Current Balance Equation Research Articles

Positively Charged Microparticle in Plasma with High-Energy Electron Beam

The processes of recharging, heating and evaporation of a positively charged microparticle (MP) introduced into the plasma with an injected high-energy electron beam are considered. It is assumed that the MP is charged outside the plasma and then introduced into the plasma by an accelerating field, where plasma and beam electrons hitting the MP heat and evaporate it. In addition to introducing the MP into the plasma, the positive MP charge provides an additional source of energy needed to heat and evaporate it. Using the OML theory, the system of current and energy balance equations was numerically solved and the conditions, under which the MP is heated to the boiling point of its substance, resulting in its intense evaporation, were determined. The influence of the energy of the electron beam on the process of MP recharging, as well as on the rate of its heating and evaporation, has been studied. An estimate of the particle entry velocity into the plasma has been made; the distances at which its recharging, heating to the boiling point and complete evaporation occur are determined. The work is carried out in order to creating plasma of a given elemental composition.

Dust particle surface potential in an argon-helium plasma using the (r,q)-distribution function

Abstract In this paper, the dust particle surface potential for argon-helium plasma is evaluated analytically and numerically in the context of negatively charged dust particles by employing a power-law r , q -distribution function. Recent studies have reported the argon-helium plasma and conducted a brief theoretical and experimental survey. To deepen our understanding further, this study aims to analyze the argon-helium plasma comprehensively using the same pattern but with the r , q -distribution function. For this purpose, the current balance equations are derived for electron, helium and argon ions, when these charge species attain the quasineutrality condition. We numerically examined the currents of plasma species for a broad range of effective distribution function parameters r and q . It is revealed that the surface potential of dust particles is significantly affected by the parameters r and q , helium ion-to-electron temperature ratio, argon ion-to-electron temperature ratio, and helium ion to argon ion number density ratio. By incorporating the multi-ion (argon-helium) species, the significance of low-temperature non-Maxwellian dusty (complex) plasma is briefly examined.

Numerical Calculations of Charging Threshold at GEO Altitudes With Two Temperature Non‐Extensive Electrons

AbstractSurface charging at geosynchronous altitude is one of the major concerns for satellites and spacecrafts. Spacecraft anomalies are often associated with extreme surface charging events, especially during substorms in which the GEO plasma is better modeled as two temperatures non‐Maxwellian plasma. In such case, we employ two temperature q‐non‐extensive distribution function to determine the onset of spacecraft surface charging which becomes complex since many parameters control the surface charging. We developed a current balance equation which better explains the charging threshold in comparison to a Maxwellian distribution function. The effect of non‐extensive parameters, temperature and density ratio on the current balance equation has been explained. The modified current balance equation predicts the critical and anti‐critical temperatures for various space‐grade materials both analytically and numerically. A significant change is observed in the quantities characterizing the charging current, average yield and density ratio in the presence of non‐extensive two temperature electrons. The mechanism underlying different charging behaviors at or near the threshold is also indicated at various plasma parametric domains. Furthermore, the general conditions of potential jump are also obtained theoretically which predicts the sudden or smooth potential transition.

Estimation of the Electron Density in the Near 3–4 RE Magnetosphere Based on the Measurement of the Interball-2 Satellite Potential

A new method is proposed for determining the electron density in rarefied plasma, based on simultaneous measurements of the Interball-2 satellite potential using IESP-2 (electric field instrument) and KM-7 (electron temperature sensor) probe devices. This makes it possible to estimate the photoelectron current density based on a procedure proposed earlier by the authors of this study. The electron concentration was determined only for the positive potential of the spacecraft. The balance equations for the satellite and the probe between the currents of the surrounding plasma electrons and photoelectrons emitted by the illuminated surface were compiled. In the magnetosphere, to bring the probe potential to the potential of the surrounding plasma, a bias current is directed into the probe, which was taken into account in the current balance equation for the probe. The electron energy used in the calculations was kTe = 1 eV. We analyzed data from ~350 orbits in the auroral region of the magnetosphere at altitudes of 2–3 RE from October 1996 to March 1998 during the period of low solar activity at the beginning of the 23rd cycle. Examples of the calculated electron density are given, which is in the range of 1–30 cm–3.

POSITIVELY CHARGED MICROPARTICLES IN PLASMA

The processes of recharging and changing the temperature of a positively charged microparticle (MP) introduced into plasma are considered. It is assumed that the MP is charged to a positive charge outside the plasma, and then enters the plasma due to the accelerating field. For various values of plasma density and temperature, a numerical solution of the energy and current balance equations of a MP is obtained. The equation that determines the evaporation of particles is solved numerically. The time dependence of the radius of a MP during evaporation has been obtained.

Spacecraft Charging Due To Energetic Electrons and Ions at Geosynchronous Altitudes

AbstractSatellites and spacecraft are usually exposed to space plasma disturbances, which vary in time at Geosynchronous Earth Orbit (GEO), affecting the charging of spacecraft and weather on the Earth. The charging currents are often described by the current‐balance equation (CBE) containing the electron‐ion (incoming/outgoing) current density fluxes and their energy distributions. The power‐law q‐distribution is the most generalized distribution that essentially characterizes more pronounced energy tails and can be reduced to standard Maxwellian distribution for q → 1. Using the equilibrium currents, the CBE is solved both analytically and numerically to study spacecraft charging within the framework of Whittaker function. It is found that energetic electron and ion‐induced currents significantly modify the charging phenomenon on the spacecraft's surface. Especially, ion‐induced currents result in the delay of negative charging at critical electron thermal energy and enhance the magnitude of the total normalized current. Apart from CuBe surface material, numerical analysis is also carried out for silver and Aluminum to determine the magnitude of total normalized current and onset of negative charging. The present findings are consistent with spacecraft charging at GEO altitudes around the Earth.

Influence of Xenon–Fluorine–Sulfur Hexafluoride (Xe+–F−–SF6−) and Argon-Fluorine-Sulfur Hexafluoride (Ar+–F−–SF6−) Streaming on Dust Surface Potential (DSP) That Has Cairn–Tsallis Distributed Plasmas

The dust grain surface potential is examined analytically and numerically in dusty plasmas containing negative/positive ion species by using the Cairn Tsallis (non-Maxwellian) dusty plasma. The equations for the dust-charging process are derived to solve the current balance equation for the xenon–fluorine–sulfur hexafluoride and argon–fluorine–sulfur hexafluoride plasmas. The charging process affected by plasma properties such as spectral indices α and q, in addition to positive ion streaming (UAr+ and UXe+) and negative ion streaming (UF− and USF6−) of both types of plasmas, is examined. Our findings suggest that considering a wide range of Xe+−F−−SF6− and Ar+−F−−SF6− masses is critical for understanding plasma physics, specifically multi-component plasmas.

Dust particle surface potential in fusion plasma with supra-thermal electrons

By solving the current balance equations, the effect of the supra-thermal electrons on the surface potential of a negatively charged dust particle in a fusion plasma is studied based on the orbital motion limited theory. A non-Maxwellian plasma is modeled by employing a q-non-extensive velocity distribution, where a decreased q-parameter (q < 1) yields increased population of supra-thermal electrons. It is found that with the decrease in the q-parameter, the surface potentials of tungsten and carbon dust particles become more negative. When the ion temperature or ion flow velocity is increased, the dust surface potential changes non-monotonically, which is first decreasing and then increasing. For a small q-parameter, the non-monotonic variation is more pronounced and the minimum value of surface potential moves toward higher values of the ion temperature or ion flow velocity. Due to the dependence of the dust particle surface potential on the supra-thermal electrons, the increased proportion of supra-thermal electrons causes the increase in the ion drag force and the decrease in the dust particle lifetime. Here, lifetime refers to the time taken for the dust surface temperature to increase from its initial value to the sublimation temperature (for carbon) or the melting temperature (for tungsten). The decrease in lifetime caused by supra-thermal electrons is significant as the dust particle radius is increased.

Transient Modeling and Optimization of a PEM Electrolyzer for Solar Photovoltaic Power Smoothing

While renewable energy fuel has always had no cost, in the past the cost of the energy conversion technology was prohibitive. Today, due to improved efficiency in the technology and substantial increases in manufacturing volume the cost to generate electricity from the renewables and the cost to store this electricity in lithium-ion batteries for four hours has made these technologies more than competitive with traditional sources. As higher renewable energy penetrations occur the variability and intermittent nature of solar photovoltaic (PV) electricity can cause steep ramping of conventional power plants, so longer term energy storage (days, weeks, instead of hours) will be needed to increase the reliability of grid operation. In Florida cloud cover of a PV field can cause rapid fluctuations of PV output requiring a fast response to smooth out the PV electric power output. A polymer electrolyte membrane (PEM) electrolyzer can serve as a utility controllable load that can be available at all times and the produced hydrogen can be sold or converted back into electricity directly through a PEM fuel cell. To study the integration of renewable solar with hydrogen for increasing grid reliability, a multi-software power control method and a transient thermal electrochemical PEM electrolyzer model has been developed.One-dimensional ("through-plane") and two-dimensional ("through-plane" and "in-plane") un-steady state models using gPROMS 2.1.1. were developed. The model considers mass, energy, momentum and current balance equations. The thermal energy balance considers the heat transfer through the backing layer, the flowfield plates and the gas and liquid flows. Kinetic parameters used in the model were determined using parameter estimation of single cell steady state polarization curves [1]. The single cell unsteady state models were extended to a stack model by adding cells in series and parallel. Real-time PV data taken from a 8.9 MWAC solar farm from Orlando Utilities Commission’s Stanton Energy Center was scaled up to 75 MWAC to design the electrolyzer that would be sized with the typical utility PV installation in Florida. The 75 MW PV data was smoothed using a power control strategy developed in MATLAB. The developed multi-software power control method and the electrochemical dynamic stack model shows the effectiveness of an electrolyzer in smoothing the PV signal to increase the grid stability and flexibility. Results are presented of different size electrolyzers to minimize short term cloud cover spikes in power while maximizing hydrogen production and the effectiveness of the electrolyzer.[1] Vincenzo Liso, Giorgio Savoia, Samuel Simon Araya, Giovanni Cinti and Søren Knudsen Kær, “Modelling and Experimental Analysis of a Polymer Electrolyte Membrane Water Electrolysis Cell at Different Operating Temperatures”, Energies, 11 (2018) 3272. doi:10.3390/en11123273

A mathematical model of the external circuits in a bipolar membrane electrodialysis stack: Leakage currents and Joule heating effect

Leakage currents existing in a bipolar membrane electrodialysis (EDBM) stack caused loss of coulombic efficiency, ranged from approximately 0.9% to 12%, and created undesirable heat that impaired its operation. A mathematical model for electrical analog of a cell pair, predicting leakage currents and Joule heating effect of the external circuits in a EDBM stack was developed by considering the electrochemical process as an electrical analog circuit. Current and potential balance equations was used to define the equivalent network, and differential calculus was applied to solve these equations. Leakage current model was validated with experimental and simulated results. On this basis, leakage currents and Joule heating effect in a pilot-scale EDBM stack were analyzed. The results revealed that leakage currents in external circuits were distributed symmetrically around the membrane stack and were significantly affected by the number of cell pairs, current density, and element resistivity. Moreover, Joule heating effect in the external circuit in the stack was quantitatively analyzed and the temperature effect was dominated by the slot closed to the electrode cell in the acid compartment. This was most pronounced (raised by 12.18 ℃ in 0.3 s) during the termination stage. Using these findings, EDBM stacks can be improved and the optimal spacers and a more reasonable process can be designed, which could boost the development of EDBMs.

Phenomenological plasma model for open-end emitter with orificed keeper hollow cathodes

Hollow cathodes are used as thermionic emitters in a variety of electric propulsion devices such as the Hall thruster. This work studies the derivation and discusses the results of a phenomenological (zero-dimensional) plasma model for a hollow cathode with open-end emitter and orificed keeper. This represents the first attempt to model the plasma in the three regions of hollow cathodes with open-end emitter geometry, i.e. the keeper orifice, the cathode–keeper gap, and the insert. The current continuity, ion balance, and plasma power balance equations are solved to compute the main plasma parameters in each of the aforementioned regions. One novelty of this work is the definition of mathematical fit functions for the dynamic viscosity and ionization and excitation rates for krypton. Moreover, the resistive losses in the cathode–anode region are estimated to model the cathode standalone diode testing with an external anode. The model delivers cathode operational parameters such as the discharge power and potential which are compared to experimental data for both xenon- and krypton-fed cathodes. Furthermore, the influence of the three regions’ geometries and the propellant flow rate as well as the discharge current on plasma parameters and cathode power budget of sample cathodes is discussed at length.

Dynamic Modeling of Hydrogen Systems for Grid Operations: PEM Electrolyzer

While solar and wind as sources of energy have always had no cost, in the past the cost of the energy conversion technology was prohibitive. Today, due to improved efficiency in the technology and substantial increases in manufacturing volume the cost to generate electricity from the sun and wind and the cost to store this electricity in lithium-ion batteries (4 hours) has made these technologies more than competitive with traditional sources. As higher renewable energy penetrations occur the variability and intermittent nature of solar photovoltaic (PV) electricity can cause ramping issues, so longer term energy storage (days, weeks, instead of hours) will be needed to increase the reliability of grid operation. A PEM electrolyzer can serve as a utility controllable load that can be available at all times and the stored hydrogen can be converted back into electricity directly through a PEM fuel cell. The hydrogen can also be mixed with natural gas to produce electricity through a gas turbine, used for transportation fuel and/or used as a chemical feedstock. The limit on energy production of a PEM fuel cell is a function of the volume of the tank. To understand the transient response of an electrolyzer under varying PV input, a thermal electrochemical dynamic model has been developed.We developed one-dimensional ("through-plane") and two-dimensional ("through-plane" and "in-plane") models. Firstly, a steady state model for a single cell was developed. The model considers mass, energy, momentum and current balance equations. Maxwell-Stefan diffusion equation is used to calculate the gas-phase species molar concentration in backing and catalyst layers. The electrochemical reactions are modeled using Butler-Volmer equation with varying surface molar concentrations of components. In addition, the thermal-electrochemical model considers the heat transfer through the backing layer, plate and the flow. Many of the kinetic parameters in the models were determined using parameter estimation with the data of single cell steady state polarization curves. These single cell steady state models were extended to a 510 kW electrolyzer stack model by adding cells in series and parallel to achieve a hydrogen flowrate of 90 Nm3/hr. To study the transient response of the electrolyzer stack a dynamic model was developed using a real-time PV input data. Results of the dynamic electrolyzer stack model under various changes with respect to the PV input will be presented. Monte-Carlo method was used to study the sensitivity of the electrolyzer design for given PV inputs. The available PV input data is scaled to meet the power requirement of a maximum of 510 kW and to meet the required hydrogen output, all while smoothing the PV output to the grid. The developed novel electrochemical dynamic model with varying PV input data shows the effectiveness of the electrolyzer in increasing the grid stability and flexibility.

Compact Modeling and Analysis of Charge and Device Capacitance for SELBOX Junctionless Transistor

A charge based compact drain current and capacitance modeling has been developed to describe the transfer and Capacitance-Voltage characteristics of the proposed device. The inversion charge density of the proposed model is defined on the basis of the surface potential model equation at the source and the drain end. These inversion charges are evaluated by the Ward Dutton partition method using the current continuity principle and charge balance equations. Using these inversion charges, a drain current model is discussed for the proposed device, which is based on implicit unified charge control expression. This model defined all the possible intrinsic capacitances analytically derived by the terminal charges associated with the terminal voltages. This compact model is valid in the weak, moderate and strong regime of the device operation. The transfer characteristics of the drain current and C-V characteristic of capacitances have been validated using 2-D numerical simulation.

Comparison of three IBSCs in terms of photo-filling, capture cross section of carriers, the concentration of IB states and overlapping of absorption coefficients in the wide range of band gaps including GaAs

Intermediate-band solar cells, IBSCs, with single IB provide better utilization of the solar spectrum than single junction solar cells. In this study, Model−B IBSC was proposed, investigated and compared with previously used two models named here as Model−A and Model−C respectively. Detailed Balance Model was applied to satisfy Current Balance Equations with the optimum photo filling of IB states in Model−B. Optimum design parameters were obtained using 104 cm−1 of band-to-band absorption coefficient, α, in the wide range of band gap materials, overlapping absorption, photo filling, f, of IB states, capture cross-section ratio of carriers, concentration of IB states, and IB layer thickness, w, under 1–46,000 sun concentration, X. Maximum limiting efficiency value of 63.2% has been obtained with 1.95 eV of band gap, for fαw≥5 and 46,000X, under non-overlapping absorption. The peak efficiency of Model−B was 16% over the Model−A and 8% over the Model−C, for equal capture cross sections under large overlapping. The peak efficiency of Model−B was 35% over Model−A, at large non-equal capture cross-sections and large overlapping. Results predicted that the materials in the wide range of band gaps could be good candidates for fabricating IBSCs using Model−B with an efficiency of 50% or above at lower sun concentration, 10,000X, even under large overlapping.

Method for estimating charge breeder ECR ion source plasma parameters with short pulse 1+ injection of metal ions

A new method for determining plasma parameters from beam current transients resulting from short pulse 1+ injection of metal ions into a charge breeder electron cyclotron resonance ion source has been developed. The proposed method relies on few assumptions, and yields local values for the ionisation times , charge exchange times , the ion confinement times τ q , as well as estimates for the minimum plasma energy contents and the plasma triple products . The method is based on fitting the current balance equation on the extracted beam currents of high charge state ions, and using the fitting coefficients to determine the postdictions for the plasma parameters via an optimisation routine. The method has been applied for the charge breeding of injected K+ ions in helium plasma. It is shown that the confinement times of K q+ charge states range from 2. ms to 16. ms increasing with the charge state. The ionisation and charge exchange times for the high charge state ions are 2. ms–12. ms and 3. ms–357. ms, respectively. The plasma energy content is found to be eV cm−3.

Modeling of functionally graded circular energy harvesters due to flexoelectricity

Flexoelectric effect can be enhanced in micro/nano scale due to its size-dependency, making it particularly suitable for energy harvesting. In this work, a theoretical model is built to characterize the functionally graded circular flexoelectric energy harvesters based on the Kirchhoff thin plate hypothesis. Using Hamilton's principle, both the force balance equation and current balance equation are obtained. Approximated closed-form solutions of the energy harvesting performances are achieved through the assumed-mode method. Numerical analysis results demonstrate that the clamped circular energy harvesters with the ratio of the electrode radius to the plate radius be 0.64 will generate the maximum electrical output. The volume fraction coefficient has a significant impact on the resonant frequency, electrical output as well as the optimal load resistance. Meanwhile, shrinking the thickness of the circular energy harvester from 10µm to 0.1µm will lead to a remarkable increase of the optimal energy conversion efficiency from 10−6 to 10−2. Furthermore, the strain gradient effect is examined to result in a higher resonant frequency while suppress the electrical output particularly if the length scale parameter is relatively large.

Dust surface potential in a generalized (r, q)‐distributed multi‐ion dusty plasma

Potential on the surface of spherical dust is theoretically determined by employing the generalized power law (r, q) distribution function (df) in a multi‐ion dusty plasma. Considering a steady‐state condition, the current balance equation is solved for negatively charged dust particulates and analysed two specific cases, namely, the negative ions as streaming and dynamic non‐thermal particles. It is numerically shown that dust grain (surface) potential is significantly modified by the variation of different plasma parameters, for example, the r and q spectral indices attributed to generalized power law df, the streaming and non‐thermal negative ions, the negative ion‐to‐electron temperature ratio and the density ratio involving the negative‐to‐positive ions. The relevance to low‐temperature laboratory non‐thermal dusty plasma is briefly discussed by incorporating two types of oxygen ion species.

Detection of an electron beam in a high density plasma via an electrostatic probe

An electron beam is detected by a 1D floating potential probe array in a relatively high density (1012–1013 cm−3) and low temperature (∼5 eV) plasma of the Magnetic Reconnection Experiment. Clear perturbations in the floating potential profile by the electron beam are observed. Based on the floating potential profile and a current balance equation to the probe array tips, the effective width of the electron beam is determined, from which we determine the radial and toroidal beam current density profiles. After the profile of the electron beam is specified from the measured beam current, we demonstrate the consistency of the current balance equation and the location of the perturbation is also in agreement with field line mapping. No significant broadening of the electron beam is observed after the beam propagates for tens of centimeters through the high density plasma. These results prove that the field line mapping is, in principle, possible in high density plasmas.

The nonlocal electron kinetics for a low-pressure glow discharge dusty plasma

The nonlocal electron kinetic model based on the Boltzmann equation is developed in low-pressure argon glow discharge dusty plasmas. The additional electron-dust elastic and inelastic collision processes are considered when solving the kinetic equation numerically. The orbital motion limited theory and collision enhanced collection approximation are employed to calculate the dust surface potential. The electron energy distribution function (EEDF), effective electron temperature Teff, and dust surface potential are investigated under different plasma and dust conditions by solving the Boltzmann and the dust charging current balance equations self-consistently. A comparison of the calculation results obtained from nonlocal and local kinetic models is made. It is shown that the appearance of dust particles leads to a deviation of the EEDF from its original profile for both nonlocal and local kinetic models. With the increase in dust density and size, the effective electron temperature and dust surface potential decrease due to the high-energy electron loss on the dust surface. Meanwhile, the nonlocal and local results differ much from each other under the same calculation condition. It is concluded that, for low-pressure (PR ≤ 1 cm*Torr) glow discharge dusty plasmas, the existence of dust particles will amplify the difference of local and nonlocal EEDFs, which makes the local kinetic model more improper to determine the main parameters of the positive column. The nonlocal kinetic model should be used for the calculation of the EEDFs and dusty plasma parameters.

KP Equation in a Three-Dimensional Unmagnetized Warm Dusty Plasma with Variable Dust Charge

In this work, we investigate the propagation of three-dimensional nonlinear dust-acoustic and dust-Coulomb waves in an unmagnetized warm dusty plasma consisting of electrons, ions, and charged dust particles. The grain charge fluctuation is incorporated through the current balance equation. Using the perturbation method, a Kadomtsev–Petviashvili (KP) equation is obtained. It has been shown that the charge fluctuation would modify the wave structures, and the waves in such systems are unstable due to high-order long wave perturbations.