Oscillations of a molecular dusty-plasma crystal
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Y PLASMA
Oscillations of a Molecular Dusty-Plasma Crystal A. M. Ignatov* Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow, 119991 Russia Pirogov Russian National Research Medical University, Moscow, 117997 Russia *e-mail: [email protected] Received March 22, 2017
Abstract—The phonon spectra of a two-layer plasma crystal are analyzed. A simple model describing nonreciprocal forces acting between dust grains is formulated. General trends in the dynamics of a single dust molecule consisting of two vertically aligned grains are described. An integral of motion analogous to energy is found in the harmonic approximation. The conditions allowing the existence of a molecular crystal for which interaction between pairs of grains weakly affects the state of an individual molecule are determined. The oscillation spectra are obtained in an explicit form. DOI: 10.1134/S1063780X17110058
1. INTRODUCTION As a rule, aerosol particles or dust grains in a weakly ionized plasma accumulate a fairly large negative charge. Under conditions of a laboratory RF discharge, they are arranged above one of the metal electrodes, which, on average, is also charged negatively. The equilibrium height at which dust grains are localized is determined by the balance between the Earth’s gravity force and the electrostatic repulsion from the electrode. In the region of dust grain localization, the electrons obey a Boltzmann distribution, while the directed velocity of ions is comparable with or exceeds the ion-acoustic velocity. The physics of the processes occurring in the near-electrode dusty plasma was discussed in a number of review articles and monographs (see, e.g., [1–3]). In the very first experiments with dusty plasmas, it was found that, under certain conditions, dust grains are arranged into vertical pairs of grains or chains consisting of a larger number of grains. Since the forces confining grains in the horizontal direction are weak, there should exist attraction forces acting between like charges and arranging them along a vertical line. In [4, 5], a mechanism of attraction related to the formation of an ion-acoustic wake excited by a charged grain in a plasma flow was proposed. The structure of plasma perturbations in the wake was later studied in detail both analytically and numerically (see, e.g., [6, 7] and references therein). In particular, it was demonstrated that, under certain conditions, a cloud of positively charged ions (the so-called ion focus) forms downstream of a negatively charged grain. This cloud provides attraction between dust grains located at different heights. For dust grains located at the same height, interaction in an unbounded plasma is always repul-
sive. However, the influence of electrostatic reflection of the wave field from the metal electrode can result in attraction [8, 9]. Attempts to obtain simple analytical expressions for the electric field distribution in the vicinity of a dust grain did not meet with success. Therefore, a simple model describing the dynamics of an ensemble o
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