Plasma Potential Distribution Research Articles

Plasma Potential Distribution along the Open Side of a Rectangular Hollow Cathode

Plasma Potential Distribution along the Open Side of a Rectangular Hollow Cathode

Particle-based simulation of atom and ion transport in HiPIMS: effect of the plasma potential distribution on the ionized flux fraction

We present a three-dimensional particle-based computer simulation of high-power impulse magnetron sputtering (HiPIMS) discharges which enables us to simulate the transport of atoms and ions in the discharge and the corresponding plasma parameters. The simulation requires a definition of the plasma potential and electron density distribution (not calculated self-consistently), for which parametric analytical formulae were devised. A numerical algorithm is used to constrain the simulation by an experimental target current waveform, which ensures that the simulation results are closely tied to the experimental discharge conditions. Simulations of a HiPIMS discharge with Ti target show the capability to calculate the spatial distributions of target material atoms and ions and also to quantify the process-gas rarefaction. We evaluated, among others, the ion return probability and the ionized fraction of the target material flux onto the substrate for various values of the potential difference across the magnetic presheath in front of the target racetrack, which is responsible for attracting most of the plasma ions towards the target. It is shown that this parameter of the plasma potential distribution strongly affects the ion return probability and, thus, it must be known quite precisely to reliably predict the ionized flux fraction on the substrate. Other parameters, such as the composition of the ion flux onto the target are less sensitive. The simulation can be run in a reasonably short time and can easily be extended by adding more plasma species (excited states or doubly ionized species) and their interactions.

A generalized external circuit model for electrostatic particle-in-cell simulations

A fully self-consistent second order accuracy model for coupling a generalized external circuit and a one-dimensional bounded electrode-driven plasma was proposed in this paper. The plasma was embedded in the circuit as a non-linear element with a potential difference. Based on Kirchhoff's voltage law and the definition of current, the problem of solving the generalized external circuit was transformed into an initial value problem of a set of first-order ordinary differential equations which can be discretized numerically by the second-order backward differential formula. The charge conservation equation at the electrode plate was coupled to the above equation, and the voltage, current, and surface charge density at the next moment were solved by a differential equation solver. Dirichlet boundary conditions of Poisson's equation were obtained through the surface charge density σ0 of the generalized external circuit equation and the plasma density ρ of the Particle-in-Cell (PIC) model. The spatial distribution of plasma potential was solved by using the second-order central difference scheme. The obtained potential at the electrode plate can be used as the Robin boundary condition of the system of generalized external circuit equations. In this model, the loose coupling between the generalized external circuit and plasma was realized by the boundary condition, and the system was fully self-consistent based on the charge conservation law and energy conservation law. We simulated the capacitively coupled plasmas (CCP) under different external circuits as the example and verified the performance of the model. This model can be used to study the influence of different external circuit structures and parameters on plasma discharge, and can be used for any plasma sources driven by electrodes, like CCP, some vacuum electronic devices, and Z-Pinches.

Multiscale simulation of hollow cathode assisted internal plasma treatment process

Hollow cathode discharges can be used for the plasma-assisted surface treatment and coating of the interior surface of blind hole geometries. Due to the geometry, it is difficult to find the setting parameters for a reproducible result. Therefore, a probabilistic simulation based on a Monte Carlo method has been performed to simulate a hollow cathode discharge in a blind hole with an aspect ratio ≫ 1. First, different neutral gas flows inside a blind hole geometry were investigated with a direct simulation Monte Carlo method and compared to impact pressure measurements. Then, the resulting neutral gas pressure distribution was used in a Particle-in-Cell plasma simulation as a background gas to determine the electrical potential distribution, the charge carrier distribution and mean energy inside the blind hole geometry. The plasma potential distribution is compared with a substrate coated with an amorphous diamond like carbon (a-C:H) thin film and shows good agreement.

Screening of Absorbing Grains in Plasma with a Flow

The electrostatic shielding of a charged absorbing object (dust grain) in a flowing collisionless plasma is investigated by usingthe linearized kinetic equation for plasma ions with a point-sink term accounting for the ion absorption on the object. The effect ofabsorption on the attractive part of the dust grain potential distribution in plasma is investigated. For subthermal ion flows, the attractive part of the grain potential in the direction perpendicular to the ion flow can be significantly reduced or completely destroyed, depending on the absorption rate (proportional to the surface area of a grain). For superthermal ion flows, however, the effect of absorption on the grain attraction in the direction perpendicular to the ion flow is shown to be exponentially weak. It is thus argued that, in the limit of superthermal ion flow, the effect of absorption on the grain potential distribution in plasma can be safely ignored for typical grain sizes relevant to complex plasmas.

Plasma structure and electron cross-field transport induced by azimuthal manipulation of the radial magnetic field in a Hall thruster E × B discharge

Plasma structure and electron cross field in the z–θ plane of a Hall thruster E×B plasma under an azimuthally inhomogeneous magnetic field are studied by both experimental and numerical approaches. The work is intended to identify a primary role of electron dynamics on the structure formation by manipulating only the strongly magnetized electrons. The plasma potential distribution shows an axial–azimuthal variation; a low magnetic field region results in spatial potential saturation further downstream. The plasma density structure shows a 1D-like azimuthal variation with less axial deformation. A dense region is observed near the location of ∇B>0, where electrons are expected to undergo the ∇B and curvature drift toward the anode where neutrals are introduced. The potential structure is in close correlation to the Hall parameter distribution, indicating that electron dynamics plays a primary role in plasma structure formation, and via multiple consecutive stepwise physical steps, it eventually affects the density structure formation. In the z–θ space, the cross-field transport by E×B and diamagnetic drifts dominantly determines the electron flow and increases the overall axial electron mobility due to the azimuthal inhomogeneity. It is shown that most of the current is carried by the largest structure, but as the macroscopic structure fades out downstream, small structures grow and share the current. By considering the conservation laws, we show that a relation between azimuthal distributions of physical properties is formed to conserve the axial flux by a balance of specific forces, a balance between the resistive force and the magnetic force in the near-anode region and a balance between the electric/pressure force and the magnetic force in the acceleration and plume region, which differs from the Boltzmann relation satisfied in the radial dimension. Based on this principle, with a simplified test case having a uniform plasma density distribution, we show an analytic relation between azimuthal distributions of the magnetic field and the plasma potential and confirm the relation by a 2D hybrid simulation.

Laboratory Simulation of Solar Wind Interaction With Lunar Magnetic Anomalies

AbstractMagnetic anomalies on the surface of the Moon interact with the solar wind plasma flow, resulting in both magnetic and electrostatic deflection/reflection of charged particles. Consequently, surface charging in these regions differs from regions without magnetic fields. Using the Colorado Solar Wind Experiment facility, this interaction is investigated with high‐energy flowing plasmas (100–800 eV beam ions) that are incident upon a magnetic dipole embedded beneath an insulating surface. The dipole moment is perpendicular to the surface. The plasma potential distribution is measured above the surface using an emissive probe. In the dipole lobe regions the surface is charged to significantly higher positive potentials by the un‐magnetized ion beam impinging on the surface while the electrons remain excluded by the magnetic field. At low ion beam energies the results agree with these expectations as the surface potential follows the ion beam energy. However, at high beam energies, the surface potentials in the electron‐shielded lobe regions remain significantly lower than the expected magnitude. Surprisingly, electrons are detected in the shielded regions by a Langmuir probe. A test particle simulation indicates that secondary electrons induced by the high energy ion beams impinging on the surface can enter the shielded regions, thus lowering the surface potential.

Resistive MHD modes in hollow cathodes external plasma

A significant number of plasma instabilities occur in the region just outside of hollow cathodes, depending on the injected gas flow, the current level and the application of an external magnetic field. In particular, the presence of an axial magnetic field induces a helical mode, affecting all the plasma parameters and the total current transported by the plasma. To explore the onset and behavior of this helical mode, the fluctuations in the plasma parameters in the current-carrying plume outside of a hollow cathode discharge have been investigated. The hollow cathode was operated at a current of 25 A, and at variable levels of propellant flow rate and applied magnetic fields. Electromagnetic probes were used to measure the electromagnetic fluctuations, and correlation analysis between each of the probe signals provided spatial-temporal characterization of the generated waves. Time-averaged plasma parameters, such as plasma potential and ion energy distribution function, were also collected in the near-cathode plume region by means of scanning emissive probe and retarding potential analyzer. The results show that the helical mode exists in the cathode plume at sufficiently high applied magnetic field, and is characterized by the presence of a finite electromagnetic component in the axial direction, detectable at discharge currents ⩾25 A. A theoretical analysis of this mode reveals that one possible explanation is consistent with the hypotheses of resistive magnetohydrodynamics, which predicts the presence of helical modes in the forms of resistive kink. The analysis has been carried out by linear perturbation of the resistive MHD equations, from which it is possible to obtain the dispersion relation of the mode and find the k–ω unstable branch associated with the instability. These findings provided the basis for more detailed investigation of resistive MHD modes and their effect in the plume of hollow cathodes developed for electric propulsion application.

Approximate determination of the plasma potential spatial distribution in the isolated dust particle vicinity

In this paper, results of two numerical models are compared. The main purpose of these models is to determine the self-consistent spatial distributions of plasma (electric potential and space charge) near isolated spherical dust particles. In the first model, the spatial distribution of the self-consistent plasma potential is determined by expanding the plasma space charge spatial distribution in Legendre polynomials; in the second model, it is determined by direct numerical integration of the Poisson equation solution. The results show that the dependences of the system main parameters (wake magnitude and position, dipole moment of the ion cloud) coincide for small values of the external electrostatic field. With an increase in the external field strength, the dependences for two models cease to coincide, which is due to the inapplicability of Legendre polynomial decomposition in the case of strong anisotropy.

Scaling of silicon nanoparticle growth in low temperature flowing plasmas

Low temperature plasmas are an emerging method to synthesize high quality nanoparticles (NPs). An established and successful technique to produce NPs is using a capacitively coupled plasma (CCP) in cylindrical geometry. Although a robust synthesis technique, optimizing or specifying NP properties using CCPs, is challenging. In this paper, results from a computational investigation for the growth of silicon NPs in flowing inductively coupled plasmas (ICPs) using Ar/SiH4 gas mixtures of up to a few Torr are discussed. ICPs produce more locally constrained and quiescent plasma potentials. These positive plasma potentials produce an electrostatic trap for negatively charged NPs, which can significantly extend the residence time of NPs in the plasma, which in turn provides a controllable period for particle growth. The computational platforms used in this study consist of a two-dimensional plasma hydrodynamics model, a three-dimensional nanoparticle growth and trajectory tracking model, and a molecular dynamics simulation for deriving reactive sticking coefficients of silane radicals on Si NPs. Trends for the nanoparticle growth as a function of SiH4 inlet fraction, gas residence time, energy deposition per particle, pressure, and reactor diameter are discussed. The general path for particle synthesis is the trapping of small NPs in the positive electrostatic potential, followed by entrainment in the gas flow upon reaching a critical particle size. Optimizing or controlling NP synthesis then depends on the spatial distribution of plasma potential, the density of growth species, and the relative time that particles spend in the electrostatic trap and flowing through higher densities of growth species upon leaving the trap.

Optimizing the ion diffusion in bipolar-pulse HiPIMS discharge (BP-HiPIMS) via an auxiliary anode

The investigation of plasma dynamics and optimization of target particle diffusion are particularly important and urgent in the recently emerging bipolar-pulse high-power impulse magnetron sputtering (BP-HiPIMS) discharge. In this paper, a novel approach, in which an external auxiliary anode was installed in front of the sputtering target, was proposed to optimize electric field distribution and guide particle diffusion, named as AABP-HiPIMS. A positive pulse voltage was applied to the auxiliary anode in synchronization with the target positive pulse voltage, which was achieved by connecting the target and auxiliary anode through a diode in series. Advantageously, no additional power supply needs to be provided in AABP-HiPIMS. The discharge characteristics of this new plasma source were investigated in detail. A theoretical model was successfully built to reveal the transformation process of the target current from the net ion current to the net electron current by systematically analyzing the collapsing process of the target sheath and charged-particle movement in E × B fields. The optimization of ion diffusion was investigated by diagnosing plasma parameters using a Langmuir probe and emissive probe together. The measurements illustrate that, as expected, the electron density in AABP-HiPIMS during the positive pulse phase has been effectively increased ∼2.5 times on average compared to that in the conventional BP-HiPIMS. Correspondingly, the plasma potential distribution illustrates that the potential gradient pointing to the auxiliary anode centre is more beneficial for control of ion diffusion and to enhance ion flux towards the downstream. Additionally, for better selection of the magnetron process parameters, the characteristic time of plasma decay during the positive pulse was estimated using the Bohm diffusion theory. The rough calculation of flight time for electrons from z = 35 to 95 mm was ∼70 μs in BP-HiPIMS and ∼50 μs in AABP-HiPIMS, respectively. The effects of negative pulse duration and positive pulse amplitude on plasma parameters were investigated. Measurements of plasma potentials suggest that adopting a relatively short duration negative pulse and a slightly higher amplitude positive pulse, as well as employing the externally applied auxiliary anode, are the optimum choices for improving both the flux and energy of deposited particles when preparing films on the floating substrate.

Radial distribution of the plasma potential in a cylindrical plasma column with a longitudinal magnetic field

The possibility of controlling the electrostatic field distribution in plasma has yielded wide prospects for modern technologies. As a magnetic field primarily allows for creating electric fields in plasma, it serves as an additional obstacle for the current flow through a medium. In the present paper, an axially symmetric system is considered in which the magnetic field is directed along the axis and concentric electrodes are located at the ends. The electrodes are negatively biased. A model which solves the problem of the radial distribution of the plasma potential inside the cylindrical plasma column supported by the end electrodes is proposed. The most commonly encountered configurations of the electrical connection for the end electrodes are considered, and the particular solutions to the problem of the radial distribution are presented. The contribution of ions and electrons to the transverse conductivity is evaluated in detail. The influence of a thermionic element on the radial profile of the plasma potential is considered. To verify the proposed model, an experimental study of the reflex discharge is carried out with both cold electrodes and a thermionic element on the axis. A comparison of the computational model results with experimental data is given. The presented model makes it possible to solve the problem concerning the plasma potential distribution in the case of an arbitrary number of end electrodes, and also to take into account the inhomogeneity of the distribution of plasma density, neutral gas pressure and electron temperature along the radius.

Plasma mass separation in configuration with potential well

The details of the charged particle separation by mass in the configuration with axial magnetic and radial electric fields are studied. The radial electric field, oriented to the discharge axis, is induced in a background reflex discharge with a hot cathode (−550 V, 8–14 A). The plasma source is based on a hot cathode arc discharge with independent metal vapor injection (18–21 V, 30 A) was situated at 18 cm from the axis. It was shown that the separated Ag + Pb mixture is transported across the magnetic field under the background discharge electric field. Effective separation is possible in such a system, while the separation coefficient increases from 4.9 to 6.2–8.4 when the mixture injection point is moved away from the background discharge axis from 18 to 23 cm. The effect of mixture injection on the plasma potential distribution is examined. It was shown that the presence of a plasma source of separated substances can cause a local (1–2 cm) distortion of the background plasma potential profile. Such distortion, as well as fluctuations of the background plasma potential, can significantly affect the width of the deposited spots of separated substances.

Improving the performance of a water ion thruster using biased electrodes

This paper investigates whether biased electrodes can improve the performance of a microwave-discharge water ion thruster, which has been proposed as a propulsion system for CubeSats. Previously, for several microwave ion sources, the beam currents have been increased by mounting a biased electrode in the discharge chamber. The effect of a biased electrode on a water ion thruster was unclear because its magnetic field profile and characteristic length compared with the microwave wavelength are different from those used in previous studies. To investigate the effect, a thruster was divided into three parts: magnets, a microwave antenna, and a discharge chamber, which is comprised of an electrically conductive sidewall and a screen grid. The parts were isolated electrically. Bias voltages from −44 to ＋ 44V were applied to the microwave antenna or magnets by an additional power supply. These bias voltages were applied with respect to the screen grid and sidewall voltage. A maximum screen current of 12.7 mA was obtained for an antenna bias voltage of 38.2V. This is 2.3 times larger than the current without a bias voltage. This increase could be caused by a combination of an increase of plasma density and ion extraction efficiency. The plasma density could increase with the gain of the total absorbed power. The ion extraction efficiency could increase due to the change in the plasma potential distribution. Overall, the mass utilization efficiency of the water ion thruster increased from 3.3% to 7.9% and the discharge loss decreased from 280 to 150W/A at the antenna bias of 38V. The performance with water electron source was evaluated. The thrust force, specific impulse, thrust-to-power ratio, thrust efficiency were 190μN, 350s, 5.9μN/W, and 1.0%, respectively at the antenna bias of 25V.

Spatial distribution of plasma parameters by a dual thermal-electrostatic probe in RF and DC magnetron sputtering discharges during deposition of aluminum doped zinc oxide thin films

Aluminum doped zinc oxide thin films deposited by magnetron plasma sputtering are essential for various optoelectronic applications. So far, the oxygen negative ions and the atomic oxygen are regarded as responsible for the poor spatial uniformity of thin film resistivity. While various methods are available for thin film characterization, understanding the growth mechanism requires spatial-resolved measurements of plasma parameters. This work uses a dual thermal-electrostatic probe that is able to reveal the spatial distribution of plasma density, electron temperature and plasma potential. The results exhibit a parabolic profile for plasma density and flat profiles for electron temperature and plasma potential, with no correlation with the strong distribution of thin film resistivity that mirrors the erosion track on the target surface.

Effect of Plasma Sheath on the Design of Electric Field Instrument Detecting Magnetosheath

The distribution of plasma potential and density around spacecraft is affected by the coupling of spacecraft and plasma, resulting in disturbing the detection of space electric field. In this paper, Spacecraft Plasma Interaction Software (SPIS for short) is used to provide a reference to design the electric field instrument detecting magnetosheath on future missions. The interaction of plasma with the spacecraft platform and the probe is simulated to investigate the thickness of plasma sheath and the relationship between current and voltage drop under different plasma conditions. Our results indicate that the thickness of plasma sheath covered spacecraft is smaller than the Debye radius, and this difference is larger at higher temperature conditions caused by photoelectrons and secondary electrons. Moreover, the current collected by the probe at a different voltage drop is also simulated. The simulated results show that the influence of current disturbance on measuring potential can be reduced by the probe with a bias current. Furthermore, the estimated optimum bias current is also listed corresponding to the detected region.

Langmuir Probe Diagnostics of Inductively Coupled Plasma Generated Using Flat Spiral Antenna

Langmuir probe (LP) diagnostics is performed on an inductively coupled plasma (ICP) generated using a flat spiral antenna. The current–voltage ( $I - V$ ) characteristics are measured using a radio frequency (RF) compensated LP to mitigate the effect of RF distortion in $I - V$ measurements. All-important plasma parameters such as electron density ( $n_{\mathrm {e}}$ ), electron temperature ( $T_{\mathrm {e}}$ ), plasma potential ( $V_{\mathrm {p}}$ ), and electron energy distribution function (EEDF) are measured in a cylindrical-shaped ICP. The plasma is generated by feeding RF (13.56 MHz) current in the planer multiple spiral antennas. It is seen that the plasma is uniform over an area with 200 mm diameter, with an electron number density in the range from $\sim 10^{11}$ to 1012 cm−3. Typically for plasma processing of materials, the required density fall in that region. Variation of plasma parameters is investigated as a function of applied RF power and operating pressure and the observed results are discussed.

Application of the view factor model on the particle-in-cell and Monte Carlo collision code.

Particle-in-cell and Monte Carlo collision (PIC-MCC) has been widely adopted as a simulation method for electric propulsion. However, neutral atoms move much more slowly than other species, which can cause a serious reduction in simulation speed. In this work, we investigate the view factor model in combination with the PIC-MCC method and propose a method for simulating three-dimensional neutral atoms. The accuracy of the PIC-MCC method can be significantly improved by updating the neutral distribution periodically. We compare the computational results with the fixed-neutral PIC-MCC model of the miniature ring-cusp discharge experiment at the University of California, Los Angeles (UCLA). The plasma distribution and potential distribution of the simulation match well with the UCLA experimental data. Compared with the fixed-neutral model, the view factor model increases the simulation time by only 33% while it improves the distribution accuracy of neutrals, plasma density, and electric potential, and reduces the simulation errors of discharge current and discharge power from 19.8% to 9.8%. The accuracy of PIC-MCC simulation has been improved at the expense of slightly increasing the computational time.

Plasma potential distribution around an infinite one-dimensional chain of dust particles

With the help of the code modification used in the authors previous works, the self- consistent distribution of density and electric potential are calculated around a one-dimensional infinite chain of dust particles. As a result, self-consistent distributions of the electric potential and space charge around a one-dimensional chain of dust particles, as well as the dependence of the dust particles charge on the interparticle distance, are obtained.

Investigation of recombination front region in detached plasmas in a linear divertor plasma simulator

Abstract We have investigated detailed plasma structure around the recombination front region (RFR), where volume electron-ion recombination (EIR) strongly occurs in detached plasmas, by using two-dimensional (2D) movable probe system as well as laser Thomson scattering diagnostics. The 2D distribution of electron density, electron temperature, and plasma potential around the RFR, has been revealed for the first time. The spatial distribution of the particle loss rate due to EIR estimated from electron temperature and electron density profiles indicated that the three-dimensional structure of the RFR adopts a cone structure. Furthermore, in the peripheral region of the RFR, the radial profile of the electron density was widened locally with increasing cross-field transport caused by plasma fluctuation. From the heat transport analysis of electrons, it was found that the thermal relaxation process between electrons and ions is important for the cooling of electrons, and that the convection of electrons regulates electron heat transport near the RFR.