The ability of a dusty plasma crystal to induce transverse motion to a relativistic electron, as a microstructure wiggler field in a free-electron laser ͑FEL͒, is presented. A dusty crystal wiggler with micrometer size can decrease FEL wavelength several orders of magnitudes. A relativistic electron dynamic through a two-dimensional monolayer hexagonal dusty crystal is analyzed. In addition to the usual transverse wiggling motion, second-harmonic amplitude is induced to the axial velocity. These conditions are compared with a magnetostatic planar wiggler, and it is shown that E 0x / V ʈ0 in dusty crystal has a role of B w in a magnetostatic wiggler. The strength of this proposed wiggler can be increased by decreasing d, decreasing d / D ratio, or increasing q d in different experimental setups.

Two-dimensional plasma crystal formation in an asymmetric confinement force is studied by numerical simulation. Some dependencies between dust and crystal parameters are presented for symmetric crystals. Relationships between dust distance and internal electrostatic potential energy of dust particles to the system parameters are deduced from numerical results. By implementation of asymmetry in horizontal electrostatic confinement force, crystals with only a few long rows, or even one row, can be formed by any arbitrary number of dust particles. Finally, a transition between numbers of rows is introduced as a function of an asymmetry factor. These crystals with only a few rows may be of interest for some theoretical and experimental researchers.

We focus on molecular dynamics simulated two-dimensional complex plasma crystals. We use rigid walls as a confinement force and produce square and rectangular crystals. We report various types of two-row crystals. The narrow and long crystals are likely to be used as wigglers; therefore, we simulate such crystals. Also, we analyze the electric fields of simulated crystals. A bit change in lattice parameters can change the internal structures of crystals and their electric fields notably. These parameters are the number of grains, grains charge, length, and width of the crystal. With the help of electric fields, we show the details of crystal structures.

Two-dimensional complex plasma crystal is a suspended single-layer of micron-size grains in a plasma. The narrow and long two-row crystals are likely to be used as electrostatic wigglers. Therefore, electric properties of such system is studied in the present work. The frequency of longitudinal electric field is twice the frequency of transverse electric field. In two-row crystals, far from the crystal center, both longitudinal and transverse electric fields decrease continuously. Frequency of longitudinal field decreases also, but the frequency of transverse field is fix. By increasing distance between the crystal rows, the frequency of transverse field does not change but the frequency of longitudinal field decreases. Value of both fields decrease while their ratio increases. By increasing longitudinal distance between the grains, the frequency of transverse field does not change but the frequency of longitudinal field increases until become twice the frequency of transverse field, and both electric fields increase while their ratio decreases. These results may be useful in various fields of physics.