**Topic/Type**:
1.5 Low-temperature, dusty and nano-plasmas, Oral

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Gennady Sukhinin ^{1, 2}, Alexander Fedoseev^{1}, Roman Khokhlov^{1, 2}
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^{1} Institute of Thermophysics SB RAS, Novosibirsk, 630090, Russia^{2} Novosibirsk State University, Novosibirsk, 630090, Russia
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\hspace*{6pt}Dust particles charge is the most important parameter, which determines almost all processes in dusty plasma. At low pressure conditions, the trapped ions cloud formed around negatively charged particles leads to a shielding of the proper charge of a dust particle. Trapped ions determine the electrostatic interaction of the particle with other dust particles and with external electric field.

There are several analytical [1], numerical and PIC Monte Carlo models [2-3] for the obtaining of trapped ions distributions. However, in all these models the non-Maxwellian character of electron energy distribution function (EEDF) in non-equilibrium plasma was not taken into account, numerical simulations were performed in a limited region that leads to incorrect asymptotes in the distribution of electric potential around strongly charged particle.

An attempt to describe the formation of trapped ions cloud without these limitations was made in [4]. In this paper, a modified hybrid model for the determination of dust particles charge and distribution of trapped ions in low-temperature plasma is presented. The model includes a sub-model for determination of EEDF in glow discharge plasma based on the solution of Boltzmann equation, and a sub-model for determination of radial distribution of ionic coat around dust particle formed as a result of resonant charge exchange collisions of ions in a parent gas. The integral equation for trapped ions distribution coupled with the Poisson equation for self-consistent potential is introduced. The kernel of the integral equation is obtained with the help of rigorous averaging of ions motion along finite trajectories in a self-consistent potential. The iterative procedures for solving the system of equations were used.

It was shown that the trapped ions charge distribution has shell structure with a strong maximum placed at the distance equal to 0.3-0.5 Debye lengths. Self-consistent potential has a slightly distorted Debye-like form. Total volume charge of free and trapped ions and electrons is strictly compensated the charge of dust particle. In low-pressure experiments, it is only possible to detect the effective charge of a dust particle that is equal to the difference between the proper charge of the particle and the charge of trapped ions.

[1] M. Lampe, et al. - Phys. Plasmas, 10, 1500 (2003).

[2] A.V. Zobnin, et al. ? Physics of Plasmas, 15, 043705 (2008).

[3] I. H. Hutchinson and L. Patacchini. - Physics of Plasmas, 14, 013505 (2007).

[4] G. I. Sukhinin, A. V. Fedoseev, S. N. Antipov, O. F. Petrov, V. E. Fortov. ? Phys. Rev. E, 79, 036404 (2009).

Financial support for this work was partly provided by RFBR Grant N 07-02-00781-a.