Dust particles in a plasma are charged negatively and are subject to various types of forces, including a drag force by plasma particles and a force due to the collective nature of a plasma. Dust particles are found in a sheath in laboratories balanced by the gravitational force and the electric force, while dust particles in space are ubiquitous, including planetary magnetospheres and interstellar space. Because of the novel nature of a complex system involving plasma particles and dust particles in a collective way, the dusty plasma is often called a complex plasma. The complex plasma is characterized by two distinctly different scales in time and in space. The plasma with electrons, ions and neutrals is characterized by the collective motion with a fast time scale and a short wavelength, while the dust particles move in a slow time scale and a long spatial scale. Some fundamental aspects of a complex plasma are reviewed and possible applications are discussed.

Debye screening potential and wake potential for a moving dust grain in a collisionless plasma with ion flow is studied. When a relative velocity of the dust grain exceeds the ion acoustic velocity, the oscillatory wake potential is formed in a circular cone behind the particle and produces potential minima in a periodic manner. The ion acoustic collective effects on dust particles contribute to the formation of the periodic structure. The characteristic spacing between the potential minima are several times of Debye wavelength in height and in radius. Such a periodic structure may be relevant to the formation of Coulomb quasilattices (plasma crystals) observed in the dusty plasma laboratory experiments.

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It is shown that charged dust grains in a sheath region with plasma ion flow can attract each other in the wake potential cone of an upstream dust particulate. Because of the periodic nature of the potential, periodic structures of the dust grains can be formed in a base plane of the cone.

A bow shock is observed in a two-dimensional supersonic flow of charged microparticles in a complex plasma. A thin conducting needle is used to make a potential barrier as an obstacle for the particle flow in the complex plasma. The flow is generated and the flow velocity is controlled by changing a tilt angle of the device under the gravitational force. A void, microparticle-free region, is formed around the potential barrier surrounding the obstacle. The flow is bent around the leading edge of the void and forms an arcuate structure when the flow is supersonic. The structure is characterized by the bow shock as confirmed by a polytropic hydrodynamic theory as well as numerical simulation.