Continuum model for the breathing oscillation of a spherical complex plasma

Journal Article · Wed Feb 15 04:00:00 EST 2006 · Physics of Plasmas

DOI:https://doi.org/10.1063/1.2168406· OSTI ID:20782488

Sheridan, T E ^[1]

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1. Department of Physics and Astronomy, Ohio Northern University, Ada, Ohio 45810 (United States)

A nonlinear equation of motion for the breathing oscillation of a spherical complex plasma is derived. A spherical complex plasma, or ''dust ball,'' is a three-dimensional arrangement of n identical charged particles interacting through a shielded Coulomb force (i.e., a Yukawa potential) with a Debye length {lambda} and confined by a three-dimensional, isotropic, parabolic potential well for which the single-particle oscillation frequency is {omega}{sub 0}. The dependence of the equilibrium radius R{sub 0} and small-amplitude breathing frequency {omega}{sub br} on {lambda} is computed. Exact analytical results are given for the continuum limit n{yields}{infinity} (i.e., a spherical Yukawa fluid). The squared breathing frequency ({omega}{sub br}/{omega}{sub 0}){sup 2}=3 for the unshielded Coulomb interaction (1/{lambda}{yields}0), irrespective of n, and increases to ({omega}{sub br}/{omega}{sub 0}){sup 2}=5 as 1/{lambda}{yields}{infinity}. The effects of a finite number of particles are modeled by assuming an inner cutoff for the Yukawa potential a distance a from any point in the complex plasma sphere. Three physical regimes are identified: a Coulomb regime where {lambda}>>R{sub 0} and corrections to the infinite-{lambda} case are small, a nearest-neighbor regime, where R{sub 0}>>a>{lambda} and nearest-neighbor interactions dominate, and a plasma regime where R{sub 0}>>{lambda} > or approx. and continuum plasma theory is applicable. For 1/{lambda}{yields}{infinity}, ({omega}{sub br}/{omega}{sub 0}){sup 2}{approx}a/{lambda} in the nearest-neighbor regime, while ({omega}{sub br}/{omega}{sub 0}){sup 2}{approx}5 in the plasma regime.

• OSTI ID: 20782488
• Journal Information: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 2 Vol. 13; ISSN PHPAEN; ISSN 1070-664X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
AMPLITUDES
CHARGED PARTICLES
CORRECTIONS
DEBYE LENGTH
DISTANCE
DUSTS
EQUATIONS OF MOTION
EQUILIBRIUM
NONLINEAR PROBLEMS
PLASMA
PLASMA CONFINEMENT
PLASMA WAVES
SPHERICAL CONFIGURATION
THREE-DIMENSIONAL CALCULATIONS
YUKAWA POTENTIAL