Azimuthal Electric Field Research Articles

Observation of strong in-plane perpendicular electric field in a radio frequency plasma with a time-varying magnetic nozzle

The spatiotemporal evolution of the electron temperature and plasma potential in a 200-W radio frequency argon discharge with a time-varying (approximately 60 kHz) magnetic nozzle was measured. Unlike in conventional static magnetic nozzles, the two-dimensional profiles of the electron temperature and plasma potential changed in sync with the applied azimuthal electric field, not with the magnetic field. The temporally resolved electric field vectors demonstrated an enhancement of the perpendicular component, where the direction fairly matched that of electron Eθ×B drift, indicating a space charge separation. This observation suggests that the applied time-varying field actively enhanced cross field electron transport, resulting in a unique potential structure and charged particle acceleration.

Polarization of electromagnetic pulses

We show the impossibility, for localized and exact solutions of the Maxwell equations, of perfect circular polarization in a fixed plane, or perfect linear polarization along a fixed direction. A measure of polarization of electromagnetic pulses is obtained by analogy with that useful in monochromatic radiation, and its limitations discussed. Using oscillatory solutions of the free-space Maxwell equations, for which all components of the electric and magnetic fields satisfy the wave equation, we construct explicit examples of TE pulses which are linearly polarized with an azimuthal electric field, TE+iTM pulses approximately linearly polarized along the propagation direction, and also approximately circularly polarized pulses. The latter have perfect circular polarization on the propagation axis.

Poloidal magnetic field in the dense plasma focus

Existence of an axial (poloidal) component of magnetic field in the dense plasma focus has been inferred using multiple diagnostics in many laboratories since 1979. It has not received much attention because its origin as well as role in plasma focus physics was unclear till recently. Recent discovery of long-lasting neutron emission perpendicular to the axis in PF-1000 and neutron fluence ratio (end/side) less than unity in Gemini shows that azimuthally accelerated and radially confined deuterons play an observable role in fusion reactions. A spontaneously generated poloidal magnetic field can provide both the azimuthal electric field necessary for acceleration and radial confinement of the ions being accelerated in the acceleration zone. A comprehensive survey of plasma focus research also confirms the role of spontaneously self-organized plasma objects in the fusion reaction process where their three-dimensional magnetic field structure provides a mechanism for accelerating and trapping ions making them repeatedly pass through a dense plasma target. With emerging appreciation of the likely role of the axial magnetic field in plasma focus neutron emission, it becomes imperative to consider models for its origin. This Letter proposes a partial theory of growth of the axial (poloidal) magnetic field via a simple dynamo, with the geomagnetic field as the seed, which converts the kinetic energy of the plasma into energy of the poloidal magnetic field. This theory leads to an experimentally testable proposition.

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.

First exploratory survey of poloidal magnetic flux emission from a dense plasma focus

Studies of neutron emission from a dense plasma focus suggest that a significant fraction of neutron emission in some shots is caused by fast deuterons that have a prominent azimuthal component of motion. Recent examples are observations of long-lasting neutron emission in the side-on direction in PF-1000 and of neutron flux asymmetry (end/side) less than unity in Gemini. Such azimuthal motion of deuterons indicates the presence of an azimuthal electric field that accelerates them and a poloidal magnetic field that keeps them within the zone of acceleration. This in turn must be accompanied by poloidal magnetic flux emission (PMFE) from the plasma focus. Recently, a diagnostic technique for detection of PMFE has been proposed and demonstrated. This paper presents results of its successful replication and the first ever exploratory survey of PMFE emission using the UNU-ICTP plasma focus at the Nanyang Technological University, Singapore.

Magnetic frame-dragging correction to the electromagnetic solution of a compact neutron star

ABSTRACT Neutron stars are usually modelled as spherical, rotating perfect conductors with a predominant intrinsic dipolar magnetic field anchored to their stellar crust. Due to their compactness, General Relativity corrections must be accounted for in Maxwell’s equations, leading to modified interior and exterior electromagnetic solutions. We present analytical solutions for slowly rotating magnetized neutron stars, taking into account the magnetic frame-dragging correction. For typical compactness values, i.e. Rs ∼ 0.5 [R*], we show that the new terms lead to a per cent order correction in the magnetic field orientation and strength compared to the case, with no magnetic frame-dragging correction. Also, we obtain a self-consistent redistribution of the surface azimuthal current. We verify the validity of the derived solution through two-dimensional particle-in-cell simulations of an isolated neutron star. Defining the azimuthal electric and magnetic field amplitudes during the transient phase as observables, we prove that the magnetic frame-dragging correction reduces the transient wave amplitude, as expected from the analytical solution. We show that simulations are more accurate and stable, when we include all first-order terms. The increased accuracy at lower spatiotemporal resolutions translates into a reduction in simulation runtimes.

A New Four‐Component L*‐Dependent Model for Radial Diffusion Based on Solar Wind and Magnetospheric Drivers of ULF Waves

AbstractWaves which couple to energetic electrons are particularly important in space weather, as they drive rapid changes in the topology and intensity of Earth's outer radiation belt during geomagnetic storms. This includes Ultra Low Frequency (ULF) waves that interact with electrons via radial diffusion which can lead to electron dropouts via outward transport and rapid electron acceleration via inward transport. In radiation belt simulations, the strength of this interaction is specified by ULF wave radial diffusion coefficients. In this paper we detail the development of new models of electric and magnetic radial diffusion coefficients derived from in‐situ observations of the azimuthal electric field and compressional magnetic field. The new models use as it accounts for adiabatic changes due to the dynamic magnetic field coupled with an optimized set of four components of solar wind and geomagnetic activity, , , , and , as independent variables (inputs). These independent variables are known drivers of ULF waves and offer the ability to calculate diffusion coefficients at a higher cadence then existing models based on Kp. We investigate the performance of the new models by characterizing the model residuals as a function of each independent variable and by comparing to existing radial diffusion models during a quiet geomagnetic period and through a geomagnetic storm. We find that the models developed here perform well under varying levels of activity and have a larger slope or steeper gradient as a function of as compared to existing models (higher diffusion at higher values).

Investigating the role of electric fields on flow harmonics in heavy-ion collisions

Using the blast-wave model, we explore the effect of electric fields on spectra and flow harmonics (especially the elliptic flow) for charged pions and protons. We incorporate the first-order correction to the single-particle distribution function due to the electric fields and the dissipative effect while calculating the invariant yields of hadrons in the Cooper–Frye prescription at the freezeout hypersurface. We find a noticeable correction to the directed and elliptic flow of pions and protons for unidirectional and azimuthal asymmetric electric fields of a magnitude in the transverse plane. Further, we observe mass dependency of the directed flow generated due to the electric fields. The splitting of particle and antiparticle’s elliptic flow due to the electric fields is also discussed.

On the Energy‐Dependent Deep (L < 3.5) Penetration of Radiation Belt Electrons

AbstractDeep penetration of outer radiation belt electrons to low L (<3.5) has long been recognized as an energy‐dependent phenomenon but with limited understanding. The Van Allen Probes measurements have clearly shown energy‐dependent electron penetration during geomagnetically active times, with lower energy electrons penetrating to lower L. This study aims to improve our ability to model this phenomenon by quantitatively considering radial transport due to large‐scale azimuthal electric fields (E‐fields) as an energy‐dependent convection term added to a radial diffusion Fokker‐Planck equation. We use a modified Volland‐Stern model to represent the enhanced convection field at lower L to match the observations of storm time values of E‐field. We model 10–400 MeV/G electron phase space density with an energy‐dependent radial diffusion coefficient and this convection term and show that the model reproduces the observed deep penetrations well, suggesting that time‐variant azimuthal E‐fields contribute preferentially to the deep penetration of lower‐energy electrons.

Cavity Mode Wave Frequency Variation Associated With Inward Motion of the Magnetopause During Interplanetary Shock Compression

AbstractA cavity mode wave, referring to a trapped or radially standing fast mode wave between different magnetospheric boundaries, has been developed in theory and reported in observation studies. In this study, we present an interplanetary shock (IPS)‐induced cavity mode wave event observed outside the plasmasphere on 31 August 2017 with multispacecraft measurements. The phase delay of 90° between the azimuthal electric field and compressional magnetic field indicates that the fast‐mode wave triggered by the IPS is a standing wave, presumably radially trapped in the cavity between the magnetopause and plasmapause. Taking advantage of the location of Van Allen Probe B spacecraft right outside the plasmapause and the Arctic and Antarctic Research Institute ground‐based high‐latitude array mapped in the noon sector, it is suggested that the observed compressional wave associates to cavity mode with its inner boundary at the plasmapause and its outer boundary at the magnetopause. The peak frequency of the wavelet spectrum of the compressional magnetic field increases from 10.5 to 12.5 mHz, which is consistent with the theoretically calculated cavity eigenfrequencies before and after the IPS. We also provide the first evidence that the peak frequency of the cavity mode increases due to the inward motion of the magnetopause during IPS compression.

14-moment maximum-entropy modeling of collisionless ions for Hall thruster discharges

Ions in Hall effect thrusters are often characterized by a low collisionality. In the presence of acceleration fields and azimuthal electric field waves, this results in strong deviations from thermodynamic equilibrium, introducing kinetic effects. This work investigates the application of the 14-moment maximum-entropy model to this problem. This method consists in a set of 14 partial differential equations (PDEs) for the density, momentum, pressure tensor components, heat flux vector, and fourth-order moment associated with the particle velocity distribution function. The model is applied to the study of collisionless ion dynamics in a Hall thruster-like configuration, and its accuracy is assessed against different models, including the Vlasov kinetic equation. Three test cases are considered: a purely axial acceleration problem, the problem of ion-wave trapping, and finally the evolution of ions in the axial-azimuthal plane. Most of this work considers ions only, and the coupling with electrons is removed by prescribing reasonable values of the electric field. This allows us to obtain a direct comparison among different ion models. However, the possibility to run self-consistent plasma simulations is also briefly discussed, considering quasi-neutral or multi-fluid models. The maximum-entropy system appears to be a robust and accurate option for the considered test cases. The accuracy is improved over the simpler pressureless gas model (cold ions) and the Euler equations for gas dynamics, while the computational cost shows to remain much lower than direct kinetic simulations.

Enhancing one-dimensional particle-in-cell simulations to self-consistently resolve instability-induced electron transport in Hall thrusters

The advent of high-power Hall thrusters and the increasing interest toward their use as a primary propulsion system for various missions have given a new boost to the efforts aiming at self-consistent predictive modeling of this thruster technology. In this article, we present a novel approach, which allows enhancing the predictive capability of one-dimensional particle-in-cell (PIC) simulations to self-consistently capture the wave-induced electron transport due to the azimuthal instabilities in Hall thrusters. The so-called “pseudo-2D” PIC scheme resulting from this approach is extensively tested in several operating conditions. The results are compared against a well-established 2D3V axial–azimuthal reference case in terms of the axial profiles of the time-averaged plasma properties, the azimuthal electric field fluctuations and their dispersion features, and the contributions of the force terms in the electron azimuthal momentum equation to the cross-field mobility. We have demonstrated that the pseudo-2D PIC provides a prediction of the above aspects that compares very closely in almost all conditions with those from the full-2D simulation. In addition, the sensitivity of the pseudo-2D simulation results to the numerical parameters associated with our approach is assessed in detail. The outcomes of these analyses have casted light on the next steps to further improve the approach.

Radial Transport of Energetic Electrons as Determined From the “Zebra Stripes” Measured in the Earth’s Inner Belt and Slot Region

The “zebra stripes” are drift-periodic structures present in the form of peaks and valleys in energetic (tens to hundreds of keV) electron spectrograms in the Earth’s inner belt and slot region. Their characteristics inform of preceding electric field disturbances. Specifically, their amplitude contains information on the radial transport of trapped particles generated by azimuthal electric field disturbances. We introduce a method to quantify radial transport from the measured amplitude of the zebra stripes, and we apply it to the zebra stripes observed on 16 February 2014. The findings are compared with results from a particle tracing code that leverages an empirical analytical model for the electric field disturbances. The measured amplitude of the zebra stripes indicates that the electric field disturbances transported the trapped population coherently, over radial distances spanning several hundreds to thousands of kilometers. The magnitude of radial transport is shown to depend on angular drift frequency and initial location (equatorial radial distance and magnetic local time) in the disturbance. The model-observation comparison suggests that the timing for electric field variations provided by the model is valid for studying radial transport in the inner belt and slot region. On the other hand, we found discrepancies when comparing radial transport magnitudes. When assuming that radial transport varies as L3, as weakly suggested by the data for set angular drift frequencies, and extrapolating observations to L = 1, the amount of experimental transport obtained is two to three times greater than numerical estimates. Outputs from the standalone version of the Rice Convection Model (RCM) suggests that the electric field disturbances are likely greater than the estimates provided by the empirical model. RCM also supports the idea that radial transport driven by the prompt penetration of magnetospheric convection varies as L3 in the inner belt and slot region.

Multi‐Event Study on the Connection Between Subauroral Polarization Streams and Deep Energetic Particle Injections in the Inner Magnetosphere

AbstractEnergetic electron flux enhancements for 100s keV energies are often observed at low L shells (L < 4) in the inner magnetosphere during geomagnetic storms. However, protons with similar energies do not penetrate as deeply as electrons. Electric fields from subauroral polarization streams (SAPS) have been proposed as a mechanism to explain the difference between the 100s keV electron and proton behavior by altering the particles’ drift paths and allowing electrons to access lower L shells than protons. Although the primary signature of SAPS is a strong radial electric field, there are corresponding westward/eastward azimuthal electric fields on the eastern/western regions of the SAPS that cause inward/outward radial transport and a differential response between the oppositely drifting electrons and protons. We examine three events where SAPS were observed by the Van Allen Probes near the same time and L shell range as 100s keV electron enhancements deep within the inner magnetosphere. The observations demonstrate that 100s keV electrons were progressively transported radially inward and trapped at low L shells that were consistent with the spatial extent of the SAPS electric fields. Proton flux enhancements were limited to <100 keV energies and were only observed temporarily in the SAPS region, indicating that these particles were on open drift paths. The particle observations are consistent with the differential drift paths for electrons and protons predicted by a simple SAPS electric field model, suggesting that SAPS play an important role in 100s keV particle dynamics at low L shells in the inner magnetosphere.

Fluid simulation of the superimposed dual-frequency source effect in inductively coupled discharges

Superimposition of dual frequencies (DFs) is one of the methods used for controlling plasma distribution in an inductively coupled plasma (ICP) source. The effects of a superimposed DF on the argon plasma characteristics have been investigated using a two-dimensional self-consistent fluid model. When both currents are fixed at 6 A, the plasma density drops with decrease in one of the source frequencies due to less efficient heating and the plasma uniformity improves significantly. Moreover, for ICP operated with superimposed DFs (i.e., 4.52 MHz/13.56 MHz and 2.26 MHz/13.56 MHz), the current source exhibits the same period as the low frequency (LF) component, and the plasma density is higher than that obtained at a single frequency (i.e., 4.52 and 2.26 MHz) with the same total current of 12 A. However, at superimposed current frequencies of 6.78 MHz/13.56 MHz, the plasma density is lower than that obtained at a single frequency of 6.78 MHz due to the weaker negative azimuthal electric field between two positive maxima during one period of 6.78 MHz. When the superimposed DF ICP operates at 2.26 and 13.56 MHz, the rapid oscillations of the induced electric field become weaker during one period of 2.26 MHz as the current ratio of 2.26 MHz/13.56 MHz rises from 24 A/7 A to 30 A/1 A, and the plasma density drops with the current ratio due to weakened electron heating. The uniformity of plasma increases due to sufficient diffusion under the low-density condition.

Evolution of electron cross-field transport induced by an equilibrium azimuthal electric field in an E × B Hall thruster discharge under an azimuthally inhomogeneous neutral supply

The electron cross-field transport by the induced azimuthal electric field in a Hall thruster exhibits the mobility scaled by $1/B$. This study investigates parameters affecting this transport over a Hall thruster's distinct regions, such as the ionization, acceleration, and plume region. The main focus is on the nonzero equilibrium azimuthal electric field induced by an azimuthally inhomogeneous neutral supply. A fast Fourier transform analysis of the plasma structure reveals that the wavenumber $k$ of the azimuthal plasma structure increases from $k=2$, which is the input condition, to $k=4$ in the plume region, and that the total axial flux caused by the azimuthal electric field is mainly induced from the structures of the dominant Fourier components. The azimuthal phase relation between plasma potential and density is formed to maximize the axial electron flux at the plume region and starts varying along with other plasma properties as electrons flow toward the acceleration region. The spatial evolution of the effective axial mobility coefficient is extracted, and its regional characteristics are discussed.

Magnetotail Dipolarizations and Ion Flux Variations During the Main Phase of Magnetic Storms

AbstractNear‐Earth tail dipolarizations are usually associated with fast plasma flows and an increase in energetic particle fluxes. Yet, the role of these dipolarizations in energetic ion flux transport toward the inner magnetosphere and in ring current (including partial ring current) development during the main phase of a geomagnetic storm is not fully understood. We investigated observations from Time History of Events and Macroscale Interactions during Substorms (THEMIS) probes A, D, and E with apogees at X ≈ −13 RE and Los Alamos National Laboratory (LANL) geosynchronous spacecraft in the midnight magnetic local time (MLT) sector (21.5–1.5 h MLT) during the main phases of storms with integrated Dst exceeding 600 nT*hr from the 2010 to 2016 THEMIS tail seasons. We selected 10 storms during which at least one of the THEMIS probes was in the midnight sector during a storm’s main phase and identified 39 dipolarization events with a Bz increase exceeding 10 nT within 500 s during these storms’ main phases. In 21 of the 39 events, an increase in the magnetic field elevation angle Θ estimated from LANL magnetospheric plasma analyzer (MPA) data was detected at geosynchronous orbit (GEO) within ±15‐min‐long time window around dipolarization onset detected by THEMIS. In only 10 of those 21 events, however, did ion fluxes at energies from 50 to 500 keV increase in three or more consecutive energy bins at LANL. Comparisons of ion spectra collected by THEMIS and LANL in these 10 events revealed a similar increase in fluxes at energies E > 20 keV. Our results indicate that a dipolarization that occupies a large portion of the nightside magnetosphere from GEO to ∼12 RE is a necessary but not sufficient condition for energetic ion flux enhancements at GEO. As suggested in previous studies, an increase in the azimuthal electric field (i.e., enhanced earthward magnetic flux transport) is most likely required for an ∼100 keV ion flux increase at GEO.

EHD instability of two rigid rotating dielectric columns in porous media

The present work analyses the linear azimuthal stability of a single interface between two cylindrical dielectric fluids. The theoretical model consists of two incompressible rotating electrified fluids throughout the porous media. The system is influenced by a uniform azimuthal electric field. The inner cylinder is filled with a viscous liquid. The outer one is occupied by an inviscid gas. The problem meets its motivation from a geophysics point of view. Therefore, for more convenience, the problem is considered in a planar configuration. Typically, the normal mode analysis is used to facilitate the stability approach. The examination resulted in a stream function, which is governed by a fourth-order ordinary differential equation with complicated variable coefficients. By means of the Mathematica software along with the special functions, the distribution of the stream function is written in terms of the modified Bessel functions. A non-dimensional procedure exposes some non-dimensional numbers, for instance, Weber, Ohnesorg, Taylor, Rossby and Darcy numbers. These numbers are considered with regard to the temporal and spatial increase of both frequency and modulation. The linear stability theory generated a very complicated transcendental dispersion equation. The influences of various physical parameters in the stability profile were studied as well.

Trajectory Analysis in a Collector with Multistage Energy Recovery for a DEMO Prototype Gyrotron. Part I. Idealized Magnetic Field Distribution

This paper presents the results of simulation of the collector of a prototype gyrotron designed for the DEMO project. Trajectory analysis in a collector with four-stage recovery of the residual beam energy based on the method of spatial separation of electrons in crossed azimuthal magnetic and axial electric fields was carried out. In this part of the research, the azimuthal magnetic field was formed using a conductor located on the axis of the device. The study was carried out for a spent electron beam with a particle velocity and coordinate distribution close to those obtained in experiments with high-power gyrotrons. As a result of optimizing the geometry and potentials of the collector sections, an overall efficiency of the gyrotron higher than 80% was achieved, which is close to the maximum efficiency with ideal separation of electron beam fractions with different energies. The data obtained will be used to design a toroidal solenoid for creating an azimuthal magnetic field.

Radiation of Chiral Gold Nanotubes under the Influence of Alternating Electric Current

In chiral gold nanotubes, alternating electric current generates an electromagnetic field; under these conditions, the nanotubes become emitting solenoid nanoantennas. With the use of the Maxwell equations and taking into account the geometry of nanotubes, their band structure, and the ballistic model of electron transfer, we have calculated the alternating axial magnetic and azimuthal electric fields generated by helical currents in chiral gold nanotubes. The calculations demonstrate that large alternating magnetic and electric fields can be generated in nanoscale volumes of gold nanotubes and that the eigenfrequencies of the field components are in the X-ray range.