Theoretical and experimental study of elliptical Debye clusters

Abstract

An elliptical Debye cluster is a system of n identical charged particles interacting through a screened Coulomb potential and confined in a two-dimensional anisotropic parabolic well. A model for this system has been developed with three parameters: n, the well anisotropy α2, and the Debye shielding parameter κ. From numerical solutions of the model, it is shown that the breathing mode persists as the anisotropy increases, and that the normalized, squared breathing frequency increases linearly with α2. Elliptical clusters with n=49 and 15 particles were studied experimentally. The anisotropic potential well was created using a rectangular aperture (17.5×30.2 mm) placed on a flat electrode. The well anisotropy was determined by measuring the center-of-mass (c.m.) oscillation frequencies along the major and minor axes of the resulting elliptical clusters using both driven and thermal oscillations. The two methods give results that are in good agreement. For n=49 particles, the square of the ratios of the c.m. frequencies was α2=2.9±0.1. From a measurement of the breathing frequency, the shielding parameter was found to be κ=2.1±0.2. For n=15 particles, α2=2.8±0.1 and κ=1.9±0.2, demonstrating that an analysis using the model gives consistent results.

Dusty plasma (Yukawa) rings

“…Forκ = 1.32 the critical value of the lattice parameter α = a/r 0 for the zigzag instability is α c = 1.13. For the ring studied here, α = 1.41 is significantly above [7,[18][19][20][21].…”

“…1. Monodisperse microscopic (8.94 ± 0.09 µm diameter) melamine dust particles are levitated in an rf plasma discharge above the capacitively-coupled powered electrode in the DONUT (Dusty ONU experimenT) apparatus [7,[18][19][20][21]. Dust confinement is due to a 2D annular potential well created by cutting an annular rectangular groove in the surface of the 89-mm powered electrode.…”

Power law behavior of the zigzag transition in Yukawa clusters

“…Monodisperse microspheres may then form strongly-coupled one-dimensional (1D) [3][4][5], two-dimensional (2D) [6][7][8] or even threedimensional systems [9]. The general 2D potential well is biharmonic for small displacements from the potential energy minimum [10][11][12]. A dusty plasma confined in a 2D biharmonic well may be either in a 1D straight line configuration, or a 2D configuration, where the transition from 1D to 2D states is via the zigzag instability [10,11,[13][14][15].…”

“…1) [7,8,12,16,18,19]. Argon gas was leaked into the vacuum chamber and the pressure was stabilized at 15.4 mtorr.…”

“…A cold 2D dusty plasma can be modeled [10,12,16] by assuming n identical particles with mass m and charge q, where the ith particle is at (x i , y i ). The potential energy U of a configuration {x i , y i } is given by the sum of the particles' potential energy with respect to the biharmonic well plus the sum of the potential energy for each pair-wise interaction,…”