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The plasma crystal formed by monodisperse particles trapped in the sheath of an rf discharge is known to show vertically aligned structures. Here, oscillations of the aligned particles are found below a threshold value of gas density as a precursor of the melting transition. Attractive forces due to the formation of a positive space-charge region below the upper particle are calculated from Monte Carlo simulations of ion trajectories in the sheath. The alignment as well as the oscillations of the plasma crystal are explained by a simple model based on the asymmetry of the forces. ͓S1063-651X͑96͒50307-7͔ PACS number͑s͒: 52.25. Vy, 52.35.Ϫg, 62.30.ϩd The formation of Wigner crystals in dusty plasmas has attracted much interest very recently. Dust particles immersed in a plasma interact by means of the Coulomb repulsion of the particle's charges acquired by electron and ion currents. Ikezi ͓1͔ theoretically predicted plasma conditions under which these particles should form regular lattices, the so-called plasma crystal. Experimentally these crystals were found by Chu and co-workers ͓2-4͔ in a magnetron rf discharge with trapped discharge-grown SiO 2 particles. Thomas et al. ͓5͔ and Melzer et al. ͓6,7͔ found plasma crystals in parallel plate rf discharges where dust particles intentionally added to the plasma are trapped in the sheath of the lower electrode, where mainly the upward-directed field force balances the gravitational force on the particles. The dust grains arrange in a flat crystal with a diameter of a few hundred interparticle distances and a thickness of up to 20 layers, with usual two-dimensional ͑2D͒ hexagonal order in the plane. In the vertical direction the particles are found to be aligned ͓4,7,8͔.In this paper we show that the alignment can be explained by nonreciprocal attractive forces on the particles due to ion streaming motion. These forces overcome the dust Coulomb repulsion. They are also responsible for the onset of particle oscillations about the aligned positions, which are compared with experimental findings.The measurements were performed in a parallel plate rf discharge at 13.56 MHz and a power input of 12 W with the lower electrode powered and the upper grounded. The discharge was operated in helium at pressures ranging from 30 to 150 Pa. Monodisperse spherical melamine/formaldehyde particles of 4.8 m and 9.4 m diameter were added to the plasma. The choice of different particle sizes provides a change of the gravitational force by a factor of about 8. The dust crystal is illuminated by a vertical or horizontal laser fan and is observed in scattered light with a video camera. The experimental setup has been decribed in detail in ͓7͔. The charge on the dust particles is determined from the resonance frequency in the potential well formed by the gravitational and electrical forces ͓6-8͔. The measured charge is Z Ϫ ϭ15 000 elementary charges corresponding to a surface potential of ϭϪ5 V for the 9.4-m particles (Z Ϫ ϭ3600,ϭϪ2.2 V for the 4.8-m particles͒. Figure 1 shows a side view of...

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