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.

The full melting of a two-dimensional plasma crystal was induced in a principally stable monolayer by localized laser stimulation. Two distinct behaviors of the crystal after laser stimulation were observed depending on the amount of injected energy: (i) below a well-defined threshold, the laser melted area recrystallized; (ii) above the threshold, it expanded outwards in a similar fashion to mode-coupling instability-induced melting, rapidly destroying the crystalline order of the whole complex plasma monolayer. The reported experimental observations are due to the fluid mode-coupling instability, which can pump energy into the particle monolayer at a rate surpassing the heat transport and damping rates in the energetic localized melted spot, resulting in its further growth. This behavior exhibits remarkable similarities with impulsive spot heating in ordinary reactive matter.

In this article, the stability of a complex plasma monolayer levitating in the sheath of the powered electrode of an asymmetric capacitively coupled radio-frequency argon discharge is studied. Compared to earlier studies, a better integration of the experimental results and theory is achieved by operating with actual experimental control parameters such as the gas pressure and the discharge power. It is shown that for a given microparticle monolayer at a fixed discharge power there exist two threshold pressures: (i) above a specific pressure $p_{\mathrm{cryst}}$, the monolayer always crystallizes; (ii) below a specific pressure $p_{\mathrm{MCI}}$, the crystalline monolayer undergoes the mode-coupling instability and the two-dimensional complex plasma crystal melts. In between $p_{\mathrm{MCI}}$ and $p_{\mathrm{cryst}}$, the microparticle monolayer can be either in the fluid phase or the crystal phase: when increasing the pressure from below $p_{\mathrm{MCI}}$, the monolayer remains in the fluid phase until it reaches $p_{\mathrm{cryst}}$ at which it recrystallizes; when decreasing the pressure from above $p_{\mathrm{cryst}}$, the monolayer remains in the crystalline phase until it reaches $p_{\mathrm{MCI}}$ at which the mode-coupling instability is triggered and the crystal melts. A simple self-consistent sheath model is used to calculate the rf sheath profile, the microparticle charges, and the microparticle resonance frequency as a function of power and background argon pressure. Combined with calculation of the lattice modes the main trends of $p_{\mathrm{MCI}}$ as a function of power and background argon pressure are recovered. The threshold of the mode-coupling instability in the crystalline phase is dominated by the crossing of the longitudinal in-plane lattice mode and the out-of plane lattice mode induced by the change of the sheath profile. Ion wakes are shown to have a significant effect too.

The kinematics of dust particles during the early stage of mode-coupling induced melting of a two-dimensional plasma crystal is explored. It is found that the formation of the hybrid mode causes the particle vibrations to partially synchronize at the hybrid frequency. Phase- and frequency-locked hybrid particle motion in both vertical and horizontal directions (hybrid mode) is observed. The system self-organizes in a rhythmic pattern of alternating in-phase and antiphase oscillating chains of particles. The spatial orientation of the synchronization pattern correlates well with the directions of the maximal increment of the shear-free hybrid mode.

In complex plasmas, dust particles are charged through their interactions with the electrons and ions of the surrounding plasma. In low-temperature laboratory plasmas, dust particles most commonly acquire a negative charge. In particular, in a laboratory glow-discharge plasma, the typical charge for a micrometer-size grain generally attains a few thousands of electronic charges. Under stable discharge conditions, this large negative charge is relatively well-characterized. However, for unsteady discharge conditions, the charge can differ and even fluctuate. In particular, when the power source of the discharge is turned off, the charged species of the plasma diffuse away and recombine into neutral species: this is a temporal afterglow. When dust particles are present inside a temporal plasma afterglow, the diffusion of charged species and the plasma decay dynamics are affected. Moreover, the dust particle charges also evolve during the afterglow period. In the late afterglow, dust particles are known to keep residual charges. The value of these residual charges strongly depends on the ambipolar-to-free diffusion transition. In addition, the presence of a constant electric field, causing ions to drift through the neutral gas, has a strong influence on the final dust particle residual charges, eventually leading to large positive residual charges. In this review article, the dynamics of temporal complex plasma afterglow are discussed. Experimental and theoretical results are presented. The basics of temporal afterglow modeling are also given.