Potential Hump Research Articles

Effects of anode evaporation process on the anode sheath characteristics in vacuum arc plasma

Abstract The anode sheath of vacuum arc plasma plays a key role in the generation of anode plasma, but the effects of anode evaporation on the anode sheath remains unclear. In this paper, a theoretical model of a collisional sheath for multi-component plasma coupled with anode evaporation is developed, and the spatial evolution of the anode sheath at different anode surface temperatures is investigated. The results indicate that the distribution of charged particles density and potential in the anode sheath monotonically decreases in the absence or reduction of anode evaporation. When the anode surface temperature exceeds 1900K, a potential hump appears within the sheath. This is due to enhanced anode evaporation increasing the metal vapor density, which intensifies electron impact ionization and charge exchange collisions, resulting in a higher net space charge density. Finally, the effects of various collision reactions and electron temperatures on the potential hump are analyzed. These findings are meaningful for understanding the anode plasma generation mechanism and regulating the anode plasma parameters.

Higher order contribution to ion-acoustic Korteweg–de Vries (KdV) soliton in unmagnetized quantum plasmas with arbitrary degeneracy of electrons

The propagation of nonlinear ion-acoustic Korteweg–de Vries (KdV) solitons and dressed solitons (with higher order contribution term) in unmagnetized quantum plasmas with arbitrary degeneracy of electrons is investigated using quantum hydrodynamic model. The reductive perturbation method is used to derive the first order nonlinear ion-acoustic KdV equation and also higher order contribution of inhomogeneous differential equation is obtained for the dressed ion-acoustic wave soliton in arbitrary degenerate electron plasmas. Moreover, the higher order inhomogeneous differential equation is solved (nonsecular solution is obtained) using the renormalization method. The conditions for the validity of the higher order correction are also discussed in detail for ion-acoustic solitons in unmagnetized arbitrary degenerate electrons plasma case. The effects of chosen values of electron temperature, equilibrium fugacity and corresponding electron density of a physical quantum plasma system and quantum diffraction parameter H (for two conditions i.e., H < 2 or H > 2) on the amplitude and width of the KdV and dressed ion-acoustic wave solitons for both electrostatic potential hump (compressive) or dip (rarefactive) structures are investigated. The numerical plots are also presented for illustration with numerical values of a physical partially degenerate electrons plasma system exist in the astrophysical or laboratory conditions.

Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges

In this work, the transition from the gradient drift instability (GDI) into an m = 1 rotating spoke in the radio frequency magnetron discharge was studied by means of the two-dimensional axial-azimuthal (z − y) particle-in-cell/Monte Carlo collision method. The kinetic model combined with the linear analysis of the perturbation revealed that the cathode sheath (axial) electric field E z triggers the GDI, deforming the local potential until the instability condition is not fulfilled and the fluctuation growth stops in which moment the instability becomes saturated. The potential deformation consequently leads to the formation of the potential hump, surrounding which the azimuthal electric field E y is present. The saturation level of E y was found to be synchronized with and proportional to the time-changing voltage applied at the cathode, resulting in the RF-modulation of the electron heating in the E y due to drift. In the saturated stage of the instability, it was shown that the rotation velocity and direction of the spoke present in the simulations agree well with the experimental observation (Panjan 2019 J. Appl. Phys. 125 203303). In the instability linear stage, the instability mode wavelength and the growth rate were also found to be in good agreement with the prediction of the GDI linear fluid theory.

Particle simulation on the ion acceleration in vacuum arc discharge

The supersonic ion jet generated in vacuum arc plasma has numerous applications, but the ion acceleration mechanism is incompletely understood. In this paper, a one-dimensional spherical vacuum arc discharge model is established, and the ion acceleration from vacuum breakdown to steady arc stage is investigated using particle-in-cell direct simulation Monte Carlo method. The results show that a potential hump exists and locates about far away from the cathode, but the potential drop provides a small contribution to the ion acceleration. A potential valley forms near the plasma–vacuum boundary and propagates towards the anode as the plasma expands during the vacuum breakdown stage. The ion mounting this valley experiences continuous acceleration by the dynamic electric field of the potential valley. As the plasma reaches the anode, a steady arc stage is gradually build-up, and the potential valley disappears. Consequently, the maximum mean ion velocity decreases. The source dominating the ion acceleration in this stage is turned into the electron–ion Coulomb collision.

Evolution from the gradient drift instability to the formation of the spoke potential hump in a partially magnetized plasma

Rotating spokes commonly occur in partially magnetized plasma devices. This work explores the evolution from the gradient drift instability into an m = 1 rotating spoke mode in a magnetically enhanced hollow cathode discharge (with emissive cathode) by means of 2D radial-azimuthal particle-in-cell/Monte Carlo collision simulations. It is shown that the formation of the spoke potential hump region can be explained as a result of the local collapse of the anode sheath due to the gradient drift instability, which is triggered within the anode sheath. The sheath non-neutrality effect on the instability is considered and incorporated in the two-fluid linear theory of gradient drift instability. The unstable modes predicted by the theory are in good agreement with the fluctuation modes developed in the particle simulations.

Magnetised and unmagnetized axisymmetric particle-in-cell simulations of ion energy distributions in cathodic vacuum arcs

Cathodic arcs are electrical discharges consisting of a succession of discrete pulses of energetic plasma travelling from the surface of a cathode toward an anode. Currently, there are no vacuum arc simulations where spots are continuously generated with a set frequency, including the far-field plasma jet, with the inclusion of kinetic behaviour for both ions and electrons. The VSim 11 particle-in-cell software was used to simulate specific vacuum arcs as axisymmetric, electrostatic, and fully kinetic, from the initial generation of each cathode spot to the streaming plasma discharge at a far field, validating the predictions against experimental data. The models were configured to match the experimental arc gun of Zohrer et al and the Mevva V experiment with the cathode materials Al and Nb. The ion and electron velocity data were collected at the far edge of the simulation domain, analogous to a physical energy detector. The simulations successfully predicted the evolution of ion charge state energy distributions, showing peak unmagnetized ion energies that agree with prior experimental data, resulting in a mean error of 3% for Al and Nb. A peak in the electrostatic potential is observed above the cathode surface, supporting the potential hump theory as the cause of the higher-than-expected ion energies observed in cathodic arc discharges. Lower than expected relative energies between ion charge states are observed, matching prior experimental results, with this coupling of ion charge states attributed to non-stationary electrostatic wave–particle interactions, as the use of collisionless simulations rules out Coulombic ion friction. Magnetised simulations incorporated a statically powered short solenoid equivalent to the coil used in the Mevva V experiment to create a diverging magnetic nozzle. The magnetised simulation results demonstrate an annular jet of magnetically confined plasma and indicate an increase in nonstationary electrostatic effects including wave–particle interactions.

The Electrodynamic Mechanism of Collisionless Multicomponent Plasma Expansion in Vacuum Discharges: From Estimates to Kinetic Theory

This paper is devoted to the study of collisionless multicomponent plasma expansion in vacuum discharges. Based on the fundamental principles of physical kinetics formulated for vacuum discharge plasma, an answer is given to the following question: What is the main mechanism of cathode plasma transport from cathode to anode, which ensures non-thermal metallic positive ion movement? Theoretical modeling is provided based on the Vlasov–Poisson system of equations for a current flow in a planar vacuum discharge gap. It was shown that the non-thermal plasma expansion is of a purely electrodynamic nature, caused by the formation of a “potential hump” in the interelectrode space and its subsequent movement under certain conditions consistent with plasma electrodynamic transportation. The presented results reveal two cases of the described phenomenon: (1) the dynamics of single-component cathode plasma and (2) multicomponent plasma (consisting of multiple charged ions) expansion.

2D particle-in-cell/Monte Carlo collisional simulation of the plasma initiation in the vacuum breakdown stage

In this paper, the plasma formation in the vacuum breakdown stage is simulated with a 2D particle-in-cell/Monte Carlo collisional model. In this model, the field is solved in a 2D cylindrical coordinate system and particles including electrons, atoms, singly, doubly, triply and fourfold charged ions are traced as super particles, each of which represents many real particles. The plasma quickly builds up from the field emission and evaporation near the field emitter with a local field of about 10 GV m−1. The plasma expands in a hemispherical shape with a high-density gradient in the vicinity of the field emitter. During the discharge, a typical structure including an ion sheath, a quasi-neutral region and an acceleration layer is obtained. The well-pronounced potential hump near the cathode, the high ion velocity in the acceleration layer and ion charge state agree well with results in previous research works. Investigation of the effects of the field enhancement factor and emitter surface temperature shows that more highly charged ions can be obtained in simulations with higher field emission current, while the plasma initiates faster and has higher density with stronger evaporation of neutral atoms.

The Influence of Primary Electrons on the Mechanism of Plasma Generation

It is shown that at high percentage content of primary electrons, plasma is generated due to the retention of ions in a potential well created by electrons and not due to the accumulation of secondary electrons in the region of a potential hump formed by ions.

Effects of negative ions on discharge characteristics of water plasma source for a miniature microwave discharge ion thruster

This work analyzes the discharge characteristics of water plasma for a miniature microwave discharge ion thruster via three-dimensional particle-in-cell simulations with Monte Carlo collisions. It incorporates the negative ions (H−, O−, and OH−) into the simulation code, aside from the three major positive ion species (H2O+, OH+, and H+), and investigates their effects on the discharge characteristics. On the one hand, the simulation results indicate that H2O+ is the dominant species and the negative ions have little effect on the positive ion density and transport. On the other hand, this study confirms the axial oscillation of the OH− negative ion density, in addition to azimuthal rotation, causing plasma instability with a periodic low-frequency anomalous diffusion. The azimuthal rotation is similar to the phenomena observed in other E × B devices, where the difference in spatial distributions of magnetized electrons and unmagnetized ions causes the local potential hump and the resultant instability. Moreover, the axial oscillation, not observed in the previous study considering only positive ions, is due to the generation of OH− by the charge transfer collision reaction between H2O and H−, and this oscillation frequency is double that of the azimuthal rotation. Both the azimuthal rotation and the axial oscillation result in the periodic double peaks of the potential time evolution. These fluctuations have an influence on electron transport across the magnetic field.This work analyzes the discharge characteristics of water plasma for a miniature microwave discharge ion thruster via three-dimensional particle-in-cell simulations with Monte Carlo collisions. It incorporates the negative ions (H−, O−, and OH−) into the simulation code, aside from the three major positive ion species (H2O+, OH+, and H+), and investigates their effects on the discharge characteristics. On the one hand, the simulation results indicate that H2O+ is the dominant species and the negative ions have little effect on the positive ion density and transport. On the other hand, this study confirms the axial oscillation of the OH− negative ion density, in addition to azimuthal rotation, causing plasma instability with a periodic low-frequency anomalous diffusion. The azimuthal rotation is similar to the phenomena observed in other E × B devices, where the difference in spatial distributions of magnetized electrons and unmagnetized ions causes the local potential hump and the resultant instability. M...

Mn substitution controlled Li-diffusion in single crystalline nanotubular LiFePO4 high rate-capability cathodes: Experimental and theoretical studies

Carbon-coated single crystalline nanotubular (NT) and nanoparticular (NP) LiFe1-xMnxPO4 (x = 0, 0.2, and 0.5) cathodes are fabricated to study the effect of compositional and microstructural changes on Li+ diffusion and electrochemical properties. Insight in to the compositional effect on Li+ diffusion is obtained from DFT facilitated climbing image nudged elastic band (CI-NEB) simulations. NT cathodes exhibit exceptionally good discharge capacities ∼60 (∼165) mAhg−1, ∼32 (∼110) mAhg−1 and ∼22 (∼82) mAhg−1 at 25C (1C) rate for x = 0, 0.2, 0.5, respectively. NP cathodes show capacity <5 mAhg−1 at 5C/2C-rate. The high-rate capability with two orders larger diffusion coefficient in nanotubes is due to improved access to Li+ intercalation channels. Whereas, nanoparticles are agglomerated, making b-axis inaccessible. While, Mn substitution affects the discharge capacity, it significantly improves capacity retention from ∼60% (x = 0) to ∼88% (x = 0.2) measured over 1000 cycles at ≥5C. From CI-NEB calculations we infer that Mn increases the activation barrier in its neighbourhood, thereby creating a steep potential hump (∼0.15 eV) for the Li+ diffusion. This largely impedes the ion transport and accounts for the steep loss of discharge capacity. We observe, while single crystalline nanotubular LiFePO4 are useful for high power density applications, Mn substitution in small quantities (x∼0.2) is ideal for cathodes with increased cyclic stability at high C-rates.

Triple probe interrogation of spokes in a HiPIMS discharge

Using a triple probe situated above the racetrack and inside the magnetic trap of a magnetron, rotating spoke-like structures have been clearly identified in a single HiPIMS pulse as periodic modulations of the electron temperature Te, electron density ne, ion saturation current Iisat, floating potential Vf and plasma potential Vp. The spokes rotate in the E × B direction with a velocity of ~8.8 km s−1.Defining the spoke shape from the footprint of the ion current, they deliver to flush-mounted probes embedded in the target, each spoke can be characterised by a dense but cool leading edge (ne ~ 2.0 × 1019 m−3, Te ~ 2.1 eV) and a relatively hotter but more rarefied trailing edge (ne ~ 1 × 1019 m−3, Te ~ 3.9 eV). Measurements of Vp show a potential hump towards the rear of the spoke, separated from regions of the highest density, with plasma potentials up to 8 V more positive than the inter-spoke regions. Azimuthal electric fields of ~1 kV m−1 associated with these structures are calculated.Transforming the triple probe time-traces to functions of the azimuthal angle θ and assuming a Gaussian radial profile for the plasma parameters, 2D spatial maps of ne, Te and Vp have been constructed as well as the target ion current density Jp from the embedded probes. The phase relationship between Te, Vp and ne can be clearly seen using this representation with ne leading Te and Vp with a phase shift between them of ~50°. Regions of maximum ion current to the target, delivered by individual spokes, coincide with the overlap of regions of high ne and Te measured above the target at a height of 15 mm. Ions created at elevated positions above the target in the observed dense region will take several micro-seconds to reach that surface, so contributing to the target ion current in the following spokes.

The “fine structure” of the slow micellar relaxation mode and the aggregation rates in the range between a potential hump and well in the work of aggregation

An analytical expression has been derived for the quasi-stationary size distribution of surfactant aggregates in a micellar system approaching the final equilibrium state. In contrast to previously known relations, the derived expression takes into account variations in the concentration of monomers during the slow relaxation and enables one to determine the previously unknown fine structure of the linearized mode of slow relaxation, i.e., its dependence on the aggregation numbers in the range between the maximum and minimum of the work of aggregation. This dependence has been reliably confirmed by the numerical solution of the set of linearized Becker–Doering difference equations, which describe the molecular mechanism of the kinetics of micellization and micellar relaxation. In turn, the expression found for the relaxation mode makes it possible to refine the analogous “fine structure” of aggregation rates at different points of the same range between the maximum and minimum of the work of aggregation, in which the aggregation rates appear to be low but exhibit a nonmonotonic behavior. This behavior is also confirmed by the numerical solution of the Becker–Doering difference kinetic equations.

Fast charge exchange ions in high power impulse magnetron sputtering of titanium as probes for the electrical potential

High power impulse magnetron sputtering (HiPIMS) plasmas exhibit a high ionization fraction of the sputtered material and ions with high kinetic energies, which produce thin films with superior quality. These ion energy distribution functions (IEDF) contain energetic peaks, which are believed to be linked to a distinct electrical potential hump inside rotating localized ionization zones, so called spokes, at target power densities above 1 kW cm−2. Any direct measurement of this electrical potential structure is, however, very difficult due to the dynamic nature of the spokes and the very high local power density, which hampers the use of conventional emissive probes. Instead, we use a careful analysis of the IEDFs for singly and doubly charged titanium ions from a HiPIMS plasma at varying target power density. The energy peaks in the IEDFs measured at the substrate depend on the point of ionization and any charge exchange collisions on the path between ionization and impact at the substrate. Thereby, the IEDFs contain a convoluted information about the electrical potential structure inside the plasma. The analysis of these IEDFs reveal that higher ionization states originate at high target power densities from the central part of the plasma spoke, whereas singly charged ions originate from the perimeter of the plasma spoke. Consequently, we observe different absolute ion energies with the energy of Ti2+ being slightly higher than two times the energy of Ti+. Additional peaks are observed in the IEDFs of Ti+ originating from charge exchange reactions from Ti2+ and Ti3+ with titanium neutrals. Based on this analysis of the IEDFs, the structure of the electrical potential inside a spoke is inferred yielding = 25 V above the plasma potential, irrespective of target power density.

Migration, Trade and Remittances: Low- and High-Skilled Workers

International migration involves the movement of people over national borders, while international trade deals with the production of goods or services in one country and their consumption in another. Economic theory assumes that migration and trade are substitutes, so that freer trade between countries with different wage levels should reduce voluntary migration as trade leads to convergence in wages. However, free-trade agreements can produce a migration hump as the pace of change accelerates and economies adjust, as migration increases before investment creates enough jobs to generate stay-at-home development despite remittances from migrants abroad. Efforts to deal with the root causes of migration must be aware of potential migration humps.

Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons.

Nonlinear ion-acoustic waves are analyzed in a nonrelativistic magnetized quantum plasma with arbitrary degeneracy of electrons. Quantum statistics is taken into account by means of the equation of state for ideal fermions at arbitrary temperature. Quantum diffraction is described by a modified Bohm potential consistent with finite-temperature quantum kinetic theory in the long-wavelength limit. The dispersion relation of the obliquely propagating electrostatic waves in magnetized quantum plasma with arbitrary degeneracy of electrons is obtained. Using the reductive perturbation method, the corresponding Zakharov-Kuznetsov equation is derived, describing obliquely propagating two-dimensional ion-acoustic solitons in a magnetized quantum plasma with degenerate electrons having an arbitrary electron temperature. It is found that in the dilute plasma case only electrostatic potential hump structures are possible, while in dense quantum plasma, in principle, both hump and dip soliton structures are obtainable, depending on the electron plasma density and its temperature. The results are validated by comparison with the quantum hydrodynamic model including electron inertia and magnetization effects. Suitable physical parameters for observations are identified.

Inverse parabolic quantum dot: The transition energy under magnetic field effect

We present here, the evolution of the transition energy with a static magnetic field, when the electron and the hole are confined in inverse parabolic quantum dot (IPQD). The unexpected behavior is found, at the weak confinement regime the conduction band minimum and the top of valance band change from s-state to p-state or d-state for confined electron and hole inside IPQD, respectively. The strength of the inverse parabolic potential (potential hump) inside a quantum dot has the upper hand in tuning the ground state momentum for both electron and hole, and consequently their interband transition energy is changed. Knowing that this is not the case for the other types of potentials. The quantum size, the magnetic field and inverse potential hump effects on electron and hole ground and excited states are discussed.

A Semifloating Gate Controlled Camel Diode Radiation Dosimeter

A camel diode (CD) gamma-ray dosimeter with dual semifloating gates (SFGs) is presented. The SFG diode performs the function of collecting holes accumulated in the potential hump of CD, and hence controls the barrier height. With the silicon depletion instead of oxide as sensitive area, the sensitivity of the dosimeter is enhanced, while the volume is reduced compared with the conventional dosimeters. Moreover, the dosimeter requires only 2 V bias to reset within 1 ms. The numerical simulation has been carried out with Sentaurus TCAD. As a result, a linear dependence of threshold voltage on absorbed dose of the gamma rays was obtained with a sensitivity of 143 mV/Gy. Due to its high sensitivity, low power, and convenient resetting operation, the design is highly suitable for radiotherapy applications.

Influence of ionisation zone motion in high power impulse magnetron sputtering on angular ion flux and NbOx film growth

The ion energies and fluxes in the high power impulse magnetron sputtering plasma from a Nb target were analysed angularly resolved along the tangential direction of the racetrack. A reactive oxygen-containing atmosphere was used as such discharge conditions are typically employed for the synthesis of thin films. Asymmetries in the flux distribution of the recorded ions as well as their energies and charge states were noticed when varying the angle between mass-energy analyser and target surface. More positively charged ions with higher count rates in the medium energy range of their distributions were detected in than in direction, thus confirming the notion that ionisation zones (also known as spokes or plasma bunches) are associated with moving potential humps. The motion of the recorded negatively charged high-energy oxygen ions was unaffected. Nb thin films at different angles and positions were synthesised and analysed as to their structure and properties in order to correlate the observed plasma properties to the film growth conditions. The chemical composition and the film thickness varied with changing deposition angle, where the latter, similar to the ion fluxes, was higher in than in direction.

Asymptotic behavior of Manakov solitons: Effects of potential wells and humps

We consider the asymptotic behavior of the soliton solutions of Manakov’s system perturbed by external potentials. It has already been established that its multisoliton interactions in the adiabatic approximation can be modeled by the complex Toda chain (CTC). The fact that the CTC is a completely integrable system, enables us to determine the asymptotic behavior of the multisoliton trains. In the present study we accent on the 3-soliton initial configurations perturbed by sech-like external potentials and compare the numerical predictions of the Manakov system and the perturbed CTC in different regimes. The results of conducted analysis show that the perturbed CTC can reliably predict the long-time evolution of the Manakov system.