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18Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2019
FUNDAMENTAL INHOMOGENEITY OF A YUKAWA PLASMA
IN A PARABOLIC TRAP
V.S. Nikolaev12, A.V. Timofeev2,1
Moscow Institute of Physics and Technology (State University), Moscow, Russia,
e-mail: vladiorussia@mail.ru 2Joint Institute for High Temperatures of the Russian Academy of Sciences, Moscow, Russia,
e-mail: timofeevalvl@gmail.com
The model of Yukawa particles in a harmonic trap is widely used for many physical systems. Among these are colloidal suspensions, ions in a Penning trap and dusty plasma structures. Longstanding terminology suggests the use of such terms as "Yukawa crystals", "phonon spectrum" and "phase transitions" in most works devoted to the topic. At the same time, even in its most simple implementation the model of Yukawa particles in a harmonic trap is incorrectly described by these terms.
As was shown by Henning et al. [1], density profile of a ground state of a confined Yukawa plasma is nonuniform. The density decays quadratically with radial distance from the center of the trap. Thus, the "lattice parameter^' is also nonuniform and increases monotonically from the center to the edge of an ordered Yukawa structure.
In this work, we consider the system of constant equal charges in a parabolic trap. The interaction of particles is described by the Yukawa potential with a fixed screening parameters. We apply the method of molecular dynamics simulations to study the crystalline systems of many particles: 200 in a 2D case and 2800 in a 3D case.
We develop an analytic model to describe the dependence of the mean square displacement (u2 )upon the local inter-particle distance Alocal. It is given by the following formula:
(u2) = A2Alocal exp(KAlocal), (1) where A is a numeric coefficient that depends explicitly upon the system parameters but not upon the inter-particle distance. Then we obtain an expression for the Lindemann parameter:
\exp(KAlocal) 5 = A I-a-■ (2)
-vl *-»local
This analytic model is adequate for temperatures far below the melting point. From (1) and (2), it follows that the thermal oscillations amplitude and the Lindemann parameter are nonuniform as well as the average inter-particle spacing. This result is confirmed via molecular dynamics simulations both qualitatively and using approximations by (1) and (2). Thus, we suggest to study Yukawa structures in a local approximation by dividing them into subsystems with close to uniform parameters.
We discuss the application of the developed analytic model to the dusty plasma experiment [2] and test the influence of charge fluctuations on the obtained results.
References
[1] C. Henning et al. 2006 Physical Review E 74 (5) 056403.
[2] M.G. Hariprasad et al. 2018 Physics of Plasmas 25 (12) 123704.
