ISSN 1063-7761, Journal of Experimental and Theoretical Physics, 2007, Vol. 104, No. 1, pp. 147–161. © Pleiades Publishing, Inc., 2007. Original Russian Text © A.V. Filippov, A.G. Zagorodny, A.I. Momot, A.F. Pal, A.N. Starostin, 2007, published in Zhurnal Éksperimental’noœ i Teoreticheskoœ Fiziki, 2007, Vol. 131, No. 1, pp. 164–179. 147 1. INTRODUCTION The screening length is an important parameter that determines the Debye plasma crystallization condi- tions, the ion drag force, the dusty plasma eigenmode spectrum, etc. [1–5]. At present, the question about the behavior of the charge screening in a low-temperature plasma has not been completely solved [6]. This prob- lem is particularly acute in the case where a macro- scopic charged body, such as a probe or a dust particle, is located in a plasma. The probe methods are widely used for diagnostics in low-temperature plasma physics [7–10]. Determining the size of the plasma perturbation region, which depends not only on the probe parame- ters, but also on the screening behavior and length, is one of the central points in interpreting the results of measurements. This also determines the dust particle interaction force in a dusty plasma, which is now an actively developing field of physics [1–5]. Almost all of the models developed in the theory of probes and in dusty plasma physics use the assumption about Debye dust particle charge screening (see, e.g., the review arti- cles [1–5]). At the same time, there is no consensus on the role of ions in the field screening. In this paper, an analytical theory for the screening of the charge of a spherical body in a plasma with an external ionization source and/or self-sustained ionization by plasma elec- trons in the hydrodynamic regime of electron and ion transport has been developed for the first time. The first results of studies to develop an analytical theory of screening in a plasma with a steady ionization source were published in [11]. In this paper, the model of a point sink that includes the absorption of electrons and ions by a real particle or a probe is used as the basis for analytical estimations. Naturally, this model is approximate and can describe the distribution of cur- rents and charges near a macroparticle only in cases where the basic equations can be linearized (e.g., in the case of small particles). Nevertheless, it may prove to be useful for solving problems of the theory of probes and dusty plasmas when additional complicating fac- tors (nonstationarity, the presence of a system’s bound- aries, etc.) are taken into account. Moreover, estimates show that this model can also be used in the case of a collisionless plasma. As an example of such model applications, we consider the problem of probe mea- surements in a glow discharge at elevated pressures and evaluate the asymptotic behavior of the macroparticle potential in a collisionless plasma. Charge Screening in a Plasma with an External Ionization Source A. V. Filippov a, *, A. G. Zagorodny b , A. I. Momot b , A. F. Pal a , and A. N. Starostin a a State Research Center of the Russian Federation, Troitsk Institute for Innovation and Fusion Research, Troitsk, Moscow oblast, 142190 Russia b Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev, 03680 Ukraine * e-mail: fav@triniti.ru Received May 11, 2006 Abstract—An asymptotic theory for the screening of the electric field of a dust particle or a spherical probe in a plasma with an external steady and/or internal (proportional to the electron density) gas ionization source has been developed for the first time. It has been established that the screening of the charge of a spherical body adsorbing the charge of the incident plasma particles is described by a superposition of two exponentials with different screening constants. The two exponentials are retained even in the absence of nonequilibrium fluxes on the macroparticle and only in the special case of an isothermal plasma does the screening become Debye one. The screening length is determined by the ratio of the electron–ion, β ei , and Langevin, β L = 4πeμ i (where μ i is the ion mobility), recombination coefficients. If β L  β ei , then it is much larger than the electron Debye length. The ions in an isothermal plasma have been found to give the same contribution to the screening as the electrons if the electron–ion recombination coefficient exceeds the Langevin ion recombination coefficient by a factor of 2 or more, β ei ≥ 2β L . The Vlasov equation is used to analyze the asymptotic behavior of the macro- particle potential in a collisionless plasma. PACS numbers: 52.25.-b, 52.27.Lw, 52.70.-m DOI: 10.1134/S1063776107010153 STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS