Approximation of the characteristics of ion drift in parent gas
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GED PARTICLE MOTION
Approximation of the Characteristics of Ion Drift in Parent Gas R. I. Golyatinaa and S. A. Maiorova, b, * a b
Prokhorov General Physics Institute, Russian Academy of Science, Moscow, 119991 Russia Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow, 127412 Russia *e-mail: [email protected] Received October 15, 2015; in final form, February 17, 2016
Abstract—The drift velocities of noble-gas and mercury ions in a constant homogeneous electric field are calculated using Monte Carlo simulations. The ion mobility is analyzed as a function of the field strength and gas temperature. The fitting parameters for calculating the drift velocity by the Frost formula at gas temperatures of 4.2, 77, 300, 1000, and 2000 K are obtained. A general approximate formula for the drift velocity as a function of the reduced field and gas temperature is derived. DOI: 10.1134/S1063780X17010032
wide range of the reduced field from 1 to 10000 Td. The calculations were performed using Monte Carlo simulations within the ion−atom collisional model described in [9–13]. The model includes ion−atom polarization interaction, resonant charge exchange, and short-range repulsion of electron shells (see [9, 10, 12, 13] for details). We have calculated almost all integral characteristics of ion drift: the drift velocity, the mobility and mean energy of ions, the longitudinal and transverse diffusion coefficients, the ion mean free path, the collision frequency, and the ion distribution functions over velocities and energies. We have also analyzed the frequencies of various types of collisions, such as center-of-mass isotropic scattering, backscattering, and small-angle scattering at large impact parameters. The obtained results allow one to analyze and refine the applicability ranges of different approaches and approximations. Among all kinetic characteristics, the drift velocity is the only parameter that can be measured directly. The other characteristics are determined using various models and relations. For example, the longitudinal and transverse diffusion coefficients are usually determined using the Nernst−Townsend−Einstein relation, the modified Einstein relation, or the Schottky theory of ambipolar diffusion in a tube. The energy characteristics of the ion flow can be found with the help of the Wannier theory [4, 5, 14], the effective collision frequency and transport cross section are calculated using the first approximation of the Chapman−Enskog theory [4, 14, 15], and approaches to calculate the drift velocity are analyzed in [16]. A more detailed formulation of the problem can found in [17–21], where results of calculations of the longitudinal and transverse diffusion coefficients for
1. INTRODUCTION Drift and diffusion of ions in an electric field (e.g., ambipolar diffusion of ions from the positive column of a glow discharge) substantially affect the properties of a gas discharge. There is extensive experimental and theoretical literature on the characteristics of ions drift in gases (see, e.g
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