Physics and applications of dusty plasmas: The Perspectives 2023

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 theory^5,27,28 together with the linearization of a BGK-type ion kinetic equation with point-sinks^29,30 or the drift-diffusion approximation^31,32 have quantified non-Yukawa aspects. In the presence of electron emission^8,33 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 proposed^57,58 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 studies^61,62 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 

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 simulations^85–88 have been reported. Interpolation between analytical limits is advisable. Many lessons can be learnt from the tokamak probe theory.^60,89

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 

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.

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 tokamaks^115,116 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 

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.

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 solver^154,155 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 

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 probes^216,217 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.

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 

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 without^231,232 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 spectroscopy^236–238 

• 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 plasmas^247,248 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.

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 microgravity^262,263 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 graphite^278,279 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 observed^293–295) 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.

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) technique^321,322 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, Z_p = 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 filamentation^364,369) 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).

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 

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.

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.

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 

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.

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 plasmas^402,403 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 time^390,391,411 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.