Spectral Characteristics of Charged Particles in Limited Chain Structures
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TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Spectral Characteristics of Charged Particles in Limited Chain Structures O. S. Vaulinaa,b,*, E. A. Sametova,b, and E. A. Lisina,b,** a
Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia b Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow oblast, 141700 Russia * e-mail: [email protected] **e-mail: [email protected] Received January 27, 2020; revised February 12, 2020; accepted February 12, 2020
Abstract—The spectral characteristics of the stochastic motion in chain structures of charged particles in the electric field of a trap have been studied. The characteristic frequencies of particles, as well as a method of their calculation, have been considered. Analytical relations have been proposed for the spectral density of displacements in small chain structures of particles interacting via a pair potential. These relations have been tested by the numerical simulation of the problem. DOI: 10.1134/S1063776120060072
1. INTRODUCTION The stochastic (thermal) motion of charged particles is widespread in nature and its study is of interest for various fields of science and technology [1–6]. A complex (dusty) plasma is an ionized gas containing charged microparticles (dust) [1–3]. Experimental and numerical studies of the stochastic motion of dust particles in a gas-discharge plasma were reported in [7–13]. The ion density of the plasma in the center of gas-discharge chambers is usually higher than the electron density [14], which results in the formation of effective traps for negatively charged dust particles [1, 2]. Laboratory experiments with a small amount of dust particles allow studies of the spectra of their natural and induced vibrations and the effect of various external actions, as well as the development of new methods of diagnostic, etc. [15–22]. Detailed information on the features of the thermal motion of interacting particles can be obtained by analyzing the spectral density of their displacements. The spectral density for random (thermal) displacements of particles is the Fourier cosine transform of the correlation function describing the time dependence of the average square of these displacements [23–25]. In contrast to other characteristics of the system (nonideality parameter, mass transfer coefficients, etc.), information on the spectral density of thermal displacements of particles makes it possible to analyze the spectrum of their eigenmodes. This allows estimating the response of the studied system to various external actions and obtaining information on the interparticle interaction potential [7–9, 26, 27].
The problem of the spectral density of displacements has been already considered in detail for the case of two interacting particles [28, 29]. In this work, we study the spectral characteristics of particles interacting via an arbitrary pair potential in low-dimensional chain structures. The results of this study can be useful for the experimental analysis of the chara
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