Since the 1980s, a new branch of plasma physics has emerged - the study of dusty plasmas. Because of similarities with complex fluids, dusty plasmas are also known as complex plasmas. This field has roots in astrophysics and became interesting for laboratory plasma research when dust formation and dust trapping was observed during plasma etching of silicon.

Dusty plasmas contain, among electrons and atomic or molecular ions, microscopic particles with sizes ranging from some ten nanometers to several ten micrometers. The dust particles become electrically charged and interact with the other plasma constituents. When the density of dust particles is sufficiently high, the electrostatic interparticle forces become important. The dust subsystem can develop collective behavior, which manifests itself as wave phenomena or, for micrometer particles carrying several thousand elementary charges, by the formation of liquid or solid phases.

The discovery of plasma crystallization, in 1994, by three independent groups, gave a strong boost to the field of dusty plasmas. For dusty plasmas with micrometer sized particles, the motion of all individual particles can be followed by fast video-cameras. This is a unique opportunity to study the collective behavior of an ensemble of charged particles at the kinetic level. In 2004, our group succeeded in creating three-dimensional spherical plasma crystals.

When microparticles are embedded in an environment with streaming ions, the particles typically form chains. This can be a hint at attractive forces. But, does this not contradict all textbooks on electrostatics? Like charged particles are known to repel each other. Closer inspection shows that this is only strictly true in a vacuum. In a plasma, the environment is made up of charged particles, electrons and positive ions. Therefore, a pair of negatively charged dust particles can accumulate sufficient positive ion charge between them to overcome the repulsion of the naked charges. The same principle works in atomic physics: a single electron is sufficient to bind two protons in the hydrogen ion molecule. But why are the microparticles forming aligned chains?

Let us consider two particles of slightly different mass, which are levitated by the sheath electric field in planes L1 and L2. The same electric field is responsible for the ion flow towards the electrode. The negatively charged upstream particle acts as an electrostatic lens and focuses the ion flow. Therefore, in the focal region, the positive ion density is enlarged and can attract the particle that is free to move in its levitation plane L2. In this way, the upstream particle attracts the downstream particle. An apparent paradoxon is the fact that, in this situation the interaction force is nonreciprocal. Does this mean that Newton's actio = reactio principle is violated? The answer is no. The downstream particle also develops an ion focus on its downstream side. But this positive surplus charge is much farther away from the upstream particle, which makes the force on the upstream particle weaker than vice versa. Again: Newton's principle is not violated for the particle pair,because we have to include the additional interaction force with the streaming medium of positive ions.

The complex structure of ion wakes becomes evident from molecular dynamics simulations. An example is shown for two particles in a magnetized plasma with a downward ion flow. The particle positions are marked with a cross-hair symbol. The focusing of ions becomes evident by the enhanced ion density (red spots) immediately behind the wake. A more diffuse ion cloud (green) embeds both particles. Further downstream, an ion-free "shadow" (dark violet) is found, which is a typical feature of strongly magnetized plasmas. The electric potential distribution is overlaid by full contours for positive potentials and dotted contours for negative potentials, in steps of 100mV.

Chain formation: Particles are aligned with the downward ion flow [from Trottenberg et al, Plasma Sources Sci. Technol. 4, 450 (1995) DOI ].

Particle wakes: (left) Levitation and attractive forces in the plasma sheath [from: Piel, Plasma Physics, 2nd ed.]. (right) Molecular dynamics simulation of a two-particle wake in the presence of a magnetic field. [from: Piel et al, Phys. Plasmas 25, 083702 (2018) DOI ].