Axial Electric Field Research Articles

Analysis of the Surface Electric Field Distribution of a 10 kV Faulty Composite Insulator

To obtain a more comprehensive knowledge of the surface electric field distribution of composite insulators, a three-dimensional (3D) simulation model of a 10 kV FXBW4-10/70 composite insulator was established, and the distribution of the axial and radial electric fields on the surface of the insulator under normal, damaged, internal defect, and fouling fault conditions were calculated and analyzed based on the finite element method. The results showed that the axial and radial electric field distributions on the surfaces of the normal composite insulators were “U” shaped, the radial electric field at the damaged location had a greater change than the axial electric field, and both the axial and radial electric fields at the internal defect location increased significantly. For the insulator covered with NaCl conductive fouling, the axial electric fields at the high-voltage (HV) and low-voltage (LV) ends showed a greater change. The results can provide a basis for the fault identification of composite insulators and the optimal design of insulation structures.

Controllability of Ion Out Flow Driven by Ambipolar Electric Field from Magnetic Mirror

A laminar flow is an ordered form of energy containers in plasma systems, hence tractable energy form to control or to convert to the other forms in plasmas. For this reason, plasma flows are utilized for various purposes, such as propulsion of spacecrafts, magnetohydrodynamic generators, and confinement of high-β fusion plasmas. In this study, we investigate properties of out flow of ions from a magnetic mirror in a laboratory experiment with a detailed measurement of axial profiles of plasma parameters for varied mirror ratios of the magnetic mirror. The experimental results reveal that the speed of the ion out flow is increased with the mirror ratio. This is considered to be attributed to enhancement of an ambipolar axial electric field accompanied by the increased mirror ratio. The relationship between the ambipolar potential height and the mirror ratio follows the relationship indicating a constant effective mirror ratio, which is an indication of an elimination of the mirror confinement effect by the enhanced ambipolar axial electric field. It is confirmed that the ion out flow satisfies the Bernoulli’s theorem and the continuity equation consistently. Accordingly, the ion out flow speed can be increased up to the speed corresponding to unity Mach number in the downstream of the magnetic mirror. Our work is the first detailed experimental confirmation of the Bernoulli’s theorem in a plasma flow system, which incorporates electrostatic potential variation in space. Another remarkable finding is that in the case of the mirror ratio lower than unity, the direction of the axial flow is reversed.

The theory of transport in helical spin-structure crystals

We study helical structures in spin-spiral single crystals. In the continuum approach for the helicity potential energy the simple electronic band splits into two non-parabolic bands. For low exchange integrals, the lower band is described by a surface with a saddle shape in the direction of the helicity axis. Using the Boltzmann equation with the relaxation due to acoustic phonons, we discover the dependence of the current on the angle between the electric field and helicity axis leading to the both parallel and perpendicular to the electric field components in the electroconductivity. The latter can be interpreted as a planar Hall effect. In addition, we find that the transition rates depend on an electron spin allowing the transition between the bands. The electric conductivities exhibit nonlinear behaviors with respect to chemical potential µ. We explain this effect as the interference of the band anisotropy, spin conservation, and interband transitions. The proposed theory with the spherical model in the effective mass approximation for conduction electrons can elucidate nonlinear dependencies that can be identified in experiments. We find the excellent agreement between the theoretical and experimental data for parallel resistivity depending on temperature at the phase transition from helical to ferromagnetic state in a single crystal. In addition, we predict that the perpendicular resistivity abruptly drops to zero in the ferromagnetic phase.

Experimental and numerical simulation study of the effect for the anode positions on the discharge characteristics of 300 W class low power Hall thrusters

Low-power Hall thruster (LHT) generally has poor discharge efficiency characteristics due to the large surface-to-volume ratio. Aiming to further refine and improve the performance of 300 W class LHT in terms of thrust and efficiency, and to obtain the most optimal operating point, the experimental study of the discharge characteristics for three different anode positions was conducted under the operation of various discharge voltages (100–400 V) and anode mass flow rates (0.65 mg·s−1 and 0.95 mg·s−1). The experimental results indicated that the thruster has the most excellent performance in terms of thrust and efficiency etc at a channel length of 27 mm for identical operating conditions. In addition, particle in cell simulations, employed to reveal the underlying physical mechanisms, show that the ionization and acceleration zone is pushed downwards towards the channel exit as the anode moves towards the exit. At the identical operating point, when the channel length is reduced from 32 to 27 mm, the ionization and acceleration zone moves towards the exit, and the parameters such as thrust and efficiency increase due to the high ionization rate, ion number density, and axial electric field. When the channel length is further moved to 24 mm, the parameters in terms of thrust (F) and efficiency ( ηa ) are reduced as a result of the decreasing ionization efficiency ( ηm ) and the larger plume divergence angle ( α ). In this paper, the results indicated that an optimum anode position ( ΔL=27 mm) exists for the optimum performance.

Stepwise development of atmospheric pressure plasma jet driven by bursts of high-voltage nanosecond pulses at multi-tens MHz

This study employs the bursts of high-voltage nanosecond pulses at multi-tens MHz to drive the helium atmospheric pressure plasma jet. Such bursts are obtained by modulating a high-voltage nanosecond pulse based on the wave reflections in a coaxial cable. The development processes and mechanisms of the plasma jet are analyzed in detail based on the discharge waveforms, discharge images, gas temperature, electron density, and axial electric field. Because the time interval between adjacent pulses is much shorter than the characteristic plasma decay time, the discharge channel driven by the first pulse still has high residual electron density and conductivity when the second pulse arrives. The first discharge channel serves as an extension of the high-voltage electrode. In this case, the second discharge starts at the end of the first discharge channel and continues to propagate forward. Driven by the bursts of high-voltage nanosecond pulses, the stepwise propagation of a guided streamer along the plasma jet is observed. The characteristic of the stepwise development of the guided streamer is stable and repeatable under the same condition and does not change at different helium flow rates if the flow is laminar. Reducing the cable length results in a higher equivalent pulse frequency in the bursts and significantly increases the plasma jet length. However, an excessively high frequency will cause a rise in gas temperature and pressure fluctuation in helium flow, resulting in a reduction in the length of the laminar region and an unstable discharge.

Surface-standing-wave formation via resonance interaction of a finite-length conductive rod with microwaves

The resonant response of a thin conducting rod with a finite length irradiated by microwaves polarized along its axis is observed. By using a thermoelastic optical indicator microscope it is shown that rod with a length of several half- wavelengths can serve as a resonator for axial surface waves. It is facilitated by noticeable reflections (approximately 30%) from the rod edges conditioned by the unique distributions of Sommerfeld wave fields along a rod. The presence of a weak axial electric field component of surface waves ensures an easy coupling with the incident plane wave polarized along the rod axis and excites the resonator. Visualization of distributions of the near-field magnetic component of surface standing waves in the vicinity of a rod allows the exploration of three longitudinal modes of a resonator with low orders. The possibility of controlling the resonant frequency by changing the length and diameter of the rod, as well as the electromagnetic characteristics of the environment, are studied. The phenomenon under study can be used to create wavefront shaping metasurfaces and for studies of the properties of a dielectric medium in the microwave region. As Sommerfeld waves propagate on the surface of a cylindrical resonator, the resonant properties are sensitive to the dielectric permittivity of the surrounding medium, which will open up the potential for using the suggested resonator in sensing applications, which is experimentally demonstrated.

Effects of amplitude modulated discharge on growth of nanoparticles in TEOS/O2/Ar capacitively coupled plasma

We investigate the effects of the amplitude modulation (AM) discharge method on the growth of nanoparticles and the relation between growth of nanoparticles and plasma generation in tetraethylorthosilicate (TEOS)/O2/Ar plasma. The laser-light scattering (LLS) intensity, which is proportional to the density and the sixth power of the size of nanoparticles in the Rayleigh scattering regime, decreases by 18% at an AM level of 10% and by 60% at an AM level of 50%. On the other hand, the ArI emission intensity, which is roughly proportional to plasma density, is higher than that for the continuous wave discharge. Thus, AM discharges suppress growth of nanoparticles in TEOS plasma. We have shown oscillations of the axial electric field Ez with the AM frequency for AM discharge by electric field measurement using an electro-optic probe. We have discussed that these fluctuations of Ez mainly lead to the vertical oscillation of the levitation position of nanoparticles trapped in the plasma sheath boundary region by taking into account the force balance equation in the axial direction on these negatively charged nanoparticles.

Nonlinear Temperature Gradient Focusing of Deoxyribose Nucleic Acid in a Microfluidic Channel With Patterned Surface Charges: A Numerical Study

Abstract We present a numerical analysis of electrophoretic transport of a biological sample, such as, deoxyribose nucleic acid (DNA) via nonlinear temperature gradient within a microfluidic channel having patterned surface charges. The transport of the electrolyte is induced by electroosmotic force by imposing an axial electric field, superposed with the wall electric field via electrodes embedded along the wall of the microchannel. We consider the periodic variation of wall zeta potential in electrokinetic motion of an electrolyte wherein the DNA sample exhibits electrophoretic migration. Temperature dependence of the thermophysical properties of the electrolyte and the electrophoretic mobility and diffusivity of the analyte sample is accounted for in the model to improve its accuracy. Nonlinear longitudinal temperature field along the microchannel is induced via Joule heating by suitably shaping the channel geometry, which enhances the concentration of DNA approximately 270 folds by applying just 500 V DC field with constant zeta potential at the walls. The study further reveals that the concentration of DNA reduces drastically when a periodic wall zeta potential is applied. Results of the study lend to the design of novel electrically actuated bio-microfluidic devices with tunable solute separation and dispersion capabilities.

Fluid simulation on effect of background magnetic field on plasma characteristics in a Hall thruster

Herein, the effect of the background magnetic field on plasma characteristics in a Hall thruster is numerically investigated using DUT-HTFS [Li et al., AIP Adv. 12, 015117 (2022)], an integrated fluid simulation platform on Hall thruster plasmas. The research shows that the background magnetic field significantly influences the distribution of the plasma density, especially the radial profiles of the plasma density near the ionization region and the acceleration region. In addition, the positions of the peak values of the electron power absorptions mainly occur near the dielectric walls of the exhaust plane, and the electron power absorption mechanism is mainly dominated by the Ohmic heating. The peak values of the axial electron current density on the inner and outer dielectric walls are higher than that on the centerline. This phenomenon is closely related to the near wall conduction mechanism of the electrons. In addition, the background magnetic field significantly influences the shapes, positions, and magnitudes of the peak values of the plasma parameters, such as the plasma density, the electron current density, the axial electric field, the electric potential, and the ionization rate. These results will help us to provide a valuable reference and reduce the risk for the experimental test programs and the applications of Hall thrusters in the future.

Electroviscoelstic Stability Analysis of Cylindrical Structures in Walters B Conducting Fluids Streaming through Porous Medium

In this research, the linear stability of a cylindrical interface between two viscoelstic Walters B conducting fluids moving through a porous medium is investigated theoretically and numerically. The fluids are influenced by a uniform axial electric field. The cylindrical structure preserves heat and mass transfer across the interface. The governing equations of motion and continuity are linearized, as are Maxwell’s equations in quasi-static approximation and the suitable boundary conditions at the interface. The method of normal modes has been used to obtain a quadratic characteristic equation in frequency with complex coefficients describing the interaction between viscoelstic Walters B conducting fluids and the electric field. In light of linear stability theory, the Routh–Hurwitz criteria are used to govern the structure’s stability. Several special cases are recoverd under suitable data choices. The stability analysis is conferred in detail via the behaviors of the applied electric field and the imaginary growth rate part with the wavenumbers. The effects of various parameters on the interfacial stability are theoretically presented and illustrated graphically through two sets of figures. Our results demonstrate that kinematic viscosities, kinematic viscoelasticities, and medium porosity improve stability, whereas medium permeability, heat and mass transfer coefficients, and fluid velocities decrease it. Finally, electrical conductivity has a critical influence on the structure’s stability.

Electro-osmotic peristaltic flow and heat transfer in an ionic viscoelastic fluid through a curved micro-channel with viscous dissipation.

Emerging systems in microfluidics are embracing bio-inspired designs in which boundaries are flexible and mimic peristaltic propulsion mechanisms encountered in nature. These devices utilize electro-kinetic body forces to manipulate very precisely ionic biofluids for a range of medical applications including. Motivated by exploring in more detail electro-hemorheological micro-pumping, in the current article, a mathematical model is developed for peristalsis propulsion of a viscoelastic biofluid in a curved microchannel with electro-osmotic effect and thermal transport under static axial electrical field and with viscous heating. The third grade Reiner-Rivlin model is deployed for blood rheology. The novelty of the current work is therefore the simultaneous consideration of electrokinetics, viscoelastic behavior with the third grade Reiner-Rivlin model and coupled flow and heat transport with viscous dissipation in peristaltic pumping in a curved micro-channel. A Poisson-Boltzmann formulation is adopted to simulate the charge number density associated with the electrical potential. Asymmetric zeta potential (25 mV) is prescribed and mobilizes an electric double layer (EDL). The governing conservation equations for mass, energy, momentum and electrical potential with associated boundary conditions are simplified using lubrication approximations and rendered dimensionless via appropriate scaling transformations. Analytical solutions are derived in the form of Bessel functions and numerical evaluations are conducted via the ND solver command in MATHEMATICA symbolic software. The simulations show that with stronger viscoelastic effect, boluses are eliminated and there is relaxation in streamlines in the core and peripheral regions of the micro-channel. Increasing Brinkman number (dissipation parameter) elevates temperatures. An increase in electrical double layer thickness initially produces a contraction in the upper bolus and an expansion (lateral) in the lower bolus in the micro-channel. With modification in zeta potential ratio parameter from positive to negative values, in the lower half of the micro-channel, axial flow deceleration is generated.

Optical diagnosis of a kHz-driven helium atmospheric pressure plasma jet

This paper focuses on utilizing several different optical diagnostics to experimentally characterize a pure helium atmospheric pressure plasma jet. Axial electric field measurements were carried out along the plasma plume through the use of a non-perturbing method based on polarization-dependent Stark spectroscopy of the helium $492.2$ nm line. The electric field is shown to increase with distance along the plume length, reaching values as high as $24.5$ kV cm $^{-1}$ . The rate of increase of the electric field is dependent on the helium gas flow rate, with lower gas flows rising quicker with distance in comparison with larger flow rates, with the typical values remaining within the same range. This sensitivity is linked to gas mixing between the helium and surrounding ambient air. Schlieren imaging of the gas flow is included to support this. The addition of a target is shown to further increase the measured electric field in close range to the target, with the magnitude of this increase being strongly dependent on the distance between the tube exit and target. The relative increase in the electric field is shown to be on average greater for a conducting target of water in comparison with plastic. A minimal equipment optical configuration, which is here referred to as fast two-dimensional monochromatic imaging, is introduced as an approach for estimating excited state densities within the plasma. Densities of the upper helium states for transitions, $1s3s$ $^{3}S_{1}$ $\rightarrow$ $1s2p$ $^{3}P^{0}_{0,1,2}$ at $706.5$ nm and $1s3s$ $^{1}S_{0}$ $\rightarrow$ $1s2p$ $^{1}P^{0}_{1}$ at $728.1$ nm, were estimated using this approach and found to be of the order of $10^{10}$ – $10^{11}$ cm $^{-3}$ .

Current Flow in a Cylindrical Nanopore with an Object-Implications for Virus Sensing.

Interest is growing in nanopores as real-time, low-cost, label-free virus size sensors. To optimize their performance, we evaluate how external electric field and ion concentrations and pore wall charges influence currents and object (disk) radius-current relationship using simulations. The physics was described using the Poisson-Nernst-Planck and Navier–Stokes equations. In a charged cylindrical nanopore with a charged disk, elevated external electric field produces higher (and polarity independent) ion concentrations and greater ion current (largely migratory). Elevated external ion concentrations also lead to higher concentrations (mainly away from the pore wall), greater axial electric field especially in the disk-pore wall space, and finally larger current. At low concentrations, current is disk radius independent. The current rises as concentrations increase. Interestingly, the rise is greater for larger disks (except when the pore is blocked mechanically). Smaller cross-sectional area for current flow or volume exclusion of electrolyte by object thus cannot be universally accepted as explanations of current blockage. Ion current rises when pore wall charge density increases, but its direction is independent of charge sign. Current-disk radius relationship is also independent of pore wall charge sign. If the pore wall and disk charges have the same sign, larger current with bigger disk is due to higher counter-ion accumulation in the object-pore wall space. However, if their signs are opposite, it is largely due to elevated axial electric field in the object-pore wall space. Finally in uncharged nanopores, current diminishes when disk radius increases making them better sensors of virus size.

Equal/unequal half mode substrate integrated waveguide filtering power dividers using an ultra-compact metamaterial unit-cell

Abstract In this paper, a novel ultra-compact metamaterial unit-cell is introduced. The proposed unit-cell consists of one modified rings which has been designed based on the fractal technique and meander technique. These techniques are used to reduce the physical size of the conventional complementary split ring resonators (CSRRs). In the proposed metamaterial unit-cell which is called the fractal/meander CSRR (FMCSRR), the slot lines in the conventional CSRRs are replaced by the fractal and meander slots, simultaneously. The FMCSRR unit-cell is a planar metamaterial element which exhibits negative permittivity and is considered as electric dipole when excited by an axial electric field. Thus, the FMCSRR unit-cell is modeled as a shunt resonator tank. Therefore, by using the proposed FMCSRR configuration, all of the interior space of the ring has been used and the slot lines have been increased. Consequently, the higher inductance has been achieved and the resonance frequency of the proposed FMCSRR unit-cell becomes lower compared with the conventional CSRR. That’s mean the electrical size of the introduced unit-cell FMCSRR unit-cell is smaller than the conventional CSRR with the same physical sizes. A microstrip notch band filter, a microstrip band-pass filter, a half mode substrate integrated waveguide (HMSIW) band-pass filter and three HMSIW filtering power dividers (FPDs) with different power division ratios of 1:1, 1:4, and 1:8 have been designed to illustrate the ability of the proposed FMCSRR unit-cell in the size reduction. All of the designed devices operated at 2.4 GHz which are suitable for WLAN applications. For verification the performance of the utilized techniques in miniaturization of the dimension, the designed equal/unequal HMSIW FPDs have been fabricated and tested. A reasonable agreement between simulated and measured results has been achieved. The results confirmation that a miniaturization about 79% has been obtained. The total size of the proposed HMSIW FPDs are about 0.09λ g × 0.09λ g. The proposed HMSIW FPDs have many advantages in terms of compact size, low insertion loss, high selectivity, easy integration with the other planar circuits, and controllable bandwidth.

Oriented external electric fields act as a “switch” of Pt-M/BC3N2 diatomic catalysts activate pristine ammonia borane dehydrogenation: A DFT study

In this paper, the Pt-M/BC3N2 (M= Ag, Al, Au, Co, Cr, Cu, Fe, Ir, Mn, Mo, Nb, Ni, Pd, Pt, Re, Rh, Ru, Se, Ta, Ti, V, W, Zn, La, Ce, Zr, Hf, Cd, Hg and Y) diatomic catalyst structure was constructed and used to activate Ammonia Borane (AB) under external axial electric field by the First-principles calculation method. By changing the size of applied electric field, we found that the activation of N-H bond in AB can be realized only on Pt-M/BC3N2 (M=Al, Zn, Hf, Y) diatomic catalyst, and the effective electric field range is different. Further calculation showed that Pt-Y/BC3N2 diatomic catalyst could not achieve the break of B-H bond. So, for Pt-M/BC3N2 (M=Al, Zn, Hf) diatomic catalyst, further, sequentially by applying an applied electric field, we achieve the break of the B-H bond in AB and the formation of 1 mol H2. This suggests that the electric field can act as a “switch” for activation of AB molecules.

Effect of axial electric field on confined water in carbon nanotube: Enhancement of thermophoresis

Strengthening the thermophoresis of nanoscale confined liquid is an intrinsic topic in nanoscale devices and systems. Unfortunately, enhancing thermophoresis via an uncontacted way is still ambiguous, while is quite desirable in technology. In this work, we propose a feasible strategy to enhance the thermophoresis of confined nano-liquid via using external electric field. Moreover, this strategy is demonstrated by a striking case, namely the electric field-intensified thermophoresis of the confined nano-liquid within carbon nanotube, with the aid of molecular dynamics simulation. The interfacial water molecules undergo a configuration transition from the disorder-like to the ordered network-like under the directional electric field-induced hydrogen bond interactions. As a result, the thermophoresis depicts a regular movement under electric field and the velocity increase as high as 99% is also achieved. This work illustrates a great promising potential in seawater desalination, cellular uptake and drug carrier, and nanofiltration membranes.

Flexible actuator by electric bending of saline solution-filled carbon nanotubes

As a two-phase hybrid material, liquid-filled carbon nanotubes (CNTs) provide a great opportunity to design dexterous flexible nano-manipulator actuated by electric field. Here, we report a group of saline solution-filled CNTs with the end constraint can realize 360° all-round bending in a suitable electric field. The molecular dynamics (MD) simulation results show that saline solution-filled CNTs can be bent under the axial-lateral compound electric field, whereas the bending deflection increases with the increase of salinity, CNTs length and electric intensity. The deformation mechanism of saline solution-filled CNTs under the electric field is clarified by exploring the movement and distribution of salt ions in CNTs under the axial electric field. Moreover, based on the bending deformation characteristics of saline solution-filled CNTs, the MD simulations for the two-finger and four-finger nano grippers grasping diamond balls are carried out to demonstrate the micromanipulation functions of saline solution-filled CNTs. The findings will provide an important theoretical basis for the design and application of micromanipulation devices based on low dimensional carbon materials.

Predicting ion concentration polarization and analyte stacking/focusing at nanofluidic interfaces.

We report on the investigation of electropreconcentration phenomena in micro-/nanofluidic devices integrating 100μm long nanochannels using 2D COMSOL simulations based on the coupled Poisson-Nernst-Planck and Navier-Stokes system of equations. Our numerical model is used to demonstrate the influence of key governing parameters such as electrolyte concentration, surface charge density, and applied axial electric field on ion concentration polarization (ICP) dynamics in our system. Under sufficiently extreme surface-charge-governed transport conditions, ICP propagation is shown to enable various transient and stationary stacking and counter-flow gradient focusing mechanisms of anionic analytes. We resolve these spatiotemporal dynamics of analytes and electrolyte ICP over disparate time and length scales, and confirm previous findings that the greatest enhancement is observed when a system is tuned for analyte focusing at the charge, excluding microchannel, nanochannel electrical double layer (EDL) interface. Moreover, we demonstrate that such tuning can readily be achieved by including additional nanochannels oriented parallel to the electric field between two microchannels, effectively increasing the overall perm-selectivity and leading to enhanced focusing at the EDL interfaces. This approach shows promise in providing added control over the extent of ICP in electrokinetic systems, particularly under circumstances in which relatively weak ICP effects are observed using only a single channel.

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

The unsteady, magneto-hydrodynamic generalized Couette flows of two immiscible fluids in a rectangular channel with isothermal walls under the influence of an inclined magnetic field and an axial electric field have been investigated. Both fluids are considered electrically conducting and the solid boundaries are electrically insulated. Approximate analytical solutions for the velocity, induced magnetic, and temperature fields have been determined using the Laplace transform method along with the numerical Stehfest's algorithm for the inversion of the Laplace transforms. Also, for the nonlinear differential equation of energy, a numerical scheme based on the finite differences has been developed. A particular case has been numerically and graphically studied to show the evolution of the fluid velocity, induced magnetic field, and viscous dissipation in both flow regions.

An integrated fluid simulation platform on Hall thruster plasmas

In this work, a newly integrated fluid simulation platform, named DUT-HTFS, is developed for the multiple physical fields in Hall thrusters. The integrated simulation platform includes three inter-related parts: the geometry module, background magnetic field module, and plasma module. Using the geometry module, three sets of meshes for a Hall thruster are obtained. One set of the mesh is for the calculation of the background magnetic fields, the second is for the electric potentials, and the third is for the plasmas. Based on the meshes and using the background magnetic field module, a numerical result of the background magnetic field in the Hall thruster is obtained and discussed. Based on the meshes and the numerical result of the background magnetic field, using the plasma module, the numerical results of the plasmas in the Hall thruster are obtained. The results of the plasma density, the electric field, the electric potential, and the ionization rate are similar to those from HPHALL (Hybrid-PIC Hall thruster code) simulations and are qualitatively consistent with the experimental results from the literature. Furthermore, varying the neutral gas pressure from 0.02 to 0.03 Torr, the numerical results of the plasmas in the Hall thruster are obtained. These results reveal that neutral gas pressure effects contributed considerably to the shape, location, and magnitude of the peak plasma properties, including the ion density, axial electric field, and ionization rate. This fluid simulation platform could provide a new angle of view for better understanding of the physical mechanism in Hall thrusters.