The theoretical description of complex (dusty) plasmas requires multiscale concepts that adequately incorporate the correlated interplay of streaming electrons and ions, neutrals and dust grains. Knowing the effective dust-dust interaction, the multiscale problem can be effectively reduced to a one-component plasma model of the dust subsystem. The goal of this paper is a systematic evaluation of the electrostatic potential distribution around a dust grain in the presence of a streaming plasma environment by means of two complementary approaches: (i) a high-precision computation of the dynamically screened Coulomb potential from the dynamic dielectric function and (ii) full 3D particle-in-cell simulations, which self-consistently include dynamical grain charging and nonlinear effects. The range of applicability of these two approaches is addressed.

Warm dense matter (WDM) -an exotic state of highly compressed matter -has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first ab initio data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim et al., Phys. Plasmas 24, 056303 (2017) and Phys. Rep. 744, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, ab initio results for the static local field correction G(q) and for the dynamic structure factor S(q, ω). These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models.In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, timedependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.

We propose and demonstrate a concept that mimics the magnetization of the heavy dust particles in a complex plasma while leaving the properties of the light species practically unaffected. It makes use of the frictional coupling between a complex plasma and the neutral gas, which allows us to transfer angular momentum from a rotating gas column to a well-controlled rotation of the dust cloud. This induces a Coriolis force that acts exactly as the Lorentz force in a magnetic field. Experimental normal mode measurements for a small dust cluster with four particles show excellent agreement with theoretical predictions for a magnetized plasma.

Solids facing a plasma are a common situation in many astrophysical systems and laboratory setups. Moreover, many plasma technology applications rely on the control of the plasma-surface interaction, i.e. of the particle, momentum and energy fluxes across the plasma-solid interface. However, presently often a fundamental understanding of them is missing, so most technological applications are being developed via trial and error. The reason is that the physical processes at the interface of a low-temperature plasma and a solid are extremely complex, involving a large number of elementary processes in the plasma, in the solid as well as fluxes across the interface. An accurate theoretical treatment of these processes is very difficult due to the vastly different system properties on both sides of the interface: quantum versus classical behavior of electrons in the solid and plasma, respectively; as well as the dramatically differing electron densities, length and time scales. Moreover, often the system is far from equilibrium. In the majority of plasma simulations surface processes are either neglected or treated via phenomenological parameters such as sticking coefficients, sputter rates or secondary electron emission coefficients. However, those parameters are known only in some cases and with very limited accuracy. Similarly, while surface physics simulations have often studied the impact of single ions or neutrals, so far, the influence of a plasma medium and correlations between successive impacts have not been taken into account. Such an approach, necessarily neglects the mutual influences between plasma and solid surface and cannot have predictive power.In this paper we discuss in some detail the physical processes a the plasma-solid interface which brings us to the necessity of coupled plasma-solid simulations. We briefly summarize relevant theoretical methods from solid state and surface physics that are suitable to contribute to such an approach and identify four methods. The first are mesoscopic simulations such as kinetic Monte Carlo (KMC) and molecular dynamics (MD) that are able to treat complex processes on large scales but neglect electronic effects. The second are quantum kinetic methods based on the quantum Boltzmann equation that give access to a more accurate treatment of surface processes using simplifying models for the solid. The third approach are ab initio simulations of surface process that are based on density functional theory (DFT) and time-dependent DFT. The fourths are nonequilibrium Green functions that able to treat correlation effects in the material and at the interface. The price for the increased quality is a dramatic increase of computational effort and a restriction to short time and length scales. We conclude that, presently, none of the four methods is capable of providing a complete picture of the processes at the interface. Instead, each of them provides complementary information, and we discuss possible combinations. PACS numbers:

Comparative studies of capacitively coupled radio-frequency discharges in helium and argon at pressures between 10 and 80 Pa are presented applying two different fluid modelling approaches as well as two independently developed particle-in-cell/Monte Carlo collision (PIC/MCC) codes. The focus is on the analysis of the range of applicability of a recently proposed fluid model including an improved drift-diffusion approximation for the electron component as well as its comparison with fluid modelling results using the classical drift-diffusion approximation and benchmark results obtained by PIC/MCC simulations. Main features of this time-and spacedependent fluid model are given. It is found that the novel approach shows generally quite good agreement with the macroscopic properties derived by the kinetic simulations and is largely able to characterize qualitatively and quantitatively the discharge behaviour even at conditions when the classical fluid modelling approach fails. Furthermore, the excellent agreement between the two PIC/MCC simulation codes using the velocity Verlet method for the integration of the equations of motion verifies their accuracy and applicability.

Abstract. The electrostatic potential of a moving dust grain in a complex plasma with magnetized ions is computed using linear response theory, thereby extending our previous work for unmagnetized plasmas [P. Ludwig et al., New J. Phys. 14, 053016 (2012)]. In addition to the magnetic field, our approach accounts for a finite ion temperature as well as ion-neutral collisions. Our recently introduced code Kielstream is used for an efficient calculation of the dust potential. Increasing the magnetization of the ions, we find that the shape of the potential crucially depends on the Mach number M . In the regime of subsonic ion flow (M < 1), a strong magnetization gives rise to a potential distribution that is qualitatively different from the unmagnetized limit, while for M > 1 the magnetic field effectively suppresses the plasma wakefield.

The existence of plasma oscillations at multiples of the magnetoplasmon frequency in a strongly coupled two-dimensional magnetized Yukawa plasma is reported, based on extensive molecular dynamics simulations. These modes are the analogues of Bernstein modes which are renormalized by strong interparticle correlations. Their properties are theoretically explained by a dielectric function incorporating the combined effect of a magnetic field, strong correlations and finite temperature.PACS numbers: 52.27.Gr, 52.27.Lw Two-dimensional (2D) systems with strong correlations, i.e. with the interaction energy exceeding the thermal energy, show a number of unusual properties ranging from anomalous phase transitions (Kosterlitz-Thouless scenario), to anomalous transport, e.g. [1,2]. Examples include electrons on helium droplets and in quantum dots [3], ions in traps [4] and dusty plasmas, e.g. [5,6]. A particular correlation effect is observed in the collective oscillation spectrum of 2D Coulomb and Yukawa liquids [5,7,8] where a transverse shear mode has been predicted by Kalman and Golden [9,10]. This mode does not exist in an ideal system but has experimentally been observed in strongly coupled systems [11,12]. Similarly, in the presence of a strong magnetic field a 2D plasma shows two coupled modes -a magnetoplasmon and a magentoshear mode (upper and lower hybrid modes) which have recently been studied in detail in the liquid and crystal phases [6][7][8].Here we show that a strongly correlated 2D Yukawa plasma (2DYP) possesses additional collective modes. We demonstrate that these are related to Bernstein modes (BM) [13] which are well known in hightemperature classical, e.g. [14,15] and quantum plasmas, e.g. [16,17]. However, these are all nearly ideal plasmas. Here we demonstrate that such modes can also exist in strongly correlated systems but they have a number of peculiar properties arising from the combined effect of correlations and the magnetic field.Model and simulation method. Our 2DYP consists of N particles in a quadratic monolayer (with periodic boundary conditions), subject to a magnetic field perpendicular to the plane and interacting by Yukawa forces. The coupled Newton's equations are (i = 1 . . . N )with the Debye screening length λ D and charge Q.Here we define the Wigner-Seitz radius a = (n 0 π)(where n 0 is the areal density) and the frequency ω 0 = (2πQ 2 n 0 /ma) 1/2 , to be distinguished from the kdependent 2D analogon of the plasma frequency,In thermodynamic equilibrium, the system is fully characterized by three parameters -the dimensionless inverse screening length κ = a/λ D , the Coulomb coupling parameter Γ = Q 2 /(ak B T ) and the dimensionless magnetic field strength, β = ω c /ω 0 , with the cyclotron frequency ω c = QB/mc. Eq.(1) is solved by a standard microcanonical MD technique, with data acquisition starting after the system has equilibriated to the desired temperature (Γ). The longitudinal and transverse collective excitation spectra, L(k, ω) and T (k, ω), respectively, are computed...

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correla-