non-equilibrium plasmas can vaporize despite the low background gas temperature. This phenomenon is the basis for a synthesis aerotaxy, in which at least one of the precursor streams is comprised of an aerosol. To date, vaporization has been observed with relatively soft elements, such as Bi,407 Ga,408 In,409 Sb,410 and Zn. Vaporization can result in interesting physical modifications of the nanoparticle population, such as size focusing.407 Furthermore, the vapor can chemically react in the plasma to synthesize condensed phase compounds, including the III–V semiconductors GaN,408 GaSb,410 and InN.409 

Particle trapping in dusty plasmas containing micrometer or sub micrometer particles has been known for a long time390,391,411 and been associated with the periodical growth behavior observed in some dusty plasmas.412 However, in the synthesis of sub-10 nm particles in widely used laminar flow reactors, Fig. 4(a), the possibility of particle trapping had long been ignored, because sub-10 nm particles can be neutral for a large fraction of time and the particle size was found to be linearly related to the gas residence time in the reactor, suggesting a continuous transit of particles through the reaction [Fig. 4(b)]. Only recently, researchers realized the importance of particle trapping in laminar flow reactors. Xiong et al.413 demonstrated that temporary electrostatic trapping of nanoparticles during their growth, typically close to the RF electrodes, leads to size filtering that enables very monodisperse size distributions [Fig. 4(c)]: small particles are electrostatically trapped and continue to grow until they reach a threshold size at which the gas drag force will overcome the electrostatic trapping force, leading to very monodispersed particles. The improved understanding of particle trapping was exploited in the synthesis of highly monodisperse silicon optically Mie-resonant particles with diameters between 60 and 220 nm, with standard deviations of the size distribution of less than 5% of the average size.414 A better understanding of temporary particle trapping during the synthesis of functional nanomaterials is required and will lead to increased control of the process as well as the ability to synthesize entirely new classes of materials, such as core–shell nanoparticles. To fully harness, the benefits of temporary particle trapping will require a better understanding of particle charging and its dependence on nanoparticle materials properties. Nanoparticle trapping may be further augmented by pulsed power operation. By intermittently turning off the plasma, particles may be released from the trap, only to be pulled back into it when the plasma is reignited. This may be utilized to creatively affect the size distribution of nanoparticles as they grow.415,416 Pulsing was also successfully used to either induce or suppress dust particle formation and growth,253,393 leading to the introduction of a critical frequency dependent on precursor presence. Control of nanoparticle growth via pulsing is still a new field with significant need to explore the relevant mechanisms in terms of the typical timescales for gas flow, particle charging, and trapping.

FIG. 4.

Schematic of temporary particle trapping in laminar flow reactor (a). (b) Traditional view: plug flow reactor. (c) Temporary trapping until particles grow to critical size. Adapted with permission from Xiong et al., J. Phys. D: Appl. Phys. 55, 235202 (2022). Copyright 2022 IOP Publishing Ltd.

FIG. 4.

Schematic of temporary particle trapping in laminar flow reactor (a). (b) Traditional view: plug flow reactor. (c) Temporary trapping until particles grow to critical size. Adapted with permission from Xiong et al., J. Phys. D: Appl. Phys. 55, 235202 (2022). Copyright 2022 IOP Publishing Ltd.

Close modal

The heating of nanoparticles in plasmas remains another topic that requires further investigation. Estimates of nanoparticle temperature in non-equilibrium plasmas have been primarily made by model calculations. Some experiments have been performed wherein these calculations were related to crystallization temperatures for materials.396,417 Unfortunately, crystallization temperatures are not well-defined quantities. Furthermore, whether nanoparticle heating can explain the observed vaporization in aerotaxy, or not, depends on the selection of a heating model and choice of the empirical accommodation coefficients. This results in significant uncertainty in the magnitude of the excess temperature, which is the main obstacle to understanding the aerotaxy mechanism. Widely applicable direct measurements of nanoparticle temperature in non-equilibrium dusty plasmas would be a significant breakthrough. Fluorescence decay thermometry may be a viable route to measure nanoparticle temperatures in dusty plasmas. Recently, there has been great success using fluorescence decay thermometry to characterize background gas temperatures in non-equilibrium plasmas.418–420 The probe, which was inserted into the plasma, consisted of a photoluminescent crystal that has a temperature-dependent emission lifetime. The photoluminescence lifetime is on the millisecond timescale, which allows for relatively straightforward measurements. For example, Cr3+-doped Al2O3 (ruby) exhibits a sharp emission line at 695 nm that has a temperature-dependent lifetime in the range of 0.01–10 ms for the temperature range of 900–300 K.421,422 In the future, this technique could be translated to nanocrystals comprised of Cr3+-doped Al2O3 (i.e., nanorubies) that would be aerosolized and introduced to the plasma, wherein their PL lifetime could be measured and related to the particle temperature in the plasma. Compared to the early work,423 this technique could be adapted to flow-through reactors, much higher particle temperatures, and sub-10 nm particles.

Carbon materials, including carbon nanotubes, graphene, nanodiamonds, carbon-based quantum dots, and even the polymer nanoparticles, are a continued area of interest. Dusty plasmas can obviate the need of catalysts that exists for other synthesis methods. One interesting example is the non-catalytic growth of graphene nanoflakes by Tatarova et al.424 Especially in biomedical applications, such as theranostics,425 it is crucial to endow the surfaces of these materials (such as nanoparticles or flakes) with specific chemical functionalities. The negative charging of nanoparticles in plasmas causes these units not coagulate into larger units. Combining plasma synthesis with subsequent plasma-assisted functionalization could provide a path toward large-scale production of nanomaterials with tailored surface functions. Aside from one step functionalization based on comixing of precursors with gases, such as NH3 or N2,425,426 possible ways include the introduction of functional groups by evaporation of liquid precursors. Liquid precursor introduction also enables the production and surface functionalization of plasma polymer nanoparticles, such as polyaniline427 as a conductive polymer, important, for example, as absorber for microwaves or for molecular electronics. Other intriguing areas include dusty plasmas that contain or generate carbon or oxides as well as multimaterial particles, such as Janus particles, metal-organic frameworks (MOFs), MoS2/carbon, and similar materials, which are crucial for applications in renewable energy, including batteries, fuel cells, hydrogen production, and storage. Additionally, nanoparticle deposition onto surfaces may contribute to the development of biomimetic surfaces, improved adhesion, electronic materials, and quantum dots for diagnostics tools. For example, Marvi et al.428 used photoluminescent semiconductor quantum dots as a plasma–surface diagnostic for nanoparticle charging. Carbon nanoparticles also play a significant role in astrophysics where laboratory dusty plasmas may serve to produce “astroanalogs.” Laboratory-produced materials, such as hydrocarbons, ice particles, and non-spherical dust particles, provide a testing ground for simulating astrophysical processes. They may be utilized to study particle cooling and heating, the role of dust particle surfaces as sites for the formation of new molecules, unidentified optical and radio frequency emission, and absorption lines, the birth and destruction of dust on planetesimals.429,430

Dust in fusion devices concerns both in situ produced particulates as well as deliberately injected populations. The former is unavoidable and constitutes a safety problem for future reactors with possible consequences for diagnostic equipment and even plasma operation. Due to this fact, studies of in situ produced dust are guided by safety and operational needs. On the other hand, investigations of the interaction of injected populations with fusion plasmas are motivated by the possibility to control plasma confinement and stability. Dust–plasma and dust–vessel interactions in fusion machines are governed not only by plasma physics but also by various aspects of surface physics, atomic physics, contact mechanics, impact mechanics, electrochemistry and computational fluid dynamics. In the following, we discuss issues of intrinsic dust in fusion reactors as well as novel applications of powder injection.

Due to the problem of fuel retention in plasma-facing components (PFCs), the decision was taken to move away from graphite-based to full-metal machines.431,432 The main in-vessel materials of interest are tungsten and beryllium, as expected in ITER.433–435 The vessel composition is naturally reflected in the composition of collected dust.436–446 Experimental evidence in tokamaks typically stem from dust collection activities and in situ camera observations, though innovative diagnostics have been proposed.54,367,447–451 To mimic the edge plasmas of future reactors but with better diagnostic access, linear plasma devices, capable of producing relevant heat fluxes, are utilized that provide detailed measurements not viable in tokamaks.111,452–457

Reactors must comply with safety limits that are imposed on the in-vessel dust inventory.458,459 The processes involved in the dust inventory evolution concern dust formation and remobilization, dust–plasma interactions, and dust–vessel mechanical collisions, as outlined in Fig. 5. The physical processes of dust impacts, dust remobilization, and dust adhesion have been successfully described within the framework of impact mechanics,111,460–462 the framework of contact mechanics,115,463 and the Lifshitz theory of van der Waals forces,120,121,464 respectively. The effects of nanometer scale surface roughness, diffusion bonding after prolonged thermal treatments, and plasma exposure on dust adhesion have been experimentally studied.119,465–468

FIG. 5.

The processes involved in dust inventory evolution, in-vessel accumulation sites, and impurity production in fusion devices. Fluid dynamics and contact mechanics problems are highlighted in red and blue, respectively. Reproduced with permission from Ratynskaia, Vignitchouk, and Tolias, Plasma Phys. Controlled Fusion 64, 044004 (2022). Copyright 2022 Authors, licensed under a Creative Commons Attribution (CC BY) license.

FIG. 5.

The processes involved in dust inventory evolution, in-vessel accumulation sites, and impurity production in fusion devices. Fluid dynamics and contact mechanics problems are highlighted in red and blue, respectively. Reproduced with permission from Ratynskaia, Vignitchouk, and Tolias, Plasma Phys. Controlled Fusion 64, 044004 (2022). Copyright 2022 Authors, licensed under a Creative Commons Attribution (CC BY) license.

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Deposit delamination, PFC cracking, unipolar arcs, and unstable molten pools in the course of high energy transients constitute the primary mechanisms of dust production in contemporary and future full metal tokamaks.55,469 Deposit flaking and PFC cracking are well-documented mechanisms of solid irregular dust production,470–472 which strongly depend on the local plasma loading pre-history. Unipolar arcing can be accompanied by the formation of micrometer-sized droplets released with speeds of several tens of m/s.446,473–476 Modeling has focused on cathode spots, where axisymmetric plasma heat fluxes and pressure gradients lead to local melting, push the melt outwards forming a crater, and produce metallic jets that breakup into droplets.477–479 The possible (shear, buoyancy, and geometry-driven) instabilities of melt layers, which are formed during off-normal events and can lead to droplet ejection, have been discussed from a theoretical perspective.55,469 Fully self-consistent calculations are computationally costly due to the scale separation between the melt extent and most unstable wavelengths. An efficient modeling strategy combines macroscopic melt simulations that estimate large-scale motion480–483 with local simulations that focus on free surface dynamics.484 Ejected droplets constitute a source of large, > 10 100 μ m, spherical dust.55,469,484

The distinct feature of dust–fusion plasma interactions lies in the importance of incident heat fluxes that are responsible for dust mass loss and strong thermionic emission in the case of tungsten. The surrounding clouds of vaporized material as well as the complex dust shape and composition can alter plasma–grain interaction and hence dust dynamics.367,485,486 Several dust codes have been developed128,487–492 to describe dust transport and survival in hot and dense fusion plasmas. Due to the low dust densities, they simulate isolated dust injected into a prescribed plasma background with given initial conditions. The coupled set of equations for the evolution of linear velocity, angular velocity, mass, enthalpy, and electric potential is solved, with the principal differences between codes lying in the physical models of the source terms (forces, heat fluxes, and collected currents).469 Rotational dynamics can also affect dust and droplet lifetime.55,149,367,469,493,494

Splashing of unstable molten metallic pools formed on PFCs is a major component of the dust inventory, especially in terms of the mass given the large droplet radii.469 Such pools are formed when PFCs receive high plasma heat fluxes in the course of edge-localized modes, vertical displacements events, and major disruptions. With ion and electron energies in the kiloelectronvolt range, melting is caused by surface heating and extended thin melt layers are formed, whose physics have been well understood and whose efficient modeling no longer poses a problem.480,482,484,495 However, there is the possibility of electrons with relativistic energies, which concerns runaway electrons (RE) formed in major disruptions. REs lead to volumetric heating and their energy deposition is characterized by non-monotonic profiles that can induce explosive material detachment.496–498 Today, no computational tools are available for the reliable modeling of the complex process of RE-PFC interaction that is associated with compressive flows and thermal shocks. Nevertheless, simulations of solid–fluid and solid–solid interactions are necessary for the prediction of the solid ejecta sizes and speeds. It is worth noting that the solid dust kinetic energy lies in the range capable of causing further wall damage upon subsequent impacts.496 Thus, in addition to the main wall damage by RE beams, there is secondary non-localized damage spread over the vessel.

An unexplored route of metallic dust formation concerns the in situ growth of nanodust during the extended pulses of DEMO type fusion reactors. Divertor operation in the semi-detached or detached regime with the use of high-Z seeding will provide more uniform plasma loading on the PFCs without compromising confinement but will also generate divertor conditions that favor dust survivability, wall sputtering, and atomic clustering. The use of heterogeneous nucleation theory,499 together with aerosol dynamics models,500–502 is envisaged for the investigation of the growth of the nanoscale particles. In these scenarios, one has to rely solely on modeling, since conventional tokamak dust diagnostics cannot detect such small sizes.

Dust transport and dust survivability models, which lie at the core of predictive inventory studies, must be able to account for the strong background magnetic field and various plasma–surface interaction processes.55,469,487,493 A peculiarity of fusion plasmas is vapor shielding; the heat flux attenuation due to the interaction of the cloud of vaporized dust material, which surrounds the grain, with the background plasma. The plume of ionized ablated material expands mainly along the magnetic field lines. The situation becomes even more complex for the case of the powder injection (see below), where plumes from different grains can overlap causing strong modification of local plasma parameters. The question of whether vapor shield can cancel out the effect of irregular dust shapes on dynamics54,144 has not been addressed yet. Available theoretical models are still rather qualitative485,486 and poorly benchmarked against experimental data.

Moreover, considering the large dust sizes and moderate initial speeds, metallic dust motion (especially for tungsten) is characterized by a strong inertial component, which makes accurate initial conditions of crucial importance for reliable predictions. In this aspect, benchmarking of modeling results against available (though often limited) data from present tokamaks and fusion-relevant devices is the most effective and promising route to constrain the expected dust sizes and release velocities. Since (re-occurring) remobilization of survived dust is an essential component of dust inventory evolution,116 the plasma-induced remobilization velocities also constitute crucial input for modeling. Despite multiple controlled remobilization experiments,112,115,463,503–506 nearly no empirical input is available concerning the release speeds due to technical limitations.115,463

Limited attention has been paid to ferromagnetic and strongly paramagnetic dust that can be lifted by the magnetic moment force and interfere with plasma startup.51,507 This was first observed in DIII-D508 and confirmed in recent studies.153,509,510 A magnetic dust population can be formed due to the change in iron crystalline phase from austenitic to ferritic during re-solidification of stainless steel droplets.509,510 We note that stainless steel use is anticipated in ITER433 and DEMO511 with significant stainless steel dust production expected in ITER.

Another distinct feature of tokamak dust concerns fuel retention.512 Oxidized tritiated tungsten dust may behave like dielectrics and sustain charge due to β-decay.444,513–516 The impact of tritiated dust on tokamak safety is a topic of on-going research.514 Detailed simulations of electrostatic self-charging have been initiated only recently.515 

Let us also mention possible advances in the science of powder injection for fusion applications. The wall is often covered with a thin layer of a low-Z material—the so-called wall “conditioning,” to prevent the penetration of high-Z impurities into the core plasma and to reduce plasma recycling. In recent years, powder droppers have been used on virtually all major devices for in situ wall conditioning.517–526 Being injected into hot fusion plasmas, powder particles (B, BN, and Li) ablate and the material is deposited on the wall. An unexpected consequence of powder injection has been reported; it appears that in many cases it eliminates violent bursts of unstable plasma, which are responsible for the strong erosion of divertor targets. The physics behind this effect is not clear yet. It is plausible that the 3D nature of powder injection leads to the modification of plasma equilibrium conditions and exhibits the stabilizing effect. Further understanding would require coupling of 3D plasma turbulence codes with dust dynamics codes to enable simultaneous modeling of powder particles transport and ablation and, thus, spatiotemporal evolution of the source of neutrals. Finally, the injection of powder could promote the plasma detachment regime, which is characterized by a very low power loading on divertor targets and, thus, of a primary interest for future reactors.527 However, this idea is still waiting for its thorough investigation.

In dusty plasmas, the solid particle sizes can cover a range from nanometers to centimeters. Starting with diameters larger than about 1 μ m , the particles become individually observable using basic illumination techniques. Then, the particle positions and velocities and, thus, their full dynamics can be deduced from optical imaging. Studies of dusty plasmas utilizing this technique represent the basis of experimental complex plasma research. While these particle systems are optically resolvable down to their individual particle dynamics, they are also subject to particle weight effects. With increasing particle size, the gravity induced acceleration becomes more and more important. Sedimentation effects start altering or even dominating studied phenomena especially for microparticle systems embedded in a low-pressure plasma environment. The latter is the reason why microgravity research is a complementary and mandatory pillar in the research on complex plasmas allowing one to access unique conditions to investigate large three-dimensional, homogeneous systems in the absence of weight-induced effects. Microgravity experiments have been successfully performed utilizing parabolic flights,528–539 sounding rockets,297 and three sequentially established and operated facilities aboard the International Space Station (ISS). The ISS based complex plasma experiment facility series consists until now of PKE-Nefedov, PK-3 Plus, and PK-4.204,540,541 These experimental setups have dominated the study of complex plasmas under low-gravity conditions without any major gap since the year 2001.

The research under weightlessness (microgravity) conditions has proven to be of major importance for the utilization of complex plasmas as a classical condensed matter model system (see Sec. VI). Microgravity has shown to be even mandatory to utilize the complete plasma bulk volume for particle confinement and, as a result, to create complex plasma system of statistically relevant size, in contrast to ground-based experiments. Phenomena that have been studied cover crystallization and melting processes, wave and shock wave propagation, lane formation, transition from laminar to turbulent flow, and driven shear flows. In most cases, the particle behavior could be resolved down to the dynamics of individual particles. The research also included studies of particle decharging in the plasma afterglow as well as particle sputtering and growth through polymerization from the gas phase. Even experiments in a plasma free background have been performed, investigating effects, such as fast agglomeration due to oppositely charged particles, an interdisciplinary study that has the potential to trigger alterations of planet formation models.542–554 

Recent results were achieved by using the facility PK-4 in the Columbus Module on the ISS for long-term and parabolic flights where short-term investigations were sufficient. One of the highlights from the parabolic flights concern the investigation of the demixing of binary complex plasmas (containing two different particle sizes) where it was found that the demixing process is mainly driven by the plasma forces on the different sized particles in contrast to first theoretical considerations where a spinodal decomposition was considered as a dominant process.555–557 

Conversely, PK-4 on the ISS allowed the detailed long-term investigation of the formation of strings in electrorheological plasmas formed in AC electric fields and could resolve their 3D structure and formation process and their influence on wave propagation.72,558–560 The strings are forming due to the interaction of the negative charged particles with positive ion wake regions. The latter are formed downstream of the microparticles due to the flow of ions in the AC electric field and their interaction with the negative charged microparticle, which act like an attractor/collimator for the ions. The question whether the arising attraction in the microparticle–plasma system is of short-range or long-range order could be resolved as short-range by careful comparison of experimental results and molecular dynamics simulations.561 

The research under reduced gravity is not only important for investigations on complex plasmas as a model system for classical condensed matter formed in the bulk of a plasma device but also for solving fundamental questions regarding the charging and screening of individual particles or the interaction with ions leading to ion drag and ion wakes. It helps also to observe strong coupling effects producing waves and shock waves in the dust component263,561–564 and the influence of the dust component on the background plasma in general. This all is important in understanding natural dusty plasmas and dusty plasmas in plasma processing (see Fig. 6).

FIG. 6.

Low-gravity complex (dusty) plasma research in the context of soft matter research, natural dusty plasmas, and dust in industrial plasma applications.

FIG. 6.

Low-gravity complex (dusty) plasma research in the context of soft matter research, natural dusty plasmas, and dust in industrial plasma applications.

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Complex plasmas are useful tools to test models of statistical physics, plasma physics, and soft-condensed matter through the study and reconstruction of the full distribution function. Since the latter is experimentally accessible, the simultaneous investigation of single-particle and collective scales is possible. This kind of potential studies is unique, especially since complex plasma allow one to obtain this insight over a wide range of system dynamics from over-damped to quasi-undamped system as well as over a wide coupling range, from loosely coupled (gaseous) to strongly coupled (crystalline) phases. As such especially the microgravity complex plasma research that opens the possibility to study full 3D systems has a wide potential in the coming research endeavor. The perspectives of low-gravity research in complex and dusty plasmas have been published recently in a white paper.565 They can be differentiated between the research as a model system of classical condensed matter physics (complex plasma) and natural dusty plasmas.

Examples of open research questions are the experimental determination of the equation of state that describes the state of matter via the relation of thermodynamical quantities,566,567 the investigation of transport properties, such as viscosity,568 heat conductivity,349 or diffusion,569 and anisotropic and non-reciprocal interactions that emerge in the presence of inhomogeneities in the system.570 

Additionally, the measurement of crystal dynamics on the atomic scale during phase transitions in solids can give new insight on the temporal development of crystal structures and the structural complexity on the surface.571 This knowledge is relevant for applications, such as materials design, through the influence of the structure on general properties of the macroscopic materials.

The supercooled state and the system behavior close to or even beyond the glass transition point are another topic of future research and can be studied by quenching the liquid system below the melting point, yielding new insight into the microscopic foundation of supercooled liquids572,573 and the elementary mechanisms which determine the stability of supercooled fluids against crystallization.

The investigation of fluid dynamics at the discrete level, especially of non-linear phenomena, such as non-linear waves545,574–576 and turbulence,577 can yield valuable insights into the underlying microscopic processes and their connection to large-scale hydrodynamic motion, e.g., how microscopic interactions lead to the development of large-scale non-linear (turbulent) motion.

Active matter consists of particles that take energy from their surroundings and convert it into non-thermal motion. The emerging motion is usually far from equilibrium and exhibits phenomena, such as swarming, aligning, clustering, self-crowding (jamming), active microrheology, active turbulence, active baths, and many more. These can be studied in complex plasmas by inserting active particles, e.g., Janus particles351,578 or anisotropic particles579 into the discharge. Introducing active particles into the plasma opens up a new research direction covering many aspects of active matter, such as the structure and ordering in an active particle system, or how the collective behavior of self-propelled particles connects to the energy input on the single-particle level.

Natural dusty plasmas are numerous in astrophysical environments, such as the Moon, asteroids, planetary rings, cometary tails, interplanetary and interstellar clouds, and Earth's mesosphere117,197,580–583 (see Sec. XIII). Many of those are low-gravity environments. Especially on planetary bodies close to Earth, dust and dusty plasma pose challenges for human exploration by its hazardous effect on technical equipment or humans. A better understanding of the physical processes of dust formation, charging, lofting, or levitation, their movement and dynamics will not only give insight into the fundamental physics but can help to improve methods of dust mitigation that will be essential for future exploration missions, especially for the Artemis program to the moon.110,584

Finally, utilizing dust particles as probes in the bulk plasma, the investigation of the trajectories can yield information on the plasma itself.186,585,586

Future research activities can be realized with the multi-user, multi-purpose facility COMPACT587 planned for the ISS as a follow-up lab to PK-4, by parabolic flights performed, e.g., with lunar-g characteristics ( 1 / 6 g )588 or directly by dusty plasma experiments in situ on the Moon.110 To complement the research under low-gravity, it is mandatory to perform advanced theoretical modeling and numerical simulations—from molecular dynamics to particle-in-cell methods—in parallel to dedicated experiments under gravity conditions using plasma and particle diagnostics not available, e.g., in COMPACT due to their size/mass and complexity.

Two-dimensional (2D) complex plasmas are single-layer suspensions of micrometer-size solid particles in the plasma sheath of a gas discharge, see Fig. 7. They have a special place in the field of complex plasmas. For one thing, the discovery of 2D plasma crystals589–592 in 1994 gave a major boost to the whole field. For another, 2D complex plasmas possess a number of unique features which make them attractive objects to study in laboratory experiments and computer simulations. First, they are relatively easy to prepare and observe, 100% of their constituent particles can normally be imaged by video cameras throughout the experiment. Second, in-plane interparticle interaction potential is approximated well by the (purely repulsive) Yukawa potential,20 which means simpler analysis, general interest, and the relevance to generic 2D phenomena (phase transitions, transport phenomena, waves, etc.). Third, unlike in 3D suspensions of particles in bulk plasmas, in 2D systems the particles levitate in the plasma sheath where the electric field is strong, therefore, the system description can be based on the linearization around finite values, not zero as in bulk plasmas. This makes 2D complex plasmas well-defined systems open to analysis and computer simulations.

FIG. 7.

(Upper panel) Snapshot of a 2D complex plasma crystal showing about 400 particles and (lower panel) the corresponding pair correlation function g(r) for particles. The image is inverted and its brightness is adjusted for better viewing. Reproduced with permission from Nosenko et al., “New radio frequency setup for studying large 2D complex plasma crystals,” AIP Adv. 8, 125303 (2018). Copyright 2018 AIP Publishing.

FIG. 7.

(Upper panel) Snapshot of a 2D complex plasma crystal showing about 400 particles and (lower panel) the corresponding pair correlation function g(r) for particles. The image is inverted and its brightness is adjusted for better viewing. Reproduced with permission from Nosenko et al., “New radio frequency setup for studying large 2D complex plasma crystals,” AIP Adv. 8, 125303 (2018). Copyright 2018 AIP Publishing.

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In our opinion, the most interesting and significant recent advances in 2D complex plasma research took place in the following areas.

1. 2D complex plasmas as model systems for plasma-specific and generic 2D phenomena

  • Thermodynamics and statistical mechanics. Entropy was measured in 2D complex plasmas.567 In 2D complex plasma experiments with shear flows, the fluctuation theorem was obeyed,593,594 leading to the temporal convergence of the fluctuation theorem,593 which was then attributed to the viscoelasticity of complex plasma.594 

  • Equation of state (EOS) and phase transitions. Using computer simulations, the EOS for 2D complex plasma liquids was obtained,595–598 from which their various physical properties were analytically derived.599–601 Shear602,603 and bulk moduli604 of 2D complex plasma solids were also obtained from simulations. For both 2D and 3D complex plasmas, it was found that the supercritical transition between the liquid-like to gas-like phases always occurs at 20 times of the corresponding melting point from various Frenkel lines,605 just corresponding to the transition between strong and weak couplings of complex plasmas. Slow dynamics of the glassy state was discovered in a 2D complex plasma experiment606 and the corresponding simulation.607 

  • Transport mechanisms. Ratchet rectification and its reversal were experimentally demonstrated by adjusting plasma conditions using naturally persistent flows of one particle chain inside asymmetric sawteeth of gears on the electrode.608 Shear viscosity was determined from the fluctuations of shear stress in shear flows.609 A Stokes layer was experimentally observed by applying a sinusoidal shear using the laser manipulation method,610 then the frequency-dependent complex viscosity was also obtained in this system.611 From various scaling laws of viscosity and the time of the atomic topological structure change, the origin of viscosity at individual particle level was discovered.612 

  • Dislocation dynamics. From dislocation dynamics in 2D complex plasma experiments with shear flows, the Orowan equation introduced in 1940s was first demonstrated to accurately determine the plastic strain rate.613 Shear softening and hardening effects of 2D dusty plasma solids in different orientations were also discovered.614 

  • Compressional shock and soliton dynamics. Thermodynamic properties after the shock propagation were analytically derived.615–617 Shock induced melting618,619 and elastic-to-plastic transition620 were both systematically investigated. Fast particles overtaking the shock front621 and the dispersive shock wave around the shock front622 were both investigated systematically. It was found that rarefaction waves are generated simultaneously when the compression is suddenly stopped.623 Compressional shocks were also performed in 2D complex plasma experiments with a well-controlled exciter to determine the resulting shock speed and width,576,624,625 so that quantitative comparisons with simulations were made. The propagation of a dissipative soliton was experimentally studied in a 2D binary complex plasma in amorphous and crystalline states.626 

  • Substrate dynamics. A substrate, or a force field with potential wells, was introduced into 2D complex plasma simulations to generate new dynamics, which can be experimentally realized using a stripped electrode, or interference of powerful laser beams. Under the modulation of 1D periodic substrates, the new phonon spectra,627 the sub-diffusion, and the reentrant melting transition,628 as well as the oscillation-like diffusion,629 were all discovered. During the depinning procedure, three dynamical phases of pinned, disordered plastic flow, and moving ordered states630,631 were found. Asymmetric 1D periodic substrates induced bidirectional flows with unbiased external excitations were also found.632 It was also found that, under 2D periodic substrates, the resulting phonon spectra633 exhibit more complicated coupling. In the depinning procedure of the system modulated by 2D periodic substrates, the direction locking effect,634 the dynamical commensuration effect,635 and the superlubric-pinned transition636 were all discovered.

  • Plasma-specific phenomena. Plasma wakes downstream of the ion flow past negatively charged particles modify the interparticle interactions making them non-reciprocal (in quasi-2D complex plasmas). This leads to rich dynamics, including the mode-coupling instability,206,363,637 coupling of non-crossing wave modes,638 and thermoacoustic instability.639 

2. Extending the scope of 2D complex plasmas

  • The most common structure of a crystallized 2D complex plasma is a triangular lattice with hexagonal symmetry. Recently, the square lattice was experimentally observed under appropriate conditions in (1) binary quasi-2D complex plasma640 and (2) monodisperse quasi-2D complex plasma.641 

  • Apart from traditional particle tracking velocimetry (PTV) and particle image velocimetry (PIV) image analysis methods, new methods based on machine learning are emerging. A supervised machine learning method was used to study a phase transition in a 2D complex plasma.388 

  • Larger 2D complex plasmas, up to 27 cm in diameter (previously 5–6 cm) consisting of up to 34 000 particles (previously 5000–15 000 particles), were recently observed.389,638

  • The scope of complex plasmas as model systems was recently extended to include active matter systems. Active matter is a collection of active particles, each of which can extract energy from their environment and convert it into directed motion, thereby driving the whole system far from equilibrium. Single active Janus particles as well as 2D complex plasmas with their inclusion were recently studied.578,642,643

In our opinion, 2D complex plasmas will continue to be in the focus of intense research. The following topics will likely receive increased attention.

  • Due to their unique characteristics as model systems, 2D complex plasmas will be used to study plasma-specific and generic 2D phenomena. This will be facilitated by recent and expected hardware developments, such as the emergence of new-generation plasma chambers,328 higher-resolution and faster video cameras, 3D imaging techniques using stereoscopy and plenoptic cameras. Therefore, more sophisticated experiments and more accurate data are expected leading to the possibility of studying more subtle effects in thermodynamics, non-equilibrium statistical mechanics, physics of transport phenomena, glassy state, phase transitions, and dislocation dynamics.

  • Some plasma wake-mediated effects predicted theoretically still await experimental verification, for example, emerging activity in bilayered dispersions of particles.644 The relationship between the discharge parameters and ion wake characteristics is not well understood. A molecular dynamics simulation of ion dynamics and particle charging was performed to self-consistently determine the particle charge and ion wake characteristics for different synthetic experimental conditions.210 Direct experimental measurement of the plasma wakes, e.g., using laser-induced fluorescence would be a much-welcome breakthrough.

  • System-size dependence of complex plasma properties is a long-standing problem. In particular, the dependence of transport coefficients on the system size is of interest. In fact, the very existence of valid transport coefficients in 2D systems is debated.645 Therefore, experiments with larger 2D systems will be necessary to address these questions.

  • Following the recent experimental discovery of square lattice,640,641 other more complicated structures predicted theoretically77 are expected to be observed in dedicated experiments.

  • Ensembles of active Janus particles suspended in a plasma are promising model systems to study active Brownian (Langevin) motion, where the particle damping and propulsion can be tuned.578,642,643 Since Janus particles can be considered an extreme case of particles with inhomogeneities, they can be used as a study model for the so-called “abnormal” particles with irregular trajectories,646 possibly helping to develop a method of controlling them in experiments with complex plasmas.

Aerosols are introduced or produced, intentionally or unintentionally, in non-thermal atmospheric-pressure plasmas (APPs) for both fundamental research and current or emerging technologies.647–651 Understanding the interactions between particles and plasmas is critically important to engineer nanoparticles648,652 and thin films with specific properties649,652,653 and is also more broadly relevant to atmospheric science and water treatment, as well as catalysis, environmental science, medical applications, and other fields.654,655

Compared with more traditional low-pressure dusty plasmas, APPs containing aerosols offer the possibility of working with a much wider range of materials, from liquids to high melting point compounds. Aerosol particles in APPs can be maintained at room temperature (e.g., with minimal evaporation for liquids)656,657 or heated to melting temperatures for solid particles.658,659 Particle charging is a common feature for both low-pressure as well as APPs, however, due to a collisional sheath (for both electrons and ions) particle charging can be different compared to low pressure dusty plasmas. For droplets, charge could for example, penetrate into the droplet and the large dielectric constant of water can lead to asymmetric charging and sheaths around droplets.660,661 A key advantage of plasma processes, both at low-pressure and at atmospheric pressure, is the possibility of controlling the separation between the background gas temperature and the energy of electrons, a condition that creates novel pathways for particle growth and interfacial chemistry. However, because of the atmospheric pressure operation, these characteristics allow for APPs to be compared more directly with colloidal or aerosol routes, also operated at atmospheric pressure, but where such pathways driven by energetic electrons are inaccessible. These characteristics place APPs containing aerosols in a related, but separate research space from that of both low-pressure dusty plasmas and colloidal chemistry.

Research progress on APPs containing aerosols has been characterized by many reactor configurations and in particular, microplasmas648,662 or small-scale plasma reactors (compared to larger traditional low-pressure plasmas).663 Furthermore, at atmospheric pressure, drag forces are large and particles are more readily carried by the gas flow; hence, APPs are often operated in a flow-through mode (e.g., plasma jets or flow-through reactors664–666) as depicted in Fig. 8. In these cases, particles evolve as they travel through the plasma where phenomena, such as nucleation, growth, chemical/phase transformation, evaporation, coagulation, condensation, fragmentation, deposition, and charging, can take place.667 When particles reach the edge of the plasma, they enter downstream the so-called spatial afterglow, through a space charge region with large electron, gas temperature, and species densities gradients.648,668 The spatial afterglow likely transforms particle properties and can have both beneficial and detrimental impact depending on the targeted application.666,668,669

FIG. 8.

Schematic representation of a flow through, atmospheric-pressure plasma containing an aerosol indicating key processes that embody plasma–aerosol particle interactions.

FIG. 8.

Schematic representation of a flow through, atmospheric-pressure plasma containing an aerosol indicating key processes that embody plasma–aerosol particle interactions.

Close modal

Solid particles within APPs have been widely investigated in the context of nanoparticle synthesis648,670 (see also Sec. VII). In these cases, atomic or molecular precursors are injected in flowing plasmas, where conditions for particle formation are deliberately created. Hence, the plasma evolves spatially, to include initially the formation of clusters, and subsequently the growth of larger particles. The transit of such particles through the afterglow, downstream of the plasma, is an important stage of the synthesis as it impacts the phase, surface states, and charge on the particles.668 These approaches have been used not only to collect nanoparticles but also to deposit films on substrates;649,652,653 however, the literature rarely assesses or even makes the distinction if particles form within the plasma prior to deposition or if the role of the plasma is purely to activate precursors. While material synthesis has shown a high degree of success, fundamental understanding of the processes is lacking with few exceptions.654,659,660,668,671–673 Other work with solid particles can have applications for material recycling, repurposing, or waste remediation. APPs interacting with liquid droplets leverage the ability to generate chemically reactive species in gas-phase plasmas to produce chemical reactions and reactive species in the liquid phase. Droplets with a large surface-to-volume ratio interspersed in the plasma are a strategy to reduce transport limitations in plasma activation of solutions.651,674 Recently, the use of liquid precursors and, therefore, the injection of liquid micrometer-droplets in APPs has been increasingly investigated for materials synthesis.675–677 This is often motivated by the absence of suitable precursors with appreciable vapor pressure. In addition, some vapor precursors may be difficult to handle or contain undesirable components (e.g., organics). Alternatively, precursors could be introduced as a liquid droplet by, for example, dissolving in an appropriate solvent and evaporating the solution in the plasma. Such an approach could be considered as an extension of the work that has been done in synthesizing nanoparticles in liquid solutions by interfacing a plasma either at the surface or inside.678,679

The droplet can be also seen as a liquid phase micro-reactor for a variety of other applications, including nitrogen fixation,680,681 production of reactive species enabling decontamination of pathogens,682,683 and water treatment.684 While plasma-induced chemistry can be highly complex,685 several studies show that the chemistry in droplets can, for certain conditions, be dominated by short-lived species.684–687 In many cases, the flux of short-lived reactive species in the plasma is large and the transport is limited by diffusion of the chemical compounds from the bulk droplet to the plasma–droplet interface.686 Furthermore, the complexity of plasma–droplet interactions is significantly enhanced by the strong mutual interaction of the plasma and droplet leading to enhanced evaporation and the introduction of vapor in the plasma with potentially large impacts on the plasma properties surrounding the droplet684,685 and even the overall plasma chemistry.688,689

Plasma–bioaerosols interactions are another unique example with specific relevance for APPs. While such interactions have received increased attention with the COVID-19 pandemic,683 the ability of a plasma to inactivate aerosolized viruses, bacteria, and fungi was already well established before the pandemic.690–694 Inactivation of bioaerosols in APPs can occur with contact times on the order of 10 ms, which is orders of magnitude faster than typical plasma-enabled inactivation of pathogens on substrates or in bulk liquids.

Plasma–aerosol interactions offer the possibility of opening up new pathways for chemical reactions in aerosol synthesis and processing. While a significant volume of literature is emerging showing the effectiveness of APPs in aerosol-based processes, the key design and operational principles that control the system performance and a thorough understanding of the underpinning fundamental mechanisms are still lacking. The inherently non-equilibrium, non-linear, and complex plasma–aerosol interactions have an excessive number of degrees of freedom that are not always holistically accessible and there is an urgent need for an enhanced understanding and predictive capabilities.

Current needs include a better understanding and control of the nucleation process as a critical step in the formation of solid nanoparticles. The impact of the afterglow on particle properties and dynamics also needs to be better understood, which in view of the large gradients at atmospheric pressure might have a more profound, but to date unquantified impact on aerosol processing. While recent studies focusing on the interaction of a plasma with single droplets has increased our understanding of plasma–droplet interactions, a quantitative understanding of (1) the ultrafast synthesis of monodispersed nanoparticles enabled by plasma–droplet interactions, (2) the plasma-induced liquid phase reactions in droplets in general, and (3) plasma interactions with bioaerosols remains lacking. Recent work on microdroplet chemistry, without a plasma, has shown uniquely different outcomes compared to bulk liquid chemistry,695,696 which suggest that APPs containing aerosols may also alter reaction mechanisms compared with APPs interacting with bulk liquids. We highlight several proposed areas of focus below.

1. Interfacial processes

The plasma–particle interface presents distinct and challenging characteristics which are of wider scientific interest. For example, electron emission processes, and the likely important role of ionic and metastable species recombination at the interface, remain poorly understood particularly for liquids. The band structure of the particles, and therefore, their composition and phase, are not only highly relevant for many applications but are also an integral part of more advanced models of interfacial processes which need to be developed.138 Furthermore, the volatile nature of many aerosol particles can lead to significant changes in the local plasma environment surrounding the particle, increasing the complexity as well as directly impacting droplet charging and reactive species fluxes.684,697

2. Spatial afterglow

The properties of the afterglow have already been found to enable quenching of nanoparticles exiting the plasma. Nonetheless, the impact of strong gradients on particles, for example, due to space charge boundary layers at atmospheric pressure, and the transition from bipolar charging to a more dominant role of ions in particle charging in the afterglow, is to date not fully understood. Spatial afterglows have some similarities with temporal afterglows in plasmas formed at reduced pressure,208,698 and the knowledge gained from these studies may be drawn upon to advance our understanding of APP spatial afterglows.699 

3. Diagnostics

Tackling some of the above-mentioned key research questions will require the implementation of in situ diagnostics that could measure (often fast) temporal changes in aerosol properties during plasma exposure and quantify the impact on the local plasma properties surrounding aerosol particles. For droplets, the recent development of on-demand-droplet dispensing technologies may provide opportunities for such in situ measurements.685,687 The ability to trap droplets would allow a detailed in situ characterization of droplets using approaches applied by the aerosol community over the last two decades.700,701

4. Modeling

Plasma–aerosol interactions are inherently three-dimensional phenomena,698 nonetheless most modeling studies have been focused on lower-dimensional models. There is an urgent need for the development of 3D models to capture the interactions occurring within plasmas containing multiple aerosol particles. A major emphasis should be on the incorporation of more detailed interfacial interaction mechanisms and on the development of simplified reactor geometries with easy access for diagnostics, which are more amenable to modeling and experimental model validation.

A better understanding of the processes underpinning plasma–aerosol interactions will not only contribute to plasma science but enable the continued impact of this area on technologies and society.

The interaction between magnetic fields and dusty plasmas plays a key role across Earth, space, and astrophysical phenomena. In Earth's magnetosphere, the interaction of the solar wind and the influx of meteors lead to a number of dusty plasma effects, such as noctilucent clouds and polar mesospheric summer echoes.702 On the moon, the levitation of charged dust particles in lunar swirls has been shown to map the topology of crustal magnetic fields.703 The alignment of dust particles in magnetized plasmas at the center of the Milky Way has allowed us to observe its magnetic fingerprints.704 While the scale and strength of magnetic fields in the universe varies, modern-day magnetized dusty plasma experiments reproduce some key normalized parameters of these environments and serve as dedicated research platforms to study these phenomena (Fig. 9).

FIG. 9.

Representative magnetized dusty plasma regimes in terms of magnetic field (B) vs ratio of electron Debye length to dust gyroradius: Saturn's rings (from NASA/JPL761), Orion's Nebula (from NASA/ESA/Robberto762), dust near the sun (from NASA/Johns Hopkins APL/Steve Gribben763), star-forming region (from ESO, McCaughrean764), Noctilucent clouds (Adapted from Ref. 765), processing plasma [Adapted with permission from Merlino and Goree, “Dusty plasmas in the laboratory, industry, and space,” Phys. Today 57(7), 32–38 (2004). Copyright 2004 AIP Publishing.], low temperature plasma chamber for nanoparticle growth with permanent magnets (courtesy of Edward Thomas, Jr., and Saikat Chakraborty Thakur), MDPX (courtesy of Edward Thomas, Jr.), tokamak (Copyright ITER Organization766), lunar dust experiment (from NASA767), lunar swirls (NASA/GSFC/Arizona State University768), and GEC reference cell (from Ref. 769).

FIG. 9.

Representative magnetized dusty plasma regimes in terms of magnetic field (B) vs ratio of electron Debye length to dust gyroradius: Saturn's rings (from NASA/JPL761), Orion's Nebula (from NASA/ESA/Robberto762), dust near the sun (from NASA/Johns Hopkins APL/Steve Gribben763), star-forming region (from ESO, McCaughrean764), Noctilucent clouds (Adapted from Ref. 765), processing plasma [Adapted with permission from Merlino and Goree, “Dusty plasmas in the laboratory, industry, and space,” Phys. Today 57(7), 32–38 (2004). Copyright 2004 AIP Publishing.], low temperature plasma chamber for nanoparticle growth with permanent magnets (courtesy of Edward Thomas, Jr., and Saikat Chakraborty Thakur), MDPX (courtesy of Edward Thomas, Jr.), tokamak (Copyright ITER Organization766), lunar dust experiment (from NASA767), lunar swirls (NASA/GSFC/Arizona State University768), and GEC reference cell (from Ref. 769).

Close modal

Here, a charged particle (electron, ion, or dust particle) is considered “magnetized” when its dynamics is substantially influenced by the magnetic force, F = q v × B , where q and v are the particle charge and velocity, and B is the magnetic field. The magnetic force should be comparable in magnitude to the other forces that influence its dynamics. This condition can be quantified by the Hall parameter, H α = ω c α / ν α n q α B / ( m α P ) , the ratio of the gyrofrequency ω c α to the species-neutral collision frequency ν α n . Here, α represents the charged particle species [electrons (e), ions (i), and dust (d)], P is the neutral pressure, and m α and q α are their mass and charge, respectively. As the Hall parameter increases with the increasing charge-to-mass ratio ( q α / m α ) , the electrons are most easily magnetized, then the ions, then the charged dust particles. Thus, to understand a system that has magnetized dust particles, we must also consider the dynamics of the magnetized plasma electrons and ions.

Weak magnetic fields of B < 0.1  T were used to provide confinement of the electrons ( H e 1 ) and weak confinement of the ions ( H i 1 ), but there is effectively no direct impact of a magnetic force on the dust particles. The influence of the magnetic field is largely restricted to modifying the background plasma, which leads a larger trapping volume for the dust particles. In experiments by Merlino et al., an axial magnetic field was used to expand the anode glow region near a biased electrode.345,705 Other studies focus on modifications of ion instabilities and shocks in these weakly magnetized plasmas.706–708 

In inhomogeneous magnetic fields, there is a modification of the potential structure of the plasma that can lead to rotation of the both two-dimensional and three-dimensional dusty plasma structures.709–715 Additionally, the formation of dusty plasma tori, i.e., a “ring” of dust that rotates in the plane perpendicular to the magnetic field, were observed to form as a result of a delicate balance between electric, neutral drag, and ion drag forces on the dust grains, where the ion drag is modified by the presence of the magnetic field.82,716–719

Dusty plasmas with magnetized electrons and ions, typically characterized by H i 1 and consequently H e 1 , usually require substantial magnetic fields of the order of B > 100 mT or even B > 1 T. Under such conditions, the dynamics of the electrons and ions are greatly influenced by the magnetic field provoking a reaction of the dust component to these altered plasma dynamics.

Laboratory experiments generally employ discharges between electrodes that tend to form filaments at elevated magnetic fields.364,370,374,720–722 These filamentary structures are elongated along the field, but restricted perpendicular to the field, and feature increased light emission and, presumably, elevated plasma density. The filaments are suggested to be a result of non-ambipolar diffusion due to restricted ion diffusion perpendicular to the field.723,724 In dense dust clouds with sub-micrometer dust particles filamentation is found to be suppressed.725 The directed magnetic field also maps features of the plasma boundaries as potential structures into the plasma.721,726–728

The presence of electric fields E in bounded discharges give rise to E × B rotations of the ions (and ion–neutral collision driven neutral gas rotation713). The ion (neutral gas) rotation drives rotations of the dust component where the rotation speed generally increases with magnetic field strength,729,730 eventually leading to a sheared rotation of the different parts of the dust cloud.729,731–734

Experiments on the dust charge trapped in the sheath of the discharge reveal only little variation of the dust charge with magnetic field strength, even for fields larger than 1 T.366,372,373 This is backed by simulations of the dust charging processes with flowing magnetized ions.82,83,88,735,736 While electron and ion currents to the dust are influenced by the magnetic field, they change in a similar manner so that the net change in the dust charge is small.

In a flowing plasma, a region of enhanced positive space charge (ion focus) is created in the wake of the dust particle due to ions that are scattered into the region downstream of the dust particle.737–740 Analytical and linear response theory calculations find that the positive space charge potential reduces with magnetic field strength.79,80,741–743 PIC and MD simulations of the ion focus support this finding.80,82,83,88,744 MD calculations show that at very high field strengths of the order of 10 T the ion focus turns into an ion “shadow” with a reduction in the positive space charge because the ions follow the magnetic field lines and cannot be scattered into the region downstream of the dust particle anymore.82,83 All this is accompanied by a reduction in the ion drag force on the dust particle with magnetic field.84 

Dust-density waves268,745–747 are excited by an ion flow past the dust particles and feature strong modulations of the dust density at frequencies of the order of the dust plasma frequency.748 Since the ion flow is affected by the magnetic field, also the dust-density wave dispersion is modified in a magnetic field.277,749,750 However, the relevant dust cyclotron frequency is still much smaller than the dust plasma frequency for micrometer-sized dust particles even at magnetic field strengths of the order of a Tesla. Moreover, the dust-density wave dispersion remains unaffected when the ion flow is along the magnetic field. One or both of these limitations are met in the experimental situations so far;277,375,376 hence, a direct influence of the magnetic field on the wave dispersion is not expected. However, the dust-density waves are found to feature stronger wave-damping at higher magnetic fields.375,376

In fusion devices with magnetic fields of the order of a few Tesla, dust particles are produced from melting of wall material or from arching and exfoliation52,54,367,751,752 (see also Sec. VIII). In fusion devices, the plasma production is electrodeless and the plasma densities are much higher than in the situations described above. The main forces on the dust are the ion drag force and “rocket forces” due to non-uniformities in the particle material and the associated different reflection coefficients of plasma particles as well as forces due to dust material ablation. However, also in these conditions, the direct influence of the magnetic field on the dust trajectories is considered negligible.54,367,752

A true magnetized dusty plasma, in which the dynamics of all charged particles are dominated by the magnetic field still remains to be fully realized in a controlled experiment. For astrophysical systems753,754 as well as next-generation fusion experiments,59,437,755 the role played by magnetized dust particles may have considerable influence on the evolution of the plasma. There are many theoretical models that seek to understand both single particle and collective particle dynamics in a magnetized dusty plasma.246,277,743,756–760 However, a key challenge of many of these models is fully incorporating the modification in the plasma dynamics and particle charging that occurs as the magnetic field dominates the electron and ion dynamics.

The future exploration of magnetized dusty plasmas remains rich with opportunities. Many of the motivating questions in space and astrophysical plasmas about the magnetization of the dust grains still remain unanswered.770,771 Recent observations of dust in the solar wind from Parker Solar Probe772–774 and investigations of dusty structures near strongly magnetized black holes775,776 show that there are still exciting questions.

The ultimate goal to achieve a direct magnetization of the dust component in experiments with H d 1 will probably require magnetic fields exceeding 1 T and sub-micrometer-sized dust particles. When dust cyclotron waves with typical wavelengths of the order of 10 cm are exploited as evidence of dust magnetization, the dust clouds have to be quite large.366 However, imaging of individual particles (a unique feature of dusty plasmas) will become difficult or even impossible. Experiments would require a control or mitigation of filament formation demanding for a deep understanding of bounded plasma discharges under strong magnetic fields. In this context, questions of particle charging,82,83,88,735,736 the generation or modification of plasma flows,80,82,83,88,744 or growth processes in reactive gases722,777 have to be newly addressed.

The development of advanced analytical models and numerical simulations is crucial to fully bridge laboratory results and space observations. Analytical theory and numerical simulations of magnetized dusty plasma have been developed to investigate the formation of Mach cones (relevant to Saturn's dusty rings),778 hydromagnetic waves and shocks (planetary ring systems),779–781 low frequency ion waves (solar atmosphere and pulsar magnetosphere),782,783 dust acoustic waves (Earth's magnetosphere and auroral regions),784 and magnetized sheaths (plasma processing and probe theory).785 

When modeling such systems, apart from a Lorentz force term, it is necessary to account for additional electrostatic fields, plasma inhomogeneities, and anisotropic interactions. The difference in charge-to-mass ratio of the different species in magnetized plasmas leads to charge separation resulting in additional electrostatic fields. This process is believed to cause the formation of lunar swirls.786,787 Another possible phenomenon is the plasma filamentation at strong magnetic fields.370,721 Depending on the strength and topology of the external magnetic field, symmetry in the particle shielding may be broken, resulting in anisotropic interaction potentials that affect many dynamical features of the dust structures in magnetized plasmas. Thus, developing self-consistent analytical models to describe these processes and incorporating these effects in numerical simulations of magnetized dusty plasmas still present one of the greatest challenges in the field.

Dusty plasma phenomena in space physics often offer possible explanations for unusual observations. The term dust is used to identify macroscopic charge carriers with a wide range of sizes, from large macro-molecules (nm radii) to pebbles (mm radii). Exposed to UV radiation and/or immersed in plasma, dust particles can exhibit unusual dynamics and can change the properties of their environment. The spatial scale of dusty-plasma-related observations in space also spans many orders of magnitudes, including the small-scale (cm) structures on the lunar surface and the propagation of interstellar dust particles through the entire solar system (hundreds of AU). The atmospheres of the Earth4 and Mercury,788 the surface of the Moon,789 asteroids,790 comets,791 and planetary rings,792 for example, all offer rich laboratories to study the fundamentals of dust charging, transport, and the possible emergence of dusty plasma collective behavior.219,793

Challenges, in general, for dusty plasma studies in space are due to the fact that we do not know the composition of the dust, we usually deal with a wide size distribution, and the dust charge remains poorly known because it depends on the dust density itself and a number of processes driven by the radiation and plasma environment. In addition, the very presence of the dust can alter the properties of their environment, acting as sinks and/or sources of the plasma, changing the energy distributions of electrons and ions, and even the composition.

We focus here on dusty plasmas that can be studied with space missions through in situ measurements. In the ionosphere of the Earth, dusty plasmas influence the charge balance and are often noticed in an observed lack of electrons in comparison to positive ions (Fig. 10). Some dust plasma collective effects are observed in situ with rocket-born instruments and also with ground-based radar. Furthermore, dedicated instruments onboard space missions can detect the mass, charge speed, and composition of dust particles, simultaneously characterizing their radiation and plasma environment, enabling the identification of phenomena that are shaped by dusty plasma processes.

FIG. 10.

An electron bite-out measured by a DC probe aboard the rocket ECOMA-6. The difference between the density of positive ions and electrons cannot be due to negative ions, and it is likely due to the charging of macrosopic aerosol particles.794 Similar electron depletion has been observed by the Cassini spacecraft at Saturn while crossing the plumes emerging from the geologically active south polar regions of the moon Enceladus.795 Adapted with permission from Friedrich et al., J. Atmos. Sol. Terr. Phys. 73, 2201–2211 (2011). Copyright 2011 Elsevier.

FIG. 10.

An electron bite-out measured by a DC probe aboard the rocket ECOMA-6. The difference between the density of positive ions and electrons cannot be due to negative ions, and it is likely due to the charging of macrosopic aerosol particles.794 Similar electron depletion has been observed by the Cassini spacecraft at Saturn while crossing the plumes emerging from the geologically active south polar regions of the moon Enceladus.795 Adapted with permission from Friedrich et al., J. Atmos. Sol. Terr. Phys. 73, 2201–2211 (2011). Copyright 2011 Elsevier.

Close modal

Dusty plasma in the ionosphere of the Earth recently became the focus of studies because it occurs at altitudes where the ionosphere–mesosphere coupling is important. This region overlaps with the zone of meteor ablation.796 Cosmic dust material that is ablated in the meteor process remains in the upper atmosphere, it forms small dust particles, called meteoric smoke, and it takes part in the ion chemistry and in the growth of ice particles observed in Noctilucent clouds.797 Noctilucent clouds were among the earliest examples of dusty plasma in space.4 These are layers of ice particles at about 82 km altitude observed during summer months above mid and high latitudes. The clouds are located above the normal cloud layers at altitudes of the ionospheric D region. They become visible to observers on the ground after sunset, when the upper layers of the atmosphere are still illuminated by the sun and sunlight is scattered by the ice particles. More recently, Noctilucent clouds are observed by backscattering of laser light with lidar, from the extinction of sunlight that they cause in the atmosphere, observed from satellite,798 and with imaging from balloons.799 All these methods are independent of dust charge and are biased to particles with sizes of several times 10 nm and larger. It is discussed that the formation of ice is more effective because of the existence of smaller meteoric smoke particles that form through the meteoric dust flux as the extinction measurements suggest that meteoric smoke is mixed with the ice.800 Also, rocket observations support the hypothesis that ice particles include smaller meteoric dust.801 

Charge interactions play a role in the formation process.802 While in situ measurements with sounding rockets confirm the existence of charged dust and the in situ detections are often correlated with the radar echoes and optical signals,801,803 the size distribution, charge, and composition of the particles remain mainly unexplored. Smaller particles can under certain conditions be traced with observations of mesospheric radar echoes that form as a result of neutral turbulence and in some cases by the interactions with the solid particles through their surface charging.804 While the participation of ice particles is confirmed for the formation of the mesospheric echoes in summer, called polar mesospheric summer echoes (PMSE), these echoes depend on a number of parameters which makes it difficult to pin down the dust/ice component and its charged interactions with the ionosphere.805 The charged dust also participates but is only rarely observed in the incoherent scattering process and a semi-empirical model to describe the incoherent scattering in the presence of charged dust was recently extended including dust with a size distribution.806 

Electrostatic dust lifting on the lunar surface is a fundamental physical process that has been suggested to explain unresolved observations for more than five decades. For example, the so-called lunar horizon glow is believed to be sunlight scattered off a cloud of ∼10 μm charged dust particles lofted or levitated ∼30 cm above the surface near the terminator, where enhanced electric fields are created due to differential charging between the sunlit and shadowed regions.108,807 Similarly, the observations by the Apollo 17 LEAM experiment of dust movement across lit-dark boundaries808 or the high-altitude nanometer-sized dust lofted up to tens of kilometers height indicated by visual observations of the Apollo astronauts809 have been suggested to be the results of dust charging and mobilization. Recent theoretical and laboratory studies show promising results to understand the dynamics of electrostatic dust lofting and levitation on the lunar surface.

A new patched charge model has been developed based on laboratory experiments, providing a breakthrough in addressing this question.197 The model shows that the emission and re-absorption of photoelectrons due to UV radiation and/or secondary electrons due to electron/ion impacts within subsurface microcavities generate large negative charges on the surrounding particles and intense inter-particle repulsive forces to lift off dust particles. Following this discovery, more laboratory experiments and modeling work have provided new insight into the dust charging and lofting properties, including the initial charge and launch velocities, lofting rates, and size distributions.810–812 

Several opportunities are coming up for the observations of dusty plasmas in the ionosphere. Ongoing Earth observations, the dedicated studies with the MATS satellite813 and the new balloon observations799 provide a basic understanding of the atmospheric structure at NLC and PMSE altitude that will help to investigate dusty plasma at these altitudes. The upcoming EISCAT3D radar with advanced capabilities for incoherent scatter observations814 will improve chances to measure the influence of dust on the incoherent scatter signal and its tri-static configuration improves the diagnostic of the PMSE formation.815 

FIG. 11.

Example of dust ejected by an atmospheric pressure Ar/HMDSO flow-through plasma and interacting with a witness sample for contamination control research (courtesy of T. J. A. Staps and T. J. M. Donders, CIMlabs, Eindhoven University of Technology, The Netherlands).

FIG. 11.

Example of dust ejected by an atmospheric pressure Ar/HMDSO flow-through plasma and interacting with a witness sample for contamination control research (courtesy of T. J. A. Staps and T. J. M. Donders, CIMlabs, Eindhoven University of Technology, The Netherlands).

Close modal

The rapidly increasing number of satellites in low-earth and geosynchronous orbits already generates a difficult-to-solve problem of accumulating space debris. Possible dusty plasma effects can alter the lifetimes of debris816 and could offer a novel way to mitigate this hazard.817 

The interest in lunar exploration is going through an unprecedented growth period as several countries are currently engaged in or planning for near future missions to the Moon.818–822 Many of these carry experiments addressing dust and dusty plasma issues on the lunar surface that are now recognized to be of high importance for both scientific and engineering application.

Dusty plasma studies in planetary magnetosphere will have ample opportunity to collect new observations by ESA's Juice mission, launched in April 2023,823 and NASA's Europa Clipper mission, to be launched at the end of 2024,824 both to Jupiter. In addition, NASA long-term plans for the exploration of outer planets include a flagship mission to orbit Uranus.825 In magnetospheres, the dynamics of small charged particles can be shaped, if not dominated, by electromagnetic forces acting simultaneously with gravity, drag, and radiation pressure. Dust particles traversing various regimes adjust their electrostatic charges as dictated by the changing plasma conditions and respond to electric and magnetic forces. Dusty plasma effects can lead to unexpected effects, including transport,826,827 ejection,828,829 and capture830 of small charged grains.807 

The heliosphere includes the solar system dust cloud where dust particles form through collisions of larger objects, and also are emitted from comets. New space observations in the vicinity of the Sun motivated studies of charged dust trajectories in the vicinity of the Sun or other stars. The trajectories of nanometer-sized dust that was released from larger particles were investigated using numerical simulations and theoretical models considering the effect of plasma corotation close to the Sun/star. As in previous studies, it was found that nanodust in the vicinity of the Sun or other stars and the effect of plasma corotation is strong for the high rotation rates and/or a low stellar wind speed.831 Trapping conditions are variable and, for instance, large fractions of trapped particles can escape during coronal mass ejections.832 

The charged dust trajectories were also investigated for the inner planetary debris disks around Vega and Fomalhaut because both stars display a thermal emission brightness that could possibly arise from hot dust near the stars.833,834 It was found that, in comparison to the Sun, the trapping conditions would occur closer to the stars because their faster rotation leads to a more closely wound-up magnetic field spiral.835 

Another example of dust being influenced by plasma is the modulation of the interstellar flux into the heliosphere with the solar cycle. While this modulation is qualitatively understood our models do not satisfactorily explain the variability and direction of the interstellar dust flux.836–838 NASA's upcoming interstellar mapping and acceleration probe (IMAP), as well as JAXA's Destiny+ missions839,840 to be launched in 2025, will carry dust instruments to monitor the flow of interstellar dust through the inner heliosphere, and observe its variability modulated by the solar cycles, however, superimposed with the solar system dust fluxes. The Parker Solar Probe and the Solar Orbiter at present explore the near solar inner heliosphere and carry antenna instruments that also measure dust impacts. From analyses so far, many of the results can be explained with the orbits of dust that are influenced of gravity force and radiation pressure.772,841 Charged dust trajectories can become particularly important in the perihelion passages, and parker solar probe can encounter particles that are in trapped orbits since the trapping can for instance occur for 30–75 nm particles that were created inward from 0.16 AU from the Sun.774 

In addition to naturally occurring phenomena, dusty plasma effects can offer a uniquely efficient approach to cleaning optical surfaces, exposed mechanical devices, thermal radiators, and astronaut's suits, all essential to mitigate dust hazards and enable the planned long-term presence of humans on the lunar surface and eventually on Mars. Dusty surfaces exposed to electron beams with optimized fluxes, energy distributions, and directions can be efficiently cleaned, removing even the smallest nm-sized dust particles.842–844 

Future space missions and ground-based observations of the near-Earth environment, lunar surface, near solar/stellar regions, comets, asteroids, planetary rings embedded in magnetospheres, our entire heliosphere, and beyond, will have to address dusty plasma issues, including dust charging, mobilization, transport, and yet to be identified, collective effects, in designing, analyzing, and interpreting new observations.

Dust particles immersed in an environment of ionized gas are known to get (mostly negatively) charged by the collection of plasma species. This feature—together with the typical characteristics of plasma and possibly with the assistance of mechanical vibrations, gas flows, electric fields, and/or photon or electron beam irradiation, may exert additional forces on the particles releasing them from surfaces or altering their location and trajectories (see Fig. 11). Hence, this charging enables opportunities to control and mitigate particle contamination issues in a multitude of scientific endeavors and applications. In the current section, we elaborate on the current status regarding (nano)particle contamination control related research and highlight some perspectives on possible high-potential future research directions. In this contribution, we mainly focus on surface release and gas phase steering of contaminating particles and less on their deposition on secondary surfaces.

It was back in 1989 that Selwyn et al. discovered for the first time the presence of plasma-generated dust particles in an IBM plasma processing reactor.390 The fact that in those experiments the micrometer-sized particles—made visible by in situ laser light scattering—appeared to remain levitated in the plasma above the surface, already indicated that plasma can affect the location and movement of such contaminants. Essentially, this was the first encounter of the most fundamental plasma-assisted contamination control mechanism, i.e., the plasma self-induced electric fields E at the plasma's borders (sheaths) interacted with the plasma-deposited surface charge Q on the particles, and generated an electric force F E = Q · E affecting the particles' positions and trajectories.

Ever since, particle contamination issues in (or due to) plasma environments have appeared in many scientific, instrumental, and industrial areas. For instance, extraterrestrial exploration (e.g., of the Moon, Mars, or other outer-space objects) can be (negatively) impacted by the accumulation of surface-released dust particles on diagnostic instruments845–847 and solar panels848 (see Sec. XIII). Often these particles are charged by ultraviolet light irradiation108,849–851 and by the solar wind plasma.807,852 In extreme ultraviolet (EUV) lithography scanners, contamination of critical imaging surfaces with particles as small as 50 nm significantly impacts the overall performance and yield of the systems and, therefore, needs to be controlled.853–855 The particles in such scanners may be embedded in and/or irradiated by a photon-induced plasma and ionizing radiation.856–860 In plasma material processing tools, surfaces to be processed may suffer from (and be dysfunctionalized by) contamination with particulates that are either released from the environment and reactor walls or that are in situ plasma-synthesized from the precursor gas and/or components that are sputtered and etched from surfaces. Especially in the 1990s, significant research efforts have been made to study particle formation, electrical charging, transport, and trapping of particles in (afterglow) plasma processes.390,861–875 In contrast to most examples, where plasma is inevitably present, sometimes plasma is generated intentionally for contamination control purpose. For instance, an in situ plasma-assisted particle seal was proposed for application in robotic feedthroughs in ultra-clean vacuum systems such as those used in semi-conductor processing equipment, EUV lithography scanners, and electron microscopes.876–879 Finally, in nuclear fusion devices, dust particles may be produced by energetic plasma–surface interactions.52,55,115 In addition to possibly having a detrimental effect on the plasma operation itself, these contaminants may be radioactive and toxic and, hence, may impact public health in the case of a large-scale accident. This topic is discussed extensively in Sec. VIII of this Perspective paper. The rapid developments of the above-mentioned areas in which dust particle contamination plays a crucial role have boosted both fundamental research endeavors and the development of new technologies to control and mitigate contamination by small particles either on (or from) surfaces or airborne.

With respect to the cleaning of surfaces from particles, be it for application in extraterrestrial missions or in (semi-)industrial processes, many proposed processes use plasma as a basis. Here, plasma-charging of the governing surfaces and contaminants in combination with plasma-self-induced electric fields in the sheath region near the surface is used to generate an electric force on the contaminants that is strong enough to overcome the adhesion force and, hence, to release the particles from the surface. Often, the stochastic nature of charge collection from the plasma by the particles and/or triboelectric charging triggers random/poorly predictable particle release.880–883 Depending on the specific environment conditions, different types of plasma have been applied. Examples include studies of contaminated surface interactions with highly transient EUV-induced plasmas,854,855 electron cyclotron resonance plasma sources in hydrogen (to mimic EUV scanner conditions),884,885 laser-induced plasma shock waves,886 plasma jets generated between two co-axial electrodes,887 and many more. Also, other procedures have been developed, which can be possibly combined with (the generation of) plasma, to influence surface contamination and promote the release of particles from surfaces. One successful method appeared the additional irradiation of particle-laden surfaces with (beams of) electrons,844,881,888–894 which has resulted in the development of the so-called “patched charge model” suggesting that highly localized electric fields in microcavities between particles mutually or between the particles and the surface are responsible for the particles' mobilization. The charge and mobilization of particles on surfaces were also found to be impacted (even in vacuum conditions) by irradiation with ultraviolet (UV) light through the photoelectric effect (e.g., explaining dust levitation from the lunar surface),108,849,850,895,896 electrostatic traveling waves,848 work function-matching coatings,845 high-speed gas jets,897,898 and surface vibrations.899,900

With respect to the mitigation of airborne particles, using plasma has advantages over methods using filters in the sense that plasma-assisted particle removal devices do not obstruct the gas flow. The most basic example for airborne particle removal is the concept of the electrostatic precipitator—invented by Hohlfeld back in 1824 (Ref. 901)—in which particles are electrostatically charged and steered by an electric field toward collector plates. This way of particle filtering has been widely applied in, for instance, coal burning energy plants,902 diesel engines,903 and indoor air cleaners.904 For application in these atmospheric conditions, often corona-like discharges are used.669 Applications in low pressure (roughly below 100 Pa) high-tech environments usually require (capacitively or inductively coupled) plasmas with much more complex geometries. As in these cases, the plasmas, used to charge the particles, also tend to shield the electric fields applied to deflect them, and pulsed plasma operation is usually considered most effective. For these technologies to be developed, in-depth understanding of particle charging and interaction with afterglow plasmas is crucial. Not only targeting this application but also other applications and fundamental curiosity, many experimental and numerical works have been carried out on particle dynamics in temporal,209,905–910 spatial,911,912 and spatiotemporal208,913,914 afterglow plasmas. Particle and aerosol interaction in atmospheric (flow-through) pressure plasmas has been investigated extensively more recently as well652,667,670,915–919 (see Sec. XI). Also, considerable research efforts have been undertaken when it comes to the understanding of the growth of contaminating particles inside chemically reactive gases253,920–929 and the suppression of them in processing plasma applications, i.e., by using sine wave930 or square-wave modulation of the (usually radio frequency) plasma driving signal.931 

In general, using plasma as a key ingredient for novel contamination, control strategies have high potential. Nevertheless, from a physics point of view, the ecosystems in such applications—especially those in high-tech industries—are rather complex, combining complex-structured and highly sensitive surfaces, (ionizing) photons, electrostatic fields, gas flows, and additional irradiation with charge carriers. Also, plasma may have undesirable side-effects and must be properly managed and confined. Before applications can be developed to their full potential, much more understanding and investigation are needed. For applications where plasma is intentionally applied for contamination control purpose, the challenge is to correctly use and steer the complex interplay between the key plasma parameters, such as electron temperature and density, decay rates in the afterglow phases, etc. (which are to a certain extent controllable), the resulting particle charge (which may vary in time and can even become positive) and the consequent surface-release, deflection, and collection methods. The complexity of the interplay lays in the fact that most processes and parameters are mutually interdependent. Possibly even more challenging is the development of contamination strategies for applications in which plasma is inevitably present, e.g., in space exploration applications, materials processing, and EUV lithography applications, as earlier discussed. In those areas, plasma configurations and key parameters are dictated externally and, hence, the right implementation of plasma-facing surfaces, external electric fields, flow conditions, and irradiation with charged particles and/or photons is essential.

In order to drive the general fundamental understanding regarding plasma-enabled (nano)particle contamination control, the following aspects are considered most important:

Plasma-induced chemistry—i.e., unraveling the influence of plasma-induced chemistry on particle morphology change and (the impact thereof on) the release of contamination from surfaces, especially in atmospheres including gases of which the induced plasma may be depositing, oxidizing, or reducing. In this context, the adsorbed layer surrounding a particle should be taken into account explicitly.932 This influence should be connected to an overall theoretical framework regarding particle release from surfaces including effects of e-beam and UV irradiation, plasma-induced and externally applied electric fields, electron and ion impact, particle and surface (de-)charging, and particle migration over the surface.

Spatially decaying and highly transient plasmas—i.e., revealing a detailed description regarding dynamics of spatially decaying and highly transient plasmas and their impact on charging of airborne particles. The stochastic particle charging nature might become dominant even for micrometer sized particles when the electron temperature approaches the ion temperature and the plasma density becomes rather low in the late afterglow phase. Although relatively much research on stochastic charging of particles has been conducted,191,880–883 more detailed understanding remains needed, especially in afterglow conditions.

Nanometer length scales—i.e., obtaining in-depth knowledge on plasma-charging dynamics of nanometer sized particles. The interesting issue of the dominance of stochastic charging processes (see the previous point) especially holds for nanoscale particles. Recent development regarding visualizing of charge on or adjacent to quantum dots may enable such advanced studies in the near future.428,933,934

To manipulate highly charged particles, utilization of electric fields is the most obvious solution.935,936 However, this approach bears a number of difficulties. First of all, a plasma is quasi-neutral and shields very efficient externally applied fields. Thus, electrostatic manipulation is limited to the plasma sheath region or requires to insert additional electrodes937,938 for manipulation purpose into the plasma. Furthermore, the applied voltages will result in currents and this can alter the discharge properties or at least change the local plasma conditions notably. However, for using particles for diagnostic purpose, the plasma should not be altered. Thus, the manipulation of dust particles by means of forces that do not affect the plasma itself is an important issue. Such forces are gravity, neutral drag, thermophoresis, and interaction with intense electromagnetic radiation, i.e., lasers. The following paragraphs will summarize these approaches and their current status and give an outlook on future perspectives of non-electric manipulation for dusty plasma research.

Although gravity itself is not a variable quantity on Earth, it is possible to use rotating systems to utilize centrifugal forces to act as if hyper-gravity conditions would apply. For this purpose, a fully functioning low pressure dusty plasma setup was mounted at TU Eindhoven on the working stage of a centrifuge, capable of inducing up to ten times the Earth’s gravitational acceleration.939 With this setup, the “weight” of micro-particles can be increased while the general plasma parameters are left unchanged. In addition, the angle of the resulting apparent gravity vector can be changed due to a rotational degree of freedom of the facilitating vacuum vessel suspension. This ability, in combination with the magnitude control of the apparent gravity, allows manipulation of the horizontal and vertical particle equilibrium positions in the plasma sheath. First experiments939,940 demonstrated that the electric field and the particle charge as a function of levitation height can be probed in the plasma sheath.

A similar approach using centrifugal forces can be applied to dust clusters via rotating electrodes. Here, the centrifugal force is perpendicular to gravity. The rotating electrode can drive a neutral gas flow which (due to viscosity in the background gas and neutral gas drag of the dust particles) gives rise to a solid body rotation of 2D dust clusters.713 In principle, these experiments are similar to those of Nosenko et al.941,942 where alternating electric fields similar to a Paul trap943 were applied to horizontal boundaries. While Nosenkos approach drives an ion flow and, thus, affects the plasma, the pure neutral gas drive does not. Interestingly, the circularly moving dust particles are not only subject to centrifugal forces but also to Coriolis forces as well. While the first allows us to measure the screening length via a force balance, the latter allows us (due to a mathematical equivalence of Lorenz and Coriolis force) to study (pseudo) magnetized dust systems377,944 (see Sec. VI).

Another option for additional non-electric forces acting on the dust are thermal gradients. The thermophoretic force is well known for rarefied gases945 and the physics are identical in a weakly ionized plasma system. Hence, with heated and/or cooled electrodes, moderate temperature gradients of about 10 K cm−1 are sufficient to compete with gravity for micro-particles. For example, Rothermel et al.946 used a vertical temperature gradient to counter act gravity and produce 3D microparticle suspensions, which have a similar void structure as those observed under microgravity.

Finally, lasers are a powerful tool for manipulation of particles without changing the plasma conditions. Laser excitations of single microparticles were used for charge determination,947,948 to excite waves,949 to study dynamical properties (shear flows, viscosity, and heat transport), and to increase the average dust kinetic temperature.950–955 The advantage of lasers is that they provide precise control on location and motion of particles in the interaction region and, thus, allow us to address individual particles as well as complete particle systems. The origin of the force is twofold: First, the photons are scattered by the dust particles and, thus, transfer momentum.956,957 Second, a part of the light is absorbed and heats the particle up. If this heating is non-isotropic (e.g., due to the sophisticated intensity pattern of Mie-scattering251), the interaction with the neutral gas causes a so-called photophoretic force.647,958

Optical tweezers959 use strong intensity gradients to trap transparent microparticles. Ito et al.960 succeeded in trapping and etching poly(methyl methacrylate) (PMMA) particles in vertical orientation against gravity. With a modified setup, structural and dynamical properties of a dust cluster have been manipulated.82,961,962 That even a vertical controlled motion of particles in the plasma sheath is possible was shown by Schneider and Kersten using two counter-propagating laser beams.963 

However, it has to be noted that intense lasers yield a heating of the particle which can cause reversible surface modifications567 or even damage the particle and lead to strong accelerations.964 

As listed above, there are a number of powerful and established non-electric methods which allow us to manipulate particles. Such experiments can be used to gain insight into the physics of the dust component. Furthermore, manipulated individual probe particles can deliver information about the surrounding plasma or sheath properties.

For example, thermophoresis was successfully used to (partially) compensate gravity and may complement the hyper-gravity experiments making the regime up to zero-gravity conditions accessible in the lab946,965 (see Secs. VI and IX). If gravity is only partly compensated and an additional radial confinement (glass box) is used, finite 3D dust clusters can be created.966,967 The experiments and simulations on these so-called Yukawa-balls allowed us to explore structural and dynamical properties of finite 3D strongly coupled systems for the first time.330 This shows that thermophoresis is a powerful tool to alter trapping conditions. Its rather simple technical realization will certainly make it a first choice in future if specific trapping conditions are needed to study structural and dynamical processes in dusty plasmas. In addition to this common thermophoresis, especially thermal creep flows968–970 might play a role for dust particle growth.971 

So far, laser manipulation has established as a standard tool to trigger or control dynamical processes in complex plasmas. Lasers are used to control the kinetic temperature of the dust component as well as to trigger collective particle motion or instabilities and the exploration of dynamical processes in complex plasmas is still ongoing. Certainly, laser manipulation will remain one of the working horses in experimental complex plasma research. A few examples for recent and future activities are studies of cold fluids and their viscoelastic properties972–976 and the excitation of selective modes.961 Furthermore, it might be possible to generalize the optical tweezers approach and generate optical lattices in order to tailor the structural properties of particle arrangements. These lattices would allow us to tailor the local confinement geometry and strength, for a systematic variation of kappa, which is so far not possible.

A peculiarity of laser manipulation of particles is that two forces are involved: radiation pressure and photophoresis. While the first only depends on the intensity of the radiation, the latter increases with neutral gas pressure and its magnitude and direction depends on the optical properties of the particles. Hence, two particle species of different material within the same plasma volume and being illuminated by the same light source will not experience the same net-force. For example, for binary systems,977 an increase in kinetic temperature of the particles via a laser heating system952 will result in a binary system, where the individual particle species have different kinetic temperatures.567 This can be utilized to study basic thermodynamics in the system, e.g., to measure entropy directly567 according to its basic statistic definition of Boltzmann and Gibbs. This example shows that the specific properties of radiation pressure and photophoresis can be tailored and utilized to explore fundamental properties of complex plasmas. Additionally, photophoresis plays and important role in configuring optical tweezers. The development of the next generation of such devices for complex plasmas will strongly benefit from being able to quantify radiation pressure and photophoresis.

On the other hand, the particles can be utilized as probes. Since the microparticles can be observed in the plasma sheath easily, they can serve, in particular, as electrostatic probes for the characterization of the potential surfaces and electric fields in this region.937,978,979 Usually, the plasma sheath, which is an important zone of energy consumption and, hence, often the essential part of a discharge for applications, is difficult to monitor by common plasma diagnostics, such as Langmuir-probes or optical spectroscopy. By monitoring the dependence of the position and motion of the particles on the discharge parameters, information can be obtained on the electric field in front of electrodes or substrate surfaces, respectively, where other plasma diagnostic methods fail.

The optical tweezers approach963,980 allows us to determine the sheath width and the forces acting on a single charged particle. Furthermore, combining this technique with a so-called dual-frequency discharge,981 different forces in the plasma sheath can be determined depending on the frequency combination of the discharge.982 The vertical movement of a particle by optical traps through the sheath region of a rf plasma toward the electrode surface opens up new possibilities to study the electric field forces, the ion drag force, or the influence of secondary electrons by using different electrode materials. Probing the sheath region with single particles provides data and information for theoretical models and simulations (see Secs. II and III) and gives new insight into the physics of this space charge region. It demonstrates that the technologically important plasma sheath becomes experimentally accessible using particles as probes. Especially, if these are combined with recent developments in electrostatic particle manipulation, the sheath properties can be studied in more detail.

Using a stepwise electric excitation of the particle983 gives an optimum with respect to accuracy and minimum measurement time. It allows us to probe the particle charge in the plasma sheath as a function of distance to the confining electrode and to quantify the repulsive Coulomb interaction force acting between two microparticles including the screening length.940 

The editors of this Perspective article, Job Beckers and Mikhail Pustylnik, are thankful to Ph.D. student Tim Donders for his support during the editing process.

Job Beckers acknowledges the financial support from the Dutch Research Council NWO (Project No. 15710).

Johannes Berndt and Eva Kovačević acknowledge the project PEGASUS (Plasma Enabled and Graphene Allowed Synthesis of Unique nano-structures), funded by the European Union's Horizon research and innovation program under Grant Agreement No. 766894 and the EU Graphene Flagship FLAG-ERA III JTC 2021 project VEGA (No. PR-11938), as well as the support obtained via ARD MATEX Region Center, France and project Orleans Metropole, France.

Dietmar Block acknowledges funding by the Deutsche Forschungsgemeinschaft (DFG) in Project Nos. BL555 3-2 and BL555 4-2.

Peter J. Bruggeman acknowledges the U.S. Department of Energy under Award No. DE-SC-0020232, the National Science Foundation under Award No. PHYS 1903151, and the Army Research Office under Grant No. W911NF-20-1-0105.

Lénaïc Couëdel acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) (Grant No. RGPIN-2019-04333).

Gian Luca Delzanno acknowledges the Laboratory Directed Research and Development Program of Los Alamos National Laboratory under Project No. 20230668ER. Los Alamos National Laboratory is operated by Triad National Security, LLC, for the National Nuclear Security Administration of U.S. Department of Energy (Contract No. 89233218CNA000001).

Yan Feng acknowledges the support from the National Natural Science Foundation of China (Grant No. 12175159).

Ranganathan Gopalakrishnan acknowledges the funding support from U.S. Department of Energy Early Career (Award No. DE-SC0021146) from the Office of Fusion Energy Sciences, U.S. Army Research Office (Award No. W911NF-23-2-0013), and NSF Plasma Physics (Award No. 1903432).

Franko Greiner thanks the Deutsche Forschungsgemeinschaf (DFG) for funding of Project No. GR1608/8-1 Dusty plasmas with high electron depletion: Investigation of fundamental mechanisms and properties through particle and plasma diagnostic.

Peter Hartmann acknowledges the Hungarian National Office for Research, Development and Innovation (NKFIH) (Grant No. K134462).

Mihaly Horányi acknowledges the NASA Solar System Exploration Research Virtual Research Institute's (SSERVI), Institute for Modeling Plasmas, Atmospheres, and Cosmic Dust (IMPACT).

Christina A. Knapek acknowledges Funding (Grant No. DLR/BMWi FKZ 50WM2161).

Uwe Konopka acknowledges that his work was supported by NASA-JPL (Subcontract Nos. 1679198 and 1655063).

Uwe Kortshagen acknowledges the support from the Army Research Office under MURI (Grant No. W911NF-18-1-0240) and from the U.S. Department of Energy under Grant No. DE-SC0022242.

Evdokiya G. Kostadinova acknowledges the U.S. National Science Foundation 2694 (Nos. NSF-1903450 and NSF-2308742).

Sergei I. Krasheninnikov acknowledges the support of the work by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences under Award No. DE-FG02-06ER54852 at UCSD.

I. Mann was supported by the Research Council of Norway through Grant Nos. NFR 275503 and NFR 240065.

Davide Mariotti acknowledges EPSRC (Award No. EP/V055232/1).

Lorin Swint Matthews acknowledges the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences (Award No. DE-SC-0021334), U.S. Department of Energy Grant No. DE-SC0021334, NVIDIA Corporation Applied Research Accelerator Program, and the U.S. National Science Foundation (No. NSF-1903450).

André Melzer acknowledges the DLR German Space Agency (50 WM 2161 and 50 WM 1962).

Maxime Mikikian acknowledges the funding (Grant Nos. DLR/BMBF 50WM9852, CNES 02/CNES/4800000059, ANR-11-JS09-0010, and ANR-19-CE40-0023).

Volodymyr Nosenko, Mikhail Y. Pustylnik, and Hubertus M. Thomas acknowledge the funding (Grant Nos. DLR/BMWi FKZ's 50WM1441, 50WP1203, 50WP0700, 50WP0203, and 50WP9852).

The work of Svetlana Ratynskaia and Panagiotis Tolias has been carried out within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Program (Grant Agreement No. 101052200-EUROfusion). Views and opinions expressed are, however, those of the author(s) only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them.

R. Mohan Sankaran acknowledges the U.S. Department of Energy under Grant No. DE-SC0018202 and the Air Force Office of Scientific Research under Grant No. FA9550-19-1-0088.

Elijah J. Thimsen acknowledges the financial support from the Army Research Office (ARO) MURI (Grant No. W911NF-18-1-0240).

Edward Thomas, Jr. acknowledges the U.S. Department of Energy (No. SC-0019176) and the U.S. National Science Foundation (No. OIA-2148653).

Yes, Dr. Andre Melzer is a co-author of this paper and associate editor at Physics of Plasmas. Hence, editing duties for Dr. Melzer regarding this paper should be avoided.

Job Beckers and Mikhail Pustylnik, the authors of Sec. I, are the editors and co-first authors of this Perspective.

Job Beckers: Writing – original draft (equal); Writing – review & editing (equal). Franko Greiner: Writing – original draft (equal). Peter Hartmann: Writing – original draft (equal). Mihaly Horanyi: Writing – original draft (equal). Holger Kersten: Writing – original draft (equal). Christina A. Knapek: Writing – original draft (equal). Uwe Konopka: Writing – original draft (equal). Uwe R. Kortshagen: Writing – original draft (equal). Evdokiya G. Kostadinova: Writing – original draft (equal). Eva Kovacevic: Writing – original draft (equal). Sergei Krasheninnikov: Writing – original draft (equal). Johanes Berndt: Writing – original draft (equal). Ingrid Mann Mann: Writing – original draft (equal). Davide Mariotti: Writing – original draft (equal). Lorin Swint Matthews: Writing – original draft (equal). Andre Melzer: Writing – original draft (equal). Maxime Mikikian: Writing – original draft (equal). Volodymyr Nosenko: Writing – original draft (equal). Mikhail Pustylnik: Writing – original draft (equal); Writing – review & editing (equal). Svetlana Ratynskaia: Writing – original draft (equal). R. Mohan Sankaran: Writing – original draft (equal). Viktor Schneider: Writing – original draft (equal). Dietmar Block: Writing – original draft (equal). Elijah Thimsen: Writing – original draft (equal). Edward Thomas, Jr.: Writing – original draft (equal). Hubertus M. Thomas: Writing – original draft (equal). Panagiotis Tolias: Writing – original draft (equal). M. A. van de Kerkhof: Writing – original draft (equal). Michael Bonitz: Writing – original draft (equal). Peter J. Bruggeman: Writing – original draft (equal). Lénaïc Couëdel: Writing – original draft (equal). Gian Luca Delzanno: Writing – original draft (equal). Yan Feng: Writing – original draft (equal). Ranganathan Gopalakrishnan: Writing – original draft (equal).

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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