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Papers by Anatoly Filippov

Research paper thumbnail of Isotropic and Anisotropic Monolayer Structures in RF Discharge Plasma

Molecules

We present the results of an experimental and analytical study of the structural and dynamic prop... more We present the results of an experimental and analytical study of the structural and dynamic properties of a monolayer consisting of dust grains in an electrostatic trap in an RF discharge plasma. The possibility of forming a monolayer with an isotropic distribution for interparticle distance and kinetic energy of particles in the structure has been experimentally shown. Isotropy has crucial importance for the study of various processes in such systems, including the kinetics of phase transitions, the formation of directed flows, wave propagation, and others.

Research paper thumbnail of Study of dust particle charge screening within the nonlocal charging theory

In papers [1,2] it was shown that in a non-equilibrium plasma with one type of positive ions the ... more In papers [1,2] it was shown that in a non-equilibrium plasma with one type of positive ions the dust particle potential was described by two exponentials, and for the case of three types of ions the potential was described by the superposition of three exponentials with three different screening constants [3]. In the present paper the EEDF non-locality influence on a dust particle potential distribution is considered in a two-component plasma of noble gases and nitrogen on the basis of a nonlocal charging model which consists of the electron and ion balance equations, the Poisson equation and the electron energy balance equation, obtained from the non-local momentum method [4]. It was found that the potential distribution in the vicinity of a dust particle is described by the sum of three exponentials. The screening constants and the pre-exponential coefficients are defined by the plasma parameters and the electron and ion sinks.[4pt] [1] A.V. Filippov et al., JETP Letters 81 (2005...

Research paper thumbnail of Charge screening in a plasma with an external ionization source

Journal of Experimental and Theoretical Physics, 2007

Research paper thumbnail of Interaction of two macroparticles in a nonequilibrium plasma

Journal of Experimental and Theoretical Physics, 2007

The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been i... more The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been investigated. An asymptotic theory of screening, which leads to a two-exponential dependence of the macroparticle potential on distance with different screening constants, is used to determine the electrostatic energy of the system of charges associated with the two macroparticles. The dependence of the electrostatic energy on interparticle distance has been found to have a minimum, as in an equilibrium plasma. The interaction force between the macroparticles has been determined; it turned out to be asymmetric-for different charges, the forces acting on the first and second macroparticles are not equal. This is the result of an asymmetric charge separation near macroparticles with differing charges and indicates that the interaction force in a nonequilibrium plasma is nonpotential. The forces are equal for identical macroparticles or in an equilibrium plasma and the potential energy of the interaction between the macroparticles has been determined for these cases. Attraction between likely charged particles with different (in magnitude) charges has been found to be possible when they come very close together. Relations to determine the modified coupling parameter for an interaction potential that consists of two exponential terms with different screening constants have been derived.

Research paper thumbnail of Kinetic description of the screening of the charge of macroparticles in a nonequilibrium plasma

JETP Letters, 2008

A new approach has been developed for the kinetic description of the screening of the charge of m... more A new approach has been developed for the kinetic description of the screening of the charge of macroparticles and the determination of the distribution of the effective potential in a nonequilibrium plasma. The main concept of the new approach is the description of the absorption of electrons and ions by a macroparticle through introducing effective point sinks in the kinetic equations describing the dynamics of plasma particles. With the use of this approach, explicit relations for the effective potential are derived with allowance for the collisions of electrons and ions with neutrals of the buffer gas and in the presence of an external magnetic field.

Research paper thumbnail of Screening of a moving charge in a nonequilibrium plasma

Research paper thumbnail of Shielding and Interaction of Dust Particles in Non-Equilibrium Plasma

Contributions to Plasma Physics, 2007

This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevat... more This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevated pressures. On the basis of asymptotic shielding theory resulting in two-exponential shielding the electrostatic energy of two charged fine particles is determined. The electrostatic energy dependence on interparticle distance proves to have a minimum as in an equilibrium plasma. The electrostatic interaction force of the particles is calculated. This force is proved to be non-symmetric: for different charges the force acting on one dust particle was not equal to the force acting on the other dust particle. This is due to non-symmetric charge separation in the vicinity of different charged dust particles. It is stated that likely charged particles repel each other and at the closest approach the attraction is only possible. Relationships to determine the modified nonideality parameter for the interaction potential, which consisted of two exponents with different shielding lengths, were obtained.

Research paper thumbnail of Electrostatic interactions between spheroidal dielectric particles

The Journal of Chemical Physics

Theory is developed to address the significant problem of electrostatic interactions between char... more Theory is developed to address the significant problem of electrostatic interactions between charged polarizable dielectric spheroids. The electrostatic force is defined by particle dimensions and charge, dielectric constants of the interacting particles and medium, and the interparticle separation distance; and it is expressed in the form of an integral over the particle surface. The switching behavior between like charge repulsion and attraction is demonstrated as depending on the ratio of the major and minor axes of spheroids. When the major and minor axes are equal, the theory yields a solution equivalent to that obtained for spherical particles. Limiting cases are presented for nonpolarizable spheroids, which describe the electrostatic behavior of charged rods, discs, and point charges. The developed theory represents an important step toward comprehensive understanding of direct interactions and mechanisms of electrostatically driven self-assembly processes.

Research paper thumbnail of Electrostatic interactions between charged dielectric particles in an electrolyte solution: constant potential boundary conditions

Soft Matter

The problem of electrostatic interactions between colloidal particles in an electrolyte solution ... more The problem of electrostatic interactions between colloidal particles in an electrolyte solution has been solved within the Debye–Hückel approximation using the boundary condition of constant potential.

Research paper thumbnail of Electrostatic Interaction of Two Point Charges in Equilibrium Plasmas within the Debye Approximation

Contributions to Plasma Physics, 2016

The influence of the outer boundary shape on the electrostatic interaction of two charged point m... more The influence of the outer boundary shape on the electrostatic interaction of two charged point macroparticles in an equilibrium plasma is studied within the Debye-Huckel approximation, i.e., based on the linearized Poisson-Boltzmann model. It is shown that the boundary shape has a strong influence on the electrostatic interaction between two macroparticles, which switches from repulsion at small interparticle distances to attraction as it approaches the half-length of the computational cell. It is found that in the case of dust particles arranged in the nodes of a simple cubic lattice, the electrostatic force acting on them is equal to zero; hence, an infinite simple cubic lattice of charged dust particles is mechanically stable. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Research paper thumbnail of Plate-like Dusty Structures in an e-Beam Sustained Glow Discharge at Atmospheric Pressure

AIP Conference Proceedings, 2005

ABSTRACT The paper is devoted to studying the dusty plasma created by the injection of dust parti... more ABSTRACT The paper is devoted to studying the dusty plasma created by the injection of dust particles into the atmospheric pressure gas ionized by an electron beam of 85-120 keV energy. The beam current density was varied within 0.1-1.0 mA/cm2. The electron gun operated in the stationary regime. The behavior of dusty particles lighted by a laser ``knife'' was observed with a digital video camera. Stable plate-like structures were observed in the cathode sheath of non-self-sustained discharge. Numerical simulation was performed by using the non-local model of the non-self-sustained discharge.

Research paper thumbnail of Electrostatic interactions and stability of dusty plasmas and the multicomponent Ornstein–Zernike equation

AIP Advances

Overlapping soliton during the concentric interaction of cylindrical dark solitons in a bounded d... more Overlapping soliton during the concentric interaction of cylindrical dark solitons in a bounded dusty plasma with dust charge variation AIP Advances 10, 055216 (2020);

Research paper thumbnail of Shielding and Interaction of Dust Particles in Non-Equilibrium Plasma

Contributions to Plasma Physics, 2007

This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevat... more This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevated pressures. On the basis of asymptotic shielding theory resulting in two-exponential shielding the electrostatic energy of two charged fine particles is determined. The electrostatic energy dependence on interparticle distance proves to have a minimum as in an equilibrium plasma. The electrostatic interaction force of the particles is calculated. This force is proved to be non-symmetric: for different charges the force acting on one dust particle was not equal to the force acting on the other dust particle. This is due to non-symmetric charge separation in the vicinity of different charged dust particles. It is stated that likely charged particles repel each other and at the closest approach the attraction is only possible. Relationships to determine the modified nonideality parameter for the interaction potential, which consisted of two exponents with different shielding lengths, were obtained.

Research paper thumbnail of Interaction of two macroparticles in a nonequilibrium plasma

Journal of Experimental and Theoretical Physics, 2007

The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been i... more The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been investigated. An asymptotic theory of screening, which leads to a two-exponential dependence of the macroparticle potential on distance with different screening constants, is used to determine the electrostatic energy of the system of charges associated with the two macroparticles. The dependence of the electrostatic energy on interparticle distance has been found to have a minimum, as in an equilibrium plasma. The interaction force between the macroparticles has been determined; it turned out to be asymmetric-for different charges, the forces acting on the first and second macroparticles are not equal. This is the result of an asymmetric charge separation near macroparticles with differing charges and indicates that the interaction force in a nonequilibrium plasma is nonpotential. The forces are equal for identical macroparticles or in an equilibrium plasma and the potential energy of the interaction between the macroparticles has been determined for these cases. Attraction between likely charged particles with different (in magnitude) charges has been found to be possible when they come very close together. Relations to determine the modified coupling parameter for an interaction potential that consists of two exponential terms with different screening constants have been derived.

Research paper thumbnail of Screening of a moving charge in a nonequilibrium plasma

JETP Letters, 2008

Based on the model of point sinks, we consider the problem on the screening of the charge of a mo... more Based on the model of point sinks, we consider the problem on the screening of the charge of a moving macroparticle in a nonequilibrium plasma. The characteristic formation times of the polarization cloud around such a macroparticle have been determined by the method of a three-dimensional integral Fourier transformation in spatial variables and a Laplace transformation in time. The screening effect is shown to be enhanced with increasing macroparticle velocity. We consider the applicability conditions for the model of point sinks and establish that the domain of applicability of the results obtained expands with decreasing gas ionization rate and macroparticle size. We consider the problem of charge screening at low velocities and establish that the stationary potential of the moving charge has a dipole component that becomes dominant at large distances. We show that the direction of the force exerted on the dust particle by the induced charges generally depends on the relationship between the transport and loss coefficients of the plasma particles in a plasma. When the Langevin ion recombination coefficient β iL = 4 π e µ i exceeds the electron-ion recombination coefficient β ei , this force will accelerate the dust particles in the presence of sinks. In the absence of sinks or when β ei > β iL , this force will be opposite in direction to the dust particle velocity. We also consider the problem on the energy and force of interaction between a moving charged macroparticle and the induced charges.

Research paper thumbnail of Kinetic description of the screening of the charge of macroparticles in a nonequilibrium plasma

JETP Letters, 2008

A new approach has been developed for the kinetic description of the screening of the charge of m... more A new approach has been developed for the kinetic description of the screening of the charge of macroparticles and the determination of the distribution of the effective potential in a nonequilibrium plasma. The main concept of the new approach is the description of the absorption of electrons and ions by a macroparticle through introducing effective point sinks in the kinetic equations describing the dynamics of plasma particles. With the use of this approach, explicit relations for the effective potential are derived with allowance for the collisions of electrons and ions with neutrals of the buffer gas and in the presence of an external magnetic field.

Research paper thumbnail of Charge screening in a plasma with an external ionization source

Journal of Experimental and Theoretical Physics, 2007

An asymptotic theory for the screening of the electric field of a dust particle or a spherical pr... more 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 = 4 π e µ i (where µ i is the ion mobility), recombination coefficients. If β L ӷ 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 ≥ 2 β L . The Vlasov equation is used to analyze the asymptotic behavior of the macroparticle potential in a collisionless plasma.

Research paper thumbnail of Isotropic and Anisotropic Monolayer Structures in RF Discharge Plasma

Molecules

We present the results of an experimental and analytical study of the structural and dynamic prop... more We present the results of an experimental and analytical study of the structural and dynamic properties of a monolayer consisting of dust grains in an electrostatic trap in an RF discharge plasma. The possibility of forming a monolayer with an isotropic distribution for interparticle distance and kinetic energy of particles in the structure has been experimentally shown. Isotropy has crucial importance for the study of various processes in such systems, including the kinetics of phase transitions, the formation of directed flows, wave propagation, and others.

Research paper thumbnail of Study of dust particle charge screening within the nonlocal charging theory

In papers [1,2] it was shown that in a non-equilibrium plasma with one type of positive ions the ... more In papers [1,2] it was shown that in a non-equilibrium plasma with one type of positive ions the dust particle potential was described by two exponentials, and for the case of three types of ions the potential was described by the superposition of three exponentials with three different screening constants [3]. In the present paper the EEDF non-locality influence on a dust particle potential distribution is considered in a two-component plasma of noble gases and nitrogen on the basis of a nonlocal charging model which consists of the electron and ion balance equations, the Poisson equation and the electron energy balance equation, obtained from the non-local momentum method [4]. It was found that the potential distribution in the vicinity of a dust particle is described by the sum of three exponentials. The screening constants and the pre-exponential coefficients are defined by the plasma parameters and the electron and ion sinks.[4pt] [1] A.V. Filippov et al., JETP Letters 81 (2005...

Research paper thumbnail of Charge screening in a plasma with an external ionization source

Journal of Experimental and Theoretical Physics, 2007

Research paper thumbnail of Interaction of two macroparticles in a nonequilibrium plasma

Journal of Experimental and Theoretical Physics, 2007

The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been i... more The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been investigated. An asymptotic theory of screening, which leads to a two-exponential dependence of the macroparticle potential on distance with different screening constants, is used to determine the electrostatic energy of the system of charges associated with the two macroparticles. The dependence of the electrostatic energy on interparticle distance has been found to have a minimum, as in an equilibrium plasma. The interaction force between the macroparticles has been determined; it turned out to be asymmetric-for different charges, the forces acting on the first and second macroparticles are not equal. This is the result of an asymmetric charge separation near macroparticles with differing charges and indicates that the interaction force in a nonequilibrium plasma is nonpotential. The forces are equal for identical macroparticles or in an equilibrium plasma and the potential energy of the interaction between the macroparticles has been determined for these cases. Attraction between likely charged particles with different (in magnitude) charges has been found to be possible when they come very close together. Relations to determine the modified coupling parameter for an interaction potential that consists of two exponential terms with different screening constants have been derived.

Research paper thumbnail of Kinetic description of the screening of the charge of macroparticles in a nonequilibrium plasma

JETP Letters, 2008

A new approach has been developed for the kinetic description of the screening of the charge of m... more A new approach has been developed for the kinetic description of the screening of the charge of macroparticles and the determination of the distribution of the effective potential in a nonequilibrium plasma. The main concept of the new approach is the description of the absorption of electrons and ions by a macroparticle through introducing effective point sinks in the kinetic equations describing the dynamics of plasma particles. With the use of this approach, explicit relations for the effective potential are derived with allowance for the collisions of electrons and ions with neutrals of the buffer gas and in the presence of an external magnetic field.

Research paper thumbnail of Screening of a moving charge in a nonequilibrium plasma

Research paper thumbnail of Shielding and Interaction of Dust Particles in Non-Equilibrium Plasma

Contributions to Plasma Physics, 2007

This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevat... more This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevated pressures. On the basis of asymptotic shielding theory resulting in two-exponential shielding the electrostatic energy of two charged fine particles is determined. The electrostatic energy dependence on interparticle distance proves to have a minimum as in an equilibrium plasma. The electrostatic interaction force of the particles is calculated. This force is proved to be non-symmetric: for different charges the force acting on one dust particle was not equal to the force acting on the other dust particle. This is due to non-symmetric charge separation in the vicinity of different charged dust particles. It is stated that likely charged particles repel each other and at the closest approach the attraction is only possible. Relationships to determine the modified nonideality parameter for the interaction potential, which consisted of two exponents with different shielding lengths, were obtained.

Research paper thumbnail of Electrostatic interactions between spheroidal dielectric particles

The Journal of Chemical Physics

Theory is developed to address the significant problem of electrostatic interactions between char... more Theory is developed to address the significant problem of electrostatic interactions between charged polarizable dielectric spheroids. The electrostatic force is defined by particle dimensions and charge, dielectric constants of the interacting particles and medium, and the interparticle separation distance; and it is expressed in the form of an integral over the particle surface. The switching behavior between like charge repulsion and attraction is demonstrated as depending on the ratio of the major and minor axes of spheroids. When the major and minor axes are equal, the theory yields a solution equivalent to that obtained for spherical particles. Limiting cases are presented for nonpolarizable spheroids, which describe the electrostatic behavior of charged rods, discs, and point charges. The developed theory represents an important step toward comprehensive understanding of direct interactions and mechanisms of electrostatically driven self-assembly processes.

Research paper thumbnail of Electrostatic interactions between charged dielectric particles in an electrolyte solution: constant potential boundary conditions

Soft Matter

The problem of electrostatic interactions between colloidal particles in an electrolyte solution ... more The problem of electrostatic interactions between colloidal particles in an electrolyte solution has been solved within the Debye–Hückel approximation using the boundary condition of constant potential.

Research paper thumbnail of Electrostatic Interaction of Two Point Charges in Equilibrium Plasmas within the Debye Approximation

Contributions to Plasma Physics, 2016

The influence of the outer boundary shape on the electrostatic interaction of two charged point m... more The influence of the outer boundary shape on the electrostatic interaction of two charged point macroparticles in an equilibrium plasma is studied within the Debye-Huckel approximation, i.e., based on the linearized Poisson-Boltzmann model. It is shown that the boundary shape has a strong influence on the electrostatic interaction between two macroparticles, which switches from repulsion at small interparticle distances to attraction as it approaches the half-length of the computational cell. It is found that in the case of dust particles arranged in the nodes of a simple cubic lattice, the electrostatic force acting on them is equal to zero; hence, an infinite simple cubic lattice of charged dust particles is mechanically stable. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Research paper thumbnail of Plate-like Dusty Structures in an e-Beam Sustained Glow Discharge at Atmospheric Pressure

AIP Conference Proceedings, 2005

ABSTRACT The paper is devoted to studying the dusty plasma created by the injection of dust parti... more ABSTRACT The paper is devoted to studying the dusty plasma created by the injection of dust particles into the atmospheric pressure gas ionized by an electron beam of 85-120 keV energy. The beam current density was varied within 0.1-1.0 mA/cm2. The electron gun operated in the stationary regime. The behavior of dusty particles lighted by a laser ``knife'' was observed with a digital video camera. Stable plate-like structures were observed in the cathode sheath of non-self-sustained discharge. Numerical simulation was performed by using the non-local model of the non-self-sustained discharge.

Research paper thumbnail of Electrostatic interactions and stability of dusty plasmas and the multicomponent Ornstein–Zernike equation

AIP Advances

Overlapping soliton during the concentric interaction of cylindrical dark solitons in a bounded d... more Overlapping soliton during the concentric interaction of cylindrical dark solitons in a bounded dusty plasma with dust charge variation AIP Advances 10, 055216 (2020);

Research paper thumbnail of Shielding and Interaction of Dust Particles in Non-Equilibrium Plasma

Contributions to Plasma Physics, 2007

This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevat... more This paper investigates the interaction of two dust particles in non-equilibrium plasma at elevated pressures. On the basis of asymptotic shielding theory resulting in two-exponential shielding the electrostatic energy of two charged fine particles is determined. The electrostatic energy dependence on interparticle distance proves to have a minimum as in an equilibrium plasma. The electrostatic interaction force of the particles is calculated. This force is proved to be non-symmetric: for different charges the force acting on one dust particle was not equal to the force acting on the other dust particle. This is due to non-symmetric charge separation in the vicinity of different charged dust particles. It is stated that likely charged particles repel each other and at the closest approach the attraction is only possible. Relationships to determine the modified nonideality parameter for the interaction potential, which consisted of two exponents with different shielding lengths, were obtained.

Research paper thumbnail of Interaction of two macroparticles in a nonequilibrium plasma

Journal of Experimental and Theoretical Physics, 2007

The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been i... more The interaction of two macroparticles in a nonequilibrium plasma at elevated pressures has been investigated. An asymptotic theory of screening, which leads to a two-exponential dependence of the macroparticle potential on distance with different screening constants, is used to determine the electrostatic energy of the system of charges associated with the two macroparticles. The dependence of the electrostatic energy on interparticle distance has been found to have a minimum, as in an equilibrium plasma. The interaction force between the macroparticles has been determined; it turned out to be asymmetric-for different charges, the forces acting on the first and second macroparticles are not equal. This is the result of an asymmetric charge separation near macroparticles with differing charges and indicates that the interaction force in a nonequilibrium plasma is nonpotential. The forces are equal for identical macroparticles or in an equilibrium plasma and the potential energy of the interaction between the macroparticles has been determined for these cases. Attraction between likely charged particles with different (in magnitude) charges has been found to be possible when they come very close together. Relations to determine the modified coupling parameter for an interaction potential that consists of two exponential terms with different screening constants have been derived.

Research paper thumbnail of Screening of a moving charge in a nonequilibrium plasma

JETP Letters, 2008

Based on the model of point sinks, we consider the problem on the screening of the charge of a mo... more Based on the model of point sinks, we consider the problem on the screening of the charge of a moving macroparticle in a nonequilibrium plasma. The characteristic formation times of the polarization cloud around such a macroparticle have been determined by the method of a three-dimensional integral Fourier transformation in spatial variables and a Laplace transformation in time. The screening effect is shown to be enhanced with increasing macroparticle velocity. We consider the applicability conditions for the model of point sinks and establish that the domain of applicability of the results obtained expands with decreasing gas ionization rate and macroparticle size. We consider the problem of charge screening at low velocities and establish that the stationary potential of the moving charge has a dipole component that becomes dominant at large distances. We show that the direction of the force exerted on the dust particle by the induced charges generally depends on the relationship between the transport and loss coefficients of the plasma particles in a plasma. When the Langevin ion recombination coefficient β iL = 4 π e µ i exceeds the electron-ion recombination coefficient β ei , this force will accelerate the dust particles in the presence of sinks. In the absence of sinks or when β ei > β iL , this force will be opposite in direction to the dust particle velocity. We also consider the problem on the energy and force of interaction between a moving charged macroparticle and the induced charges.

Research paper thumbnail of Kinetic description of the screening of the charge of macroparticles in a nonequilibrium plasma

JETP Letters, 2008

A new approach has been developed for the kinetic description of the screening of the charge of m... more A new approach has been developed for the kinetic description of the screening of the charge of macroparticles and the determination of the distribution of the effective potential in a nonequilibrium plasma. The main concept of the new approach is the description of the absorption of electrons and ions by a macroparticle through introducing effective point sinks in the kinetic equations describing the dynamics of plasma particles. With the use of this approach, explicit relations for the effective potential are derived with allowance for the collisions of electrons and ions with neutrals of the buffer gas and in the presence of an external magnetic field.

Research paper thumbnail of Charge screening in a plasma with an external ionization source

Journal of Experimental and Theoretical Physics, 2007

An asymptotic theory for the screening of the electric field of a dust particle or a spherical pr... more 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 = 4 π e µ i (where µ i is the ion mobility), recombination coefficients. If β L ӷ 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 ≥ 2 β L . The Vlasov equation is used to analyze the asymptotic behavior of the macroparticle potential in a collisionless plasma.