Charged Macroparticles Research Articles

Plasmonic excitations in double-walled carbon nanotubes

The interactions of charged particles moving paraxially in multi-walled carbon nanotubes may excite electromagnetic modes. This wake effect has recently been proposed as a potential novel method of short-wavelength high-gradient particle acceleration and for obtaining brilliant radiation sources. In this work, the excitation of wakefields in double-walled carbon nanotubes is studied by means of the linearized hydrodynamic theory. General expressions have been derived for the excited longitudinal and transverse wakefields and related to the resonant wavenumbers which can be obtained from the dispersion relation. In the absence of friction, the stopping power of the wakefield driver, modelled here as a charged macroparticle, can be written solely as a function of these resonant wavenumbers. The dependencies of the wakefields on the radii of the double-walled carbon nanotubes and the driving velocity have been studied. Double-walled carbon nanotubes with inter-wall distances much smaller than the internal radius may be a potential option to obtain higher wakefields for particle acceleration compared to single-walled carbon nanotubes.

Quantum mechanical approach to plasma waves with helical wavefront

Plasma waves with helical wavefront are studied theoretically from the quantum mechanical viewpoint and are shown to produce a spinning motion of a charged macroparticle in a complex plasma. The electrostatic helical perturbations are described by the wave function for a Laguerre–Gaussian beam mode with the radial/angular mode numbers n/l. The interaction and the transfer of angular momentum from the wave to a particle are analyzed by the method of second quantization with the help of the Feynman diagram. Laguerre function, instead of the Born approximation, is introduced to describe plasma waves with helical wavefront. A pair of dust particles in a complex plasma exchange a quasiparticle (virtual plasmon) resulting in the acquisition of angular momentum, which makes a dust particle spin in motion with rotational frequency Ωϕ. The resonance condition ω−kvz−lΩϕ=0 and the conservation of angular momentum IdΩϕ=lℏ determine the rotational frequency, where ω and k are frequency and axial wave number of the helical wave, and vz and Id are axial velocity and the moment of inertia of a dust particle.

Positively Charged Macroparticles in Low-Temperature Plasma

The evolution of a positively charged metallic macroparticle placed into the low-temperature plasma is considered. The influence of the value of the initial macroparticle charge on the dynamics of the electrical potential and temperature of the macroparticle, as well as the possibility of evaporation of a macroparticle due to its interaction with plasma particles are studied. The system of equations of the energy balance and the current balance based on the OML theory, that takes into account the changing of macroparticle potential and its temperature over the time is solved numerically. The solution of the system of equations shows the evolution of the macroparticle potential and temperature within the time interval from the moment when the macroparticle is placed in the plasma until the moment the macroparticle has charged to the floating potential. The positive charge of the macroparticle excludes the thermionic emission and secondary electron emission from the macroparticle surface, as well as the mechanisms of cooling of the macroparticle associated with these emission processes. Analytical expressions that determine the macroparticle potential, the electron current on the macroparticle, as well as the power transferred by plasma electrons in the case when the energy of attraction of electrons to the macroparticle strongly exceeds the energy of thermionic electrons, the energy of secondary electrons and the energy of plasma ions are obtained. A simplified system of equations of the energy balance and the current balance for a positively charged macroparticle is solved; the solution of the simplified equations matches with the solution of the general equations in the region of positive values of the macroparticle potential. Calculations show that during the charging of the macroparticle, its temperature increases up to the boiling point of the macroparticle substance. An equation that determines the conditions under which evaporation of macroparticles is possible has been obtained and solved numerically. The possibility of evaporation of macroparticles of a given size (critical value of the radius) due to initial charging to high positive values of potential is shown. The dependencies of the critical value of the radius on the initial value of the potential for tungsten and copper macroparticles that can be evaporated in a low-temperature plasma are obtained. These solutions bound the region of the parameters where evaporation of a macroparticle is possible and where it is not. The critical values of the potential for copper and tungsten particles with sizes of 0.1 and 1 μm are calculated. The dependence of the radius of a macroparticle on time during the process of vaporization is obtained.

About the force of electrostatic interaction between two spheroidal macroparticles in the Poisson-Boltzmann model

Electrostatic interaction of two charged spheroidal macroparticles is analyzed within the linearized Poisson-Botzmann model.Interparticle forces are calculated through finite-element method in the regimes of weak and moderate screening with constant surface potentials in the absence of external field. Keywords: linearized Poisson-Botzmann model, two charged macroparticles, spheroidal macroparticles, colloidal particles, dusty plasmas.

О силе электростатического взаимодействия двух сфероидальных макрочастиц в модели Пуассона-Больцмана

Еlectrostatic interaction of two charged spheroidal macroparticles is analyzed within the linearized Poisson–Botzmann model.Interparticle forces are calculated through finite-element method in the regimes of weak and moderate screening with constant surface potentials in the absence of external field.

Friction properties of thick tetrahedral amorphous carbon coating with different surface defects under dry contact conditions

Surface defects of tetrahedral amorphous carbon coatings are typically defined as spikes, droplets, and pores. In this study, a hybrid filtering method using a fixed physical and electrical filter (duct bias voltage) in a filtered cathodic vacuum arc system was used to control the surface defects. The introduction of the duct bias can control to trap the negatively charged macro-particles which is transported to the base material due to a floating potential and duct wall sheath that depend on the positive voltage. The applied positive duct bias voltage was 10, 15, 20, and 30 V. The results of this experiment revealed that as the duct bias voltage increased up to 30 V, the spikes and droplets were almost completely removed on the tetrahedral amorphous carbon surface and only the pores remained. The pores could not create a rough surface for the relative motion between interfaces due to which the friction coefficient increased as the duct bias voltage increased up to 30 V. It was concluded that the spike and droplet defects were positive elements and were required to introduce a carbon-based transfer interface and maintain a stable coefficient of friction.

Coupled MHD – Hybrid Simulations of Space Plasmas

Heliospheric plasmas require multi-scale and multi-physics considerations. On one hand, MHD codes are widely used for global simulations of the solar-terrestrial environments, but do not provide the most elaborate physical description of space plasmas. Hybrid codes, on the other hand, capture important physical processes, such as electric currents and effects of finite Larmor radius, but they can be used locally only, since the limitations in available computational resources do not allow for their use throughout a global computational domain. In the present work, we present a new coupled scheme which allows to switch blocks in the block-adaptive grids from fluid MHD to hybrid simulations, without modifying the self-consistent computation of the electromagnetic fields acting on fluids (in MHD simulation) or charged ion macroparticles (in hybrid simulation). In this way, the hybrid scheme can refine the description in specified regions of interest without compromising the efficiency of the global MHD code.

EFFECT OF PULSED SUBSTRATE BIASING ON MACROPARTICLE IN VACUUM ARC

An analytical model of the interaction of macroparticle (MP) with vacuum arc plasma in plasma immersion ion implantation (PIII) is presented. The proposed model is based on combination of the theory of charge dynamics of MP and sheath model for PIII. In the framework of this model, the MP charge dynamics during voltage pulse as well as during interval between pulses is investigated. It is obtained that MP charge and MP behavior depend on pulsed bias parameters such as pulse duration, duty cycle and bias amplitude. It is shown that pulsed substrate biasing is effective method to control of the MPs in plasma processing.

Large-Scale Transport of Charged Macroparticles Induced by Dust–Acoustic Solitons

We have studied experimentally the oscillatory process in the dusty plasma in the glow discharge stratum. It is shown that the oscillations are induced by the dust–acoustic instability, as a result of which dust–acoustic solitons are excited. The motion of dust particles in the electric field of solitons has been analyzed. It has been established that a soliton leads to a large-scale unidirectional transport of charged particles in the direction of its motion. The experimental results have been interpreted theoretically using the MHD model of the plasma.

Analysis of macroparticle charge screening in a nonequilibrium plasma based on the kinetic collisional point sink model

The screening of macroparticles in a nonequilibrium plasma is considered on the basis of the Vlasov kinetic equations supplemented with the collisional term in the Bhatnagar–Gross–Krook approximation and the point sink method. In this method, the absorption of electrons and ions by a macroparticle is described by introducing effective point sinks into the kinetic equations for plasma electrons and ions. Explicit expressions are derived for the potential distribution around a macroparticle and effective charges that determine the behavior of the potential at large distances taking into account collisions of electrons and ions with neutral buffer gas atoms. We consider the cases of a constant collision frequency and constant mean free paths of electrons and ions in the buffer gas. Numerical calculations are performed for dusty isothermal and nonisothermal plasmas in helium, neon, argon, krypton, and xenon at pressures of 10–1 to 104 Pa, which are typical of experiments with dusty plasmas.

Initiation of dusty structures in chain reactions under the action of gyrotron radiation on a mixture of metal and dielectric powders with an open boundary

A dusty plasma formed in chain exothermal reactions initiated by radiation of a high-power gyrotron in mixtures of metal and dielectric powders has been described. An oscillatory character of such chain reactions, as well as the appearance of dust particles at the first (explosive) stage, has been detected. The tracks, velocities, and sizes of dust particles have been measured. It has been revealed that ensembles of dust particles appear in a reactor after switching-off of the gyrotron against the background of development of chemical reactions. The time of existence of these ensembles is three or four orders of magnitude larger than the duration of a microwave radiation pulse. The quasistationary state of the low-temperature plasma with charged macroparticles appears because of both the chemical heating of the mixture in the reactor and thermophoresis. It has been shown that dust particles are necessary as crystallization nuclei for the creation (or deposition) of complex composites of nano- and micromaterials produced in secondary plasma chemical synthesis.

Effect of the size of charged spherical macroparticles on their electrostatic interaction in an equilibrium plasma

The effect of the size of two charged spherical macroparticles on their electrostatic interaction in an equilibrium plasma is analyzed within the linearized Poisson–Botzmann model. It is established that, under the interaction of two charged dielectric macroparticles in an equilibrium plasma, the forces acting on each particle turn out to be generally unequal. The forces become equal only in the case of conducting macroparticles or in the case of dielectric macroparticles of the same size and charge. They also turn out to be equal when the surface potentials of the macroparticles remain constant under the variation of interparticle distances. Formulas are proposed that allow one to calculate the interaction force with a high degree of accuracy under the condition that the radii of macroparticles are much less than the screening length, which is usually satisfied in experiments with dusty plasmas.

Interaction in equilibrium plasmas of charged macroparticles located in nodes of cubic lattices

Interaction of two charged pointlike macroparticles located at nodes of simple cubic (sc), body-centered cubic (bcc) and face-centered cubic (fcc) lattices in an equilibrium plasma is studied within 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 halflength of a computational cell. It is found that in a case of dust particles arranged in the nodes of the sc, bcc and fcc lattices, the electrostatic force acting on them is equal to zero and the nature of the interaction changes from repulsion to attraction; hence, the infinite sc, bcc and fcc lattices of charged dust particles are thermodynamically stable at rather low temperatures.

Interaction of macroparticles localized in Wigner–Seitz cells of various types of cubic lattices in an equilibrium plasma

The interaction of two charged point macroparticles located in Wigner–Seitz cells of simple cubic (SC), body-centered cubic (BCC), or face-centered cubic (FCC) lattices in an equilibrium plasma has been studied within the Debye approximation or, more specifically, based on the linearized Poisson–Boltzmann model. The shape of the outer boundary is shown to exert a strong influence on the pattern of electrostatic interaction between the two macroparticles, which transforms from repulsion at small interparticle distances to attraction as the interparticle distance approaches half the length of the computational cell. The macroparticle pair interaction potential in an equilibrium plasma is shown to be nevertheless the Debye one and purely repulsive for likely charged macroparticles.

Toward analytical description of the electrostatic potential of charged macroparticle in weakly ionized plasma

The results of the numerical studies of the electrostatic potential distribution around a solitary charged absorbing macroparticle embedded into weakly ionized strongly collisional plasma within the drift-diffusion approximation is presented. Nonisothermal and isothermal plasma as well as various grain sizes are considered. The comparison of calculated potential and plasma particles distributions with analytical expressions is performed. The possibility to describe the potential distribution with superposition of Debye and Coulomb potentials with effective charges is studied in details. The dependence of the scaling parameter for screening length and effective charges on macroparticle size and electron-to-ion temperature ratio is studied.

Electrostatic, elastic and hydration-dependent interactions in dermis influencing volume exclusion and macromolecular transport

Interstitial exclusion refers to the limitation of space available for plasma proteins and other macromolecules based on collagen and negatively charged glycosaminoglycans (GAGs) in the interstitial space. It is of particular importance to interstitial fluid and plasma volume regulation. Here we present a novel mechanical and mathematical model of the dynamic interactions of structural elements within the interstitium of the dermis at the microscopic level that may explain volume exclusion of charged and neutral macroparticles. At this level, the interstitium is considered to consist of elements called extracellular matrix (ECM) cells, again containing two main interacting structural components on a fluid background including anions and cations setting up osmotic forces: one smaller GAG component, having an intrinsic expansive electric force, and one bigger collagen component, having an intrinsic elastic force. Because of size differences, the GAG component interacts with a fraction of the collagen component only at normal hydration. This fraction, however, increases with rising hydration as a consequence of the modeled form of the interaction force between the GAGs and collagen. Collagen is locally displaced at variable degrees as hydration changes. Two models of GAGs are considered, having largely different geometries which demands different, but related, forms of GAG–collagen interaction forces. The effects of variable fixed charges on GAGs and of GAG density in tissue are evaluated taking into account observed volume exclusion properties of charged macromolecules as a function of tissue hydration. The presented models may improve our biophysical understanding of acting forces influencing tissue fluid dynamics. Such knowledge is significant when evaluating the transport of electrically charged and neutral macromolecules into and through the interstitium, and therefore to drug uptake and the therapeutic effects of macromolecular agents.

Charging of nonspherical macroparticles in a plasma.

The current theories of macroparticle charging in a plasma are limited to spheres, and are unsuitable for the multitude of nonspherical objects existing in astrophysical, atmospheric, laboratory, and fusion plasmas. This paper extends the most widely used spherical charging theory, orbit motion limited theory, to spheroids and, as such, provides a comprehensive study of the charging of nonspherical objects in a plasma. The spherical charging theory is shown to be a reasonable approximation for a considerable range of spheroids. However, the electric potential of highly elongated spheroids can be almost twice the spherical value. Furthermore, the total charge on the spheroids increases by a significantly larger factor than their potential.

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

AbstractThe influence of the outer boundary shape on the electrostatic interaction of two charged point macroparticles in an equilibrium plasma is studied within the Debye‐Hückel 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)

Coulomb structures of charged macroparticles in static magnetic traps at cryogenic temperatures

Electrically charged (up to 107e) macroscopic superconducting particles with sizes in the micrometer range confined in a static magnetic trap in liquid nitrogen and in nitrogen vapor at temperatures of 77–91 K are observed experimentally. The macroparticles with sizes up to 60 μm levitate in a nonuniform static magnetic field B ~ 2500 G. The formation of strongly correlated structures comprising as many as ~103 particles is reported. The average particle distance in these structures amounts to 475 μm. The coupling parameter and the Lindemann parameter of these structures are estimated to be ~107 and ~0.03, respectively, which is characteristic of strongly correlated crystalline or glasslike structures.

Electrostatic interaction of two charged macroparticles in an equilibrium plasma

This article is a critical review of publications devoted to studying the electrostatic interaction of two charged macroparticles in an equilibrium plasma. It is shown from an analysis of the force of interaction based on the Maxwell stress tensor that two macroparticles with identical charges in the Poisson–Boltzmann model always repel each other both in isothermal and nonisothermal plasmas. At distances between macroparticles for which the Boltzmann exponents can be linearized, the interaction between macroparticles is completely described by the Debye–Huckel model. The correction to free energy due to the electrostatic interaction in the system of two macroparticles is determined by integrating the correction to the internal energy and by direct calculation of the correction for entropy. It is shown that the free energy coincides with the Yukawa potential. The coincidence of the interaction energy obtained by integrating the force of interaction with the free energy leads to the conclusion about the potential nature of the force of interaction between two macroparticles in an equilibrium plasma. The effect of the outer boundary on the electrostatic interaction force is analyzed; it is shown that the type of interaction depends on the choice of the boundary conditions at the outer boundary. It is also shown that the accumulation of space charge near the outer boundary can lead to the attraction of similarly charged particles at distances comparable with the radius of the outer boundary.