Development of a self-consistent model of dust grain charging at elevated pressures using the method of moments

A model of dust grain charging is constructed using the method of moments. The dust grain charging process in a weakly ionized helium plasma produced by a 100-keV electron beam at atmospheric pressure is studied theoretically. In simulations, the beam current density was varied from 1 to 10⁶ μA/cm². It is shown that, in a He plasma, dust grains of radius 5 μm and larger perturb the electron temperature only slightly, although the reduced electric field near the grain reaches 8 Td, the beam current density being 10⁶ μA/cm². It is found that, at distances from the grain that are up to several tens or hundreds of times larger than its radius, the electron and ion densities are lower than their equilibrium values. Conditions are determined under which the charging process may be described by a model with constant electron transport coefficients. The dust grain charge is shown to be weakly affected by secondary electron emission. In a beam-produced helium plasma, the dust grain potential calculated in the drift-diffusion model is shown to be close to that calculated in the orbit motion limited model. It is found that, in the vicinity of a body perturbing the plasma, there may be no quasineutral plasma presheath with an ambipolar diffusion of charged particles. The conditions for the onset of this presheath in a beam-produced plasma are determined. __________ Translated from Fizika Plazmy, Vol. 29, No. 3, 2003, pp. 214–226. Original Russian Text Copyright ? 2003 by Filippov, Dyatko, Pal’, Starostin.     

Charge and potential of a dust grain versus the intergrain distance and establishment of the latter in a low-pressure plasma

Results from experimental studies of ordered dust structures in plasma are reviewed. The experimental conditions and the data on the grain size and intergrain distance in plasma dust crystals are analyzed. It is shown that intergrain distance is a function of the grain size. The range of the ratio of the dust grain size to the Debye radius within which plasma dust crystals can form is determined. A volume cell surrounding a dust grain in plasma is considered. It is found that the potential and charge of the grain depend substantially on the intergrain distance. The charge, potential, and potential energy of a dust grain in a plasma dust crystal, as well as the electrostatic force exerted by the plasma field on the grain, are calculated by the method of molecular dynamics as functions of the intergrain distance. The corresponding analytic approximations and the criterion for the establishment of a steady-state intergrain distance are proposed.     

Effect of the shape of the electron energy distribution function on the dust grain charge and its screening in glow discharge plasmas

The dust grain charge in the plasma of a glow discharge in noble gases and nitrogen is calculated in the orbit motion limited model for reduced fields in the range of E/N = 1–20 Td. The calculations were performed using the electron energy distribution functions (EEDFs) obtained by solving the Boltzmann equation numerically with allowance for elastic and inelastic electron scattering and analytically with allowance for only elastic scattering and (for nitrogen) excitation of rotational levels, as well as using a Maxwellian EEDF. In the latter case, either the characteristic electron energy or mean electron energy multiplied by two thirds was used as the electron temperature. It is shown that the calculations with the use of a Maxwellian EEDF yield larger values of the grain charge as compared to those calculated with EEDFs obtained by solving the Boltzmann equation. The range of E/N values is determined in which analytical expressions for the EEDF obtained with allowance for elastic scattering and excitation of rotational levels are applicable to calculating the grain charge. The effect of the EEDF shape on the screening of the dust grain charge in plasma is investigated. The Debye screening length in case of a Maxwellian EEDF is shown to be shorter than that obtained with EEDFs calculated by numerically solving the Boltzmann equation.     

A nanoparticle in plasma

Charge and energy fluxes onto a nanoparticle under conditions typical of laboratory plasmas are investigated theoretically. Here, by a nanoparticle is meant a grain the size of which is much smaller than both the electron Larmor radius and Debye length and the thermionic emission from which is not limited by the space charge. Under conditions at which thermionic emission plays an important role, the electric potential and temperature T _p of a nanoparticle are determined by solving a self-consistent set of equations describing the balance of energy and charge fluxes onto the nanoparticle. It is shown that, when the degree of plasma ionization exceeds a critical level, the potential of the nanoparticle and the energy flux onto it increase with increasing nanoparticle temperature, so that, starting from a certain temperature, the nanoparticle potential becomes positive. The critical degree of ionization starting from which the potential of a nanoparticle is always positive is determined as a function of the plasma density and electron temperature. The nanoparticle temperature T _p corresponding to the equilibrium state of a positively charged nanoparticle is found as a function of the electron density for different electron temperatures.     

The conceptual development of stationary plasma thrusters

The history of the development of the concept of the stationary plasma thruster is described. The data obtained indicate the possibility of creating extended (over a distance substantially longer than the Debye radius) electric fields in a fully ionized plasma with a relatively high electron temperature (T_e>10 eV) and a conductivity close to the classical one. Based on these results, a number of fundamentally new plasma-dynamic systems were proposed; in particular, the principles of plasma optics were formulated and verified experimentally. In the course of these investigations, new physical processes, such as the formation of the distribution function of the electrons in their collisions with the wall and the effect of the near-wall conductivity, were discovered. The structure of the Debye layer for the case in which the coefficient of the secondary electron emission of a dielectric wall is larger than unity was investigated.     

Mechanisms of dust grain charging in plasma with allowance for electron emission processes

The process of dust grain charging is described with allowance for secondary, ion-induced, photoelectric, and thermal electron emission from the grain surface. The roughness of the grain surface is taken into account. An intermediate charging regime involving ion–atom collisions and electron ionization in the perturbed plasma region is analyzed using the moment equations and Poisson’s equation. A calculation method is proposed that allows one to take into account the influence of all the above effects and determine the radius of the plasma region perturbed by the dust grain.     

Study of the plasma in a preformed Z-pinch constriction

The development of a preformed constriction in cylindrical agar-agar loads at currents of up to 3 MA is studied experimentally. The loads 3–5 mm in diameter have a mass density of 0.1 g/cm³ and are filled with different materials. Due to the implosion of the constriction to a minimum size of 40–70 μm, a hot dense plasma (with the electron density n _e=10²² cm⁻³, electron temperature T _e=0.8–1.5 keV, and ion temperature T _i=3–12 keV) is produced. It is found that the ion temperature substantially exceeds the electron temperature. The lifetime of the high-temperature plasma determined from the FWHM of a soft X radiation (SXR) pulse is shorter than 5 ns, the radiation power of photons with energies of ≥1 keV is higher than 0.5×10¹⁰ W, and their total energy attains 50 J. High-speed photography in the VUV, SXR, and optical spectral regions indicates the protracted generation of the high-temperature plasma. Calculations by the two-dimensional ideal MHD model of the Z-pinch show that the most important consequence of the protracted plasma generation in the constriction region is that the current is intercepted by a freshly produced plasma. In the course of plasma generation, the current near the axis inside the region of radius 50 μm is at most one-half of the total current. After the plasma generation comes to an end, almost the entire current is concentrated in this region for several nanoseconds; this process is accompanied by a sharp increase in the plasma temperature. __________ Translated from Fizika Plazmy, Vol. 27, No. 12, 2001, pp. 1101–1110. Original Russian Text Copyright ? 2001 by Bakshaev, Blinov, Vikhrev, Gordeev, Dan’ko, Korolev, Medovshchikov, Nedoseev, Smirnova, Tumanov, Chernenko, Shashkov.     

First results obtained with a sweeping pulsed radar reflectometer in the Globus-M tokamak

A weeping pulsed radar reflectometer designed for measuring the spatial electron density distribution in the Globus-M spherical tokamak with a minor plasma radius of a=24 cm, a major radius of R=36 cm, a toroidal field of B _T=0.5 T, a plasma current of I _p=200 kA, and an average density of n=(3–10)×10¹³ cm^?3 is described. The reflectometer operation is based on the reflection of microwaves with a carrier frequency f from a plasma layer with the critical density n=(0.0111f)², where n is the electron density in units of 10¹⁴ cm^?3 and f is the microwave frequency in GHz. By simultaneously probing the plasma at different frequencies, it is possible to recover the electron density profile. Microwave pulses with different frequencies are obtained by frequency sweeping. To increase the range of measured densities, channels with fixed frequencies are also used; as a result, the instrument has eleven frequency channels: a 19.5-GHz channel, eight channels in the 26-to 40-GHz frequency range, a 51.5-GHz channel, and a 60-GHz channel, which corresponds to eleven points in the density profile: 0.47×10¹³ cm^?3, eight points in the (0.8–1.95)×10¹³-cm^?3 range, 3.27×10¹³ cm^?3, and 4.5×10¹³ cm^?3. The reflectometer allows detailed measurements of the density profile with a time resolution of several tens of microseconds, which can be useful, in particular, in studying the processes related to the formation of an internal transport barrier in plasma. The first results obtained using this reflectometer in the Globus-M tokamak under various operating conditions are discussed.     

Formation of nonquasineutral vortex plasma structures with a zero net current

A nonquasineutral vortex structure with a zero net current is described that arises as a result of electron drift in crossed magnetic and electric fields, the latter being produced by charge separation on a spatial scale of about the magnetic Debye radius r _B = |B|/(4πen _e ). In such a structure with a radius of r ～ r _B , the magnetic field is maintained by a drift current on the order of the electron Alfvén current J _Ae = m _e c ³/(2e) and can become as strong as B ? m _e c ²/(er). Estimates show that, in a plasma with a density of n _e = 10²¹?10²³ cm^?3 and with nonzero electron vorticity driven by high-power laser radiation on a time scale on the order of θ _pe ^?1 , magnetic fields with a strength of B ～ 10⁸?10⁹ G are generated on micron and submicron scales. The system with closed current that is considered in the present paper can also serve as a model of hot spots in the channel of a Z-pinch.     

Screening of the dust grain charge in a nonequilibrium plasma with two positive ion species

The screening of the grain charge in a nonequilibrium plasma is studied with allowance for electron and ion fluxes to the grain surface and the bulk processes of production and loss of charged particles in an argon plasma. The objective of the paper is to investigate how the conversion of monatomic Ar⁺ ions into diatomic Ar₂⁺ ions influences the screening of the dust grain charge in a plasma produced by an external gas ionization source. It is found that the conversion of positive ions leads to the onset of a second ion species in the plasma and, as a consequence, to a three-exponential screening of the grain charge; moreover, in a certain range of plasma parameters, all three screening constants are of the same order of magnitude. Analytical results are compared with the data of numerical simulations carried out based on the drift-diffusion approximation.     

High-Power X-Ray Line Radiation of the Plasma Produced in a Collision of High-Energy Plasma Flows

Results are presented from experimental studies of a pulsed source of soft X-ray (SXR) emission with photon energies in the range of 0.4–1 keV and an output energy of 2–10 kJ. SXR pulses with a duration of 10–15 μs were generated in collisions of two plasma flows propagating toward one another in a longitudinal magnetic field. The plasma flows with velocities of (2–4) × 10⁷ cm/s and energy contents of 70–100 kJ were produced by two electrodynamic coaxial accelerators with pulsed gas injection. Nitrogen and neon, as well as their mixtures with deuterium, were used as working gases. The diagnostic equipment is described, and the experimental results obtained under different operating conditions are discussed. In particular, X-ray spectroscopy was used to study the high-temperature plasma produced in a collision of two plasma flows. The observed intensities of spectral lines are compared with the results of detailed kinetic calculations performed in a steady-state approximation. The calculations of the nitrogen and neon kinetics have shown that the electron temperature of a nitrogen plasma can be most conveniently determined from the intensity ratio of the resonance lines of He- and H-like nitrogen ions, while that of a neon plasma, from the intensity ratio between the resonance line of He-like Ne IX ions and the 3p?2s line of Li-like Ne VIII ions. In the experiments with plasma flows containing nitrogen ions, the electron temperature was found to be ≈120 eV, whereas in the experiments with plasma flows containing neon ions, it was 160–170 eV.     

Lithium Doping to Enhance Thermoelectric Performance of MgAgSb with Weak Electron–Phonon Coupling

Despite the unfavorable band structure with twofold degeneracy at the valence band maximum, MgAgSb is still an excellent p‐type thermoelectric material for applications near room temperature. The intrinsically weak electron–phonon coupling, reflected by the low deformation potential E_def ≈ 6.3 eV, plays a crucial role in the relatively high power factor of MgAgSb. More importantly, Li is successfully doped into Mg site to tune the carrier concentration, leading to the resistivity reduction by a factor of 3 and a consequent increase in power factor by ≈30% at 300 K. Low lattice thermal conductivity can be simultaneously achieved by all‐scale hierarchical phonon scattering architecture including high density of dislocations and nanoscale stacking faults, nanoinclusions, and multiscale grain boundaries. Collectively, much higher average power factor ≈25 μW cm^?1 K^?2 with a high average ZT ≈ 1.1 from 300 to 548 K is achieved for 0.01 Li doping, which would result in a high output power density ≈1.56 W cm^?2 and leg efficiency ≈9.2% by calculations assuming cold‐side temperature T_c = 323 K, hot‐side temperature T_h = 548 K, and leg length = 2 mm.     

Formation and development of a leader channel in air

A self-consistent model is constructed that makes it possible to investigate the formation of a leader channel in air and the evolution of the channel parameters in the developed stage, when the leader is as long as several meters or more. The initial stage of the formation of the channel is characterized by a rapid increase in the electron density and gas temperature, which is a consequence of the onset of thermal-ionizational instability. The radius of a fully developed plasma column at the current I=1 A in air at atmospheric pressure is R _h?10^?2 cm. Then, because of the gas-dynamic and thermal expansion, the plasma radius R _h increases considerably; as a result, the electric field and the reduced field E/N in the corresponding parts of the channel decrease. In the case under consideration, the field in the “oldest” parts of the leader drops to 200 V/cm and even lower and the reduced field becomes as weak as E/N≤10 Td. In this case, the densities of the main species of neutral and charged particles at the center of the channel remain close to their thermodynamically equilibrium values. The results of calculations are compared with the available experimental data.     

Investigation of the charge and potential of a dust grain in a low-pressure plasma with allowance for ionization in the intergrain space

The formation of the ion flow to a dust grain and the distribution of the electric potential in a low-pressure dusty plasma are investigated theoretically with allowance for ionization in the intergrain space. Poisson’s equation similar to the Langmuir plasma-sheath equation is solved numerically with the use of partial analytic solutions at the boundary of the Seitz-Wigner cell and in thin layers in the intergrain space. The charge and potential of a dust grain are found as functions of the grain radius and cell size. The grain potential and the total cell potential energy as functions of the cell size display weak minima, whose positions correspond to the observed intergrain distance in dusty crystals.     

Numerical simulations of ion and electron transport in a low-temperature dusty plasma

Charged particle transport and kinetic processes in a low-temperature dusty plasma are numerically simulated. Dust grains are represented as spheres with a given radius. The self-consistent electric field in the plasma surrounding a charged dust grain is calculated taking into account the perturbations of plasma quasineutrality near the grains. It is shown that applying an external electric field leads to a rearrangement of the plasma space charge and a break of the spherical symmetry of the electron and ion density distributions around the grain. The mutual influence of two identical charged dust grains is considered, and the energy of the electrostatic interaction between the grains is calculated. It is shown that this energy has a minimum at a certain finite distance between the grains.     

Nonlinear nitrous oxide (N2O) response to nitrogen fertilizer in on‐farm corn crops of the US Midwest

Row‐crop agriculture is a major source of nitrous oxide (N₂O) globally, and results from recent field experiments suggest that significant decreases in N₂O emissions may be possible by decreasing nitrogen (N) fertilizer inputs without affecting economic return from grain yield. We tested this hypothesis on five commercially farmed fields in Michigan, USA planted with corn in 2007 and 2008. Six rates of N fertilizer (0–225 kg N ha^?1) were broadcast and incorporated before planting, as per local practice. Across all sites and years, increases in N₂O flux were best described by a nonlinear, exponentially increasing response to increasing N rate. N₂O emission factors per unit of N applied ranged from 0.6% to 1.5% and increased with increasing N application across all sites and years, especially at N rates above those required for maximum crop yield. At the two N fertilizer rates above those recommended for maximum economic return (135 kg N ha^?1), average N₂O fluxes were 43% (18 g N₂O–N ha^?1 day^?1) and 115% (26 g N₂O–N ha^?1 day^?1) higher than were fluxes at the recommended rate, respectively. The maximum return to nitrogen rate of 154 kg N ha^?1 yielded an average 8.3 Mg grain ha^?1. Our study shows the potential to lower agricultural N₂O fluxes within a range of N fertilization that does not affect economic return from grain yield.     

Double layer in a cylindrical hollow-cathode discharge

A dc cylindrical coaxial glow discharge with an inner grid anode has been studied. The region between the two electrodes is seen dark, while a brightly glowing region forms inside the grid anode up to the center. The current-voltage characteristic of a dc cylindrical glow discharge in nitrogen is similar to that of a normal glow discharge, while the normal glow discharge voltage decreases with increasing pressure. The minimum plasma potentials are observed in the hollow cathode region due to the accumulation of electrons at the back of the grid anode. At the center, some of the passed electrons are converged, so their potential is decreased. These electrons have a sufficient time to be redistributed to form one group with a Maxwellian electron energy distribution function. The electron temperature measured by electric probes varies from 1.6 to 3.6 eV, while the plasma density varies from 3.9 × 10¹⁶ to 7 × 10¹³ m⁻³, depending on the discharge current and probe position. The plasma density increases as the electrons move radially from the grid toward the central region, while their temperature decreases.     

Density measurements in a tenuous plasma by a high-frequency resonator with a periodic structure

It is proposed to measure plasma densities in the range of 10⁵–10⁹ cm^?3 by a high-frequency resonator with a periodic structure consisting of annual high-frequency electrodes mounted on oppositely directed racks. The method proposed substantially increases the proportionality factor between the electron density and the shift of the resonator eigenfrequency. This factor is determined by the calibration method using an electron beam with given parameters. The calibration ensures an accuracy of about 10% for density measurements in a plasma produced by a 5-MeV proton beam propagating in air at pressures of 10^?2–10^?5 torr.     

Diagnostics of MHD instability in the Globus-M spherical tokamak

The paper describes a diagnostic system for studying MHD plasma perturbations in the Globus-M spherical tokamak (a major radius of 0.36 m, a minor radius of 0.24 m, and an aspect ratio of 1.5). The system includes a poloidal and a toroidal array consisting of 28 and 16 Mirnov probes, respectively, as well as a 32-channel proportional soft X-ray detector. Methods are described for calculating the poloidal and toroidal numbers of the dominant helical perturbations by using data from probe measurements. Results are presented of processing the experimental data from some tokamak discharges with a plasma current of 150–250 kA, an average electron density of up to 10²⁰ m^?3, and a toroidal magnetic field of 0.4 T. Specific features of MHD perturbations and their influence on the parameters of the plasma column in different stages of a discharge are briefly discussed.     

Dynamics of the implosion of a tungsten wire array onto the central aluminum wire

Results are presented from the studies of the magnetic implosion of a tungsten wire liner onto an aluminum wire at currents of 2.0–2.6 MA. The experiments were carried out in the S-300 high-power pulsed facility at the Russian Research Centre Kurchatov Institute. The liner is composed of 50 wires 6 μm in diameter and 1 cm in length, which are equally spaced on a circle 1 cm in diameter. An aluminum wire 120 μm in diameter is positioned at the array axis. The liner implosion was accompanied by the generation of VUV and soft X-ray emission. The parameters of the pinch plasma produced during the liner implosion onto the aluminum wire were determined from the time-resolved spectral measurements by a five-channel polychromator. The ion and electron densities turned out to be equal to n _i≈4×10¹⁹ cm⁻³ and n _e≈4×10²⁰ cm⁻³, respectively, and the electron temperature was T _e≈40 eV. The radiation energy measured in the range 50–600 eV was 2–10 kJ. The sources of soft X-ray emission in hydrogen-and helium-like aluminum lines were the bright spots and local objects (clouds) formed in the plasma corona at an electron temperature of 200–500 eV and electron density of 10²¹–10²² cm⁻³. The possibility of both the generation of an axial magnetic field during the liner implosion and the conversion of the energy of this field into soft X-ray emission is discussed. __________ Translated from Fizika Plazmy, Vol. 28, No. 6, 2002, pp. 514–521. Original Russian Text Copyright ? 2002 by Bakshaev, Blinov, Dan'ko, Ivanov, Klír, Korolev, Kravárik, Krása, Kubeš, Tumanov, Chernenko, Chesnokov, Shashkov, Juha.