Radial Component Of Electric Field Research Articles

Erosion/re-deposition modeling in an ITER divertor-like high-density, low-temperature plasma beam

Transport of hydrocarbon impurities in a high-density (>1020 m−3), low-temperature (<2 eV) plasma beam was studied with the ERO code. The high ion density and low temperature cause strong Coulomb collisionality between plasma ions and impurity ions. The collisionality is so strong that ions typically do not complete their Larmor orbits. The high collisionality causes impurity entrainment: impurity ions quickly acquire a velocity close to the plasma flow velocity. This causes a relatively high surface impact energy: the calculated mean impact energy of CHx was 8.1 eV in a plasma with Te = 0.7 eV. Simulation results were compared to an a-C : H erosion experiment in the linear plasma generator Pilot-PSI. The large uncertainties in literature values for the sticking probability of hydrocarbon radicals are shown to cause a serious uncertainty in the calculated re-deposition pattern. In contrast, the radial electric field component perpendicular to the axial magnetic field lines did not have a major effect on the redeposition profile.

Polarization coupling of vector Bessel–Gaussian beams

We report polarization coupling of radial and azimuthal electric field components of a vector light beam as predicted by the fact that the vector Helmholtz equation is expressed as coupled differential equations in cylindrical coordinates. To clearly observe the polarization variation of a beam as it propagates, higher order transverse modes of a vector Bessel–Gaussian beam were generated by a gain distribution modulation technique, which created a narrow ring-shaped gain region in a Nd:YVO4 crystal. The polarization coupling was confirmed by the observation that the major polarization component of a vector Bessel–Gaussian beam alternates between radial and azimuthal components along with the propagation.

Radial transport in the far scrape-off layer of ASDEX Upgrade during L-mode and ELMy H-mode

The radial turbulent particle flux and the Reynolds stress in the scrape-off layer (SOL) of ASDEX Upgrade were investigated for two limited L-mode (low confinement) and one ELMy H-mode (high confinement) discharge. A fast reciprocating probe was used with a probe head containing five Langmuir probes. One of the probe pins was protruding radially above the other pins. The radial electric field component was derived from the difference of the floating potentials of the protruding pin and another pin nearby. The poloidal electric field component was derived from the difference of the floating potentials of two probes on the same poloidal meridian. In both cases, equal electron temperatures on all probe pins had to be assumed. Of the other pins one was biased to ion saturation (−70 V), whereas one was swept to record the current–voltage characteristic. A detailed statistical analysis of the plasma conditions in L- and H-modes and, more specifically, also during and in between type-I edge-localized mode (ELM) events is presented. We found evidence for similarities in the statistics of transport in L-mode, during ELM events and in between ELMs, suggesting that in all three cases the transport is undertaken by blobs and filamentary structures, respectively. During the intervals in between ELMs the blob structures appear to be relatively smaller as compared with the L-mode.

Dust particle radial confinement in a dc glow discharge

A self-consistent nonlocal model of the positive column of a dc glow discharge with dust particles is presented. Radial distributions of plasma parameters and the dust component in an axially homogeneous glow discharge are considered. The model is based on the solution of a nonlocal Boltzmann equation for the electron energy distribution function, drift-diffusion equations for ions, and the Poisson equation for a self-consistent electric field. The radial distribution of dust particle density in a dust cloud was fixed as a given steplike function or was chosen according to an equilibrium Boltzmann distribution. The balance of electron and ion production in argon ionization by an electron impact and their losses on the dust particle surface and on the discharge tube walls is taken into account. The interrelation of discharge plasma and the dust cloud is studied in a self-consistent way, and the radial distributions of the discharge plasma and dust particle parameters are obtained. It is shown that the influence of the dust cloud on the discharge plasma has a nonlocal behavior, e.g., density and charge distributions in the dust cloud substantially depend on the plasma parameters outside the dust cloud. As a result of a self-consistent evolution of plasma parameters to equilibrium steady-state conditions, ionization and recombination rates become equal to each other, electron and ion radial fluxes become equal to zero, and the radial component of electric field is expelled from the dust cloud.

Enhanced collective focusing of intense neutralized ion beam pulses in the presence of weak solenoidal magnetic fields

The design of ion drivers for warm dense matter and high energy density physics applications and heavy ion fusion involves transverse focusing and longitudinal compression of intense ion beams to a small spot size on the target. To facilitate the process, the compression occurs in a long drift section filled with a dense background plasma, which neutralizes the intense beam self-fields. Typically, the ion bunch charge is better neutralized than its current, and as a result a net self-pinching (magnetic) force is produced. The self-pinching effect is of particular practical importance, and is used in various ion driver designs in order to control the transverse beam envelope. In the present work we demonstrate that this radial self-focusing force can be significantly enhanced if a weak (B ∼ 100 G) solenoidal magnetic field is applied inside the neutralized drift section, thus allowing for substantially improved transport. It is shown that in contrast to magnetic self-pinching, the enhanced collective self-focusing has a radial electric field component and occurs as a result of the overcompensation of the beam charge by plasma electrons, whereas the beam current becomes well-neutralized. As the beam leaves the neutralizing drift section, additional transverse focusing can be applied. For instance, in the neutralized drift compression experiments (NDCX) a strong (several Tesla) final focus solenoid is used for this purpose. In the present analysis we propose that the tight final focus in the NDCX experiments may possibly be achieved by using a much weaker (few hundred Gauss) magnetic lens, provided the ion beam carries an equal amount of co-moving neutralizing electrons from the preceding drift section into the lens. In this case the enhanced focusing is provided by the collective electron dynamics strongly affected by a weak applied magnetic field.

The 2D plasma potential distribution in a HiPIMS discharge

Using an emissive probe the spatial-temporal distribution of the plasma potential Vp in a high power impulse magnetron sputtering discharge has been measured. The magnetron (with a planar circular titanium target) was operated in argon gas at a fixed pressure of 0.54 Pa, a pulse frequency of 100 Hz with a 100 µs on-time and average power of 650 W. In the early part of the voltage pulse (∼6–8 µs), Vp attains deep negative values (∼−150 V) at positions close to the target (10 mm) and above the racetrack, diminishing with distance, but never reaching ground potential, even at excursions of 80 mm. In the confined plasma region, extraordinarily high axial and radial electric field components, up to several kV m−1, are calculated from the plasma potential measurements.As the plasma develops and the discharge current reaches a maximum (at ∼40 µs), Vp is elevated everywhere in the plasma, however, still with deep negative values (down to −40 V) at positions closest to the target. From the derived electric fields and modelled (vacuum) magnetic field, the 2D distribution of E × B electron drift velocities has been determined. During the early discharge phase, a broad drift channel is predicted above the racetrack, with drift speeds up to ∼3 × 105 ms−1 centred ∼30 mm above the target racetrack. As the discharge develops, these speeds reduce by about a factor 3 and the centre of the velocity distribution moves further away from the target and inwards towards the discharge axis, resembling that observed in dc and pulsed-dc magnetron operation.

Relationship between ULF wave mode mix, equatorial electric fields, and ground magnetometer data

[1] The magnetized plasma of near-Earth space supports the shear and fast Alfven, ultralow-frequency (ULF; 1–100 mHz), magnetohydrodynamic wave modes. The fast mode may propagate across the magnetic field, spreading ULF wave energy throughout the magnetosphere, and couple with the shear Alfven mode to form field line resonances (FLRs). The FLR electric field in the magnetosphere may have sufficiently large amplitudes to energize electrons and enhance radiation belt particle diffusion rates. Ozeke et al. (2009) recently described a technique that related the observed north-south ULF magnetic component at the ground, bνg, with the radial electric field component in the equatorial plane of the magnetosphere, eνeq, via the fields in the ionosphere. In this paper we use a fully coupled ULF wave model to determine the ratio eνeq/bνg for a 5 mHz FLR formed at high latitudes. We find that Ozeke et al. (2009) underestimated the ULF wave magnetic field on the ground which varies with ionosphere Hall conductance. This difference is found to be caused by assuming a decoupled wave mode model for the ionosphere fields. Any relationship that involves ULF wavefields in the ionosphere must include the effects of ULF wave mode mixing.

Anisotropy induced wave birefringence in bounded supercritical plasma confined in a multicusp magnetic field

Laboratory observation of rotation of the polarization axis (θc∼20°–40° with respect to vacuum) of a penetrating electromagnetic wave through a bounded supercritical plasma (plasma frequency ωp&amp;gt;wave frequency ω), confined in a multicusp magnetic field is reported. Birefringence of the radial and polar wave electric field components (Er and Eθ) has been identified as the cause for the rotation, similar to a magneto-optic medium, however, with distinct differences owing to the presence of wave induced resonances. Numerical simulation results obtained by solving the Maxwell’s equations by incorporating the plasma and magnetostatic field inhomogeneities within a conducting boundary shows a reasonable agreement with the experimental results.

A Probe Head for Simultaneous Measurements of Electrostatic and Magnetic Fluctuations in ASDEX Upgrade Edge Plasma

AbstractFor ASDEX Upgrade (AUG) a new probe head was developed for simultaneous measurements of electric and magnetic fluctuations in the edge plasma region. The probe head consists of a cylindrical graphite case. On the front side six graphite pins are mounted. With this arrangement the poloidal and radial electric field components, the ion saturation current and the current‐voltage characteristic can be registered simultaneously. Inside the graphite case a magnetic sensor is mounted by which the three components of magnetic field fluctuations are measured. During the AUG discharges the probe head is inserted up to three times for 100 ms each by the midplane manipulator into the scrape‐off layer (© 2010 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Equilibrium charge density on a thin curved wire

We address the electrostatic problem of a thin, curved, and cylindrical conductor (a conducting filament) and show that the corresponding linear charge density slowly tends to uniformity as the inverse of the logarithm of a characteristic parameter, which is the ratio of the diameter to the smaller of the length and minimum radius of curvature of the filament. An alternative derivation of this result based on energy minimization is given. These results follow from a general asymptotic analysis of the electric field components and potential near a charged filament in the limit of vanishing diameter. It is found that the divergent parts of the radial and azimuthal electric field components are determined by the local charge density, while the axial component is determined by the local dipole density. For a straight filament our results reduce to those known for conducting needles. For curved filaments, the configuration of charges and fields is no longer azimuthally symmetric, and there is an additional length scale arising from the finite radius of curvature of the filament. The basic uniformity result survives the added complications, which include an azimuthal variation in the surface charge density of the filament. As with the variations in linear charge density along the filament, the azimuthal variations vanish with the characteristic parameter, only more rapidly. These findings allow us to derive an asymptotic formula for the capacitance of a curved filament that generalizes a result first obtained by Maxwell. The examples of a straight filament with uniform and linearly varying charge densities and a circular filament with a uniform charge distribution are treated analytically and found to agree with the general analysis. Numerical calculations illustrating the slow convergence of linear charge distribution to uniformity for an elliptical filament are presented. An interactive computer program implementing and animating the numerical calculations is available.

FDTD Electromagnetic Analysis of a Wind Turbine Generator Tower Struck by Lightning

Transient current distributions within the grounding systems of a wind-turbine-generator (WTG) tower struck by lightning and its neighboring WTG tower, and transient electric field inside these towers have been calculated using the finite-difference time-domain (FDTD) method. The grounding terminal for the generator inside the lightning-struck WTG tower is connected to that inside the neighboring WTG tower through a long insulated wire. About 40% of the lightning current flows in the grounding grid of the neighboring tower at 30μ s. Inside the towers, the radial component of electric field is most significant. Its peak value is about 1kV/m near the base of each tower when a lightning current having a magnitude of 30kA and a 10-to-90% risetime of 2.5μ s is injected. The electric field decreases with increasing the height of the observation point in the towers. When the grounding terminals are buried below the substructure (the grounding grids are connected via an underground insulated wire), the electric field inside the tower is significantly reduced.

An Improvement of a Thin Wire Representation for FDTD Electromagnetic and Surge Calculations

In this paper, we have shown that FDTD calculations for a conductor system having a radius smaller than 0.15Δs or larger than 0.65Δs (Δs is the lateral side length of cells employed), represented using arbitrary-radius-wire representation techniques proposed by Noda and Yokoyama, and Railton et al., with a time increment determined from the upper limit of Courant's stability condition, result in numerical instability. The reason for this numerical instability is that the speed of waves propagating outward in the radial direction from the wire in the immediate vicinity of the wire exceeds the speed of light, and therefore, Courant's condition is not satisfied there. Furthermore, we have improved the arbitrary-radius-wire representation proposed by Noda and Yokoyama. In representing a wire whose radius is smaller than the equivalent radius (r0 =0.230Δs) using the improved technique, the permeability for calculating the axial magnetic field components closest to the wire and for calculating the circulating magnetic field components closest to and half cell away from the tip of the wire is modified in addition to the permeability and the permittivity for calculating the circulating magnetic field components and the radial electric field components, closest to the wire, respectively. In representing a wire whose radius is larger than r0 using the technique, the permittivity for calculating the axial electric field components closest to the wire is modified in addition to the permittivity and the permeability for calculating the radial electric field components and the circulating magnetic field components, respectively. The improved technique is effective in representing a wire whose radius ranges from 0.0001Δs to 0.9Δs.

Phase singularities of high numerical aperture radially and azimuthally polarized beams in the focal region

The phase singularities of high numerical aperture (NA) radially and azimuthally polarized Bessel–Gaussian beams of order 1 in the focal region are studied, and the dependence of phase singularities of the radial, longitudinal and azimuthal electric field components on the truncation parameter and NA is illustrated and compared by numerical examples.

On a possible relationship between density depletions in the SAA region and storm-enhanced densities in the conjugate hemisphere

During the great magnetic storm of July 15, 2000, the ROCSAT-1 satellite with an orbital altitude of 640 km detected a large density depletion region at low latitudes (<35°) in the southern hemisphere while storm-enhanced density (SED) was observed in the northern hemisphere. Convective electric fields deduced from measurements of the ROCSAT-1 drift meters and retarding potential analyzer (RPA) indicate negligible electric fields in the eastern portion of the SED region where density enhancement was evident, suggesting a lack of ion upward motion at the equator of the SED longitudes. However, a localized electric field enhancement was observed in association with South Atlantic magnetic anomaly density structures (MADS) during the event. The zonal electric field component was eastward corresponding to radial convection, and the radial electric field component on the magnetic meridional plane was outward corresponding to westward convection. In general, both components of the observed convective electric fields were enhanced inside the density depletion region and reduced inside the density enhancement. The electric field patterns are consistent with those arising from a circular region of flux tubes with enhanced conductance in the presence of a background electric field. The mapping of the MADS region and convective electric fields from the southern hemisphere to the northern hemisphere suggests that these localized electric fields could drive ionospheric plasma from the conjugate MADS region to the SED at higher latitudes. We thus propose a new idea that the conjugate MADS region could be the plasma source for producing the SED.

Gyrokinetic Simulation of Particle and Heat Transport in the Presence of Wide Orbits and Strong Profile Variations in the Edge Plasma

A full f nonlinear 5D gyrokinetic electrostatic particle-in-cell code ELMFIRE using an implicit direct solution method for ion polarization drift and electron parallel velocity response to electric field and its validation are described. The developed code is applied for transport analysis in a tokamak plasma at steep pressure gradient. The role of turbulence and neoclassical equilibrium in determining the flux surface averaged radial electric field component are investigated, as well as the role of the latter in affecting the saturation level of the turbulence.

Simultaneous ground-based and satellite observations of Pc5 geomagnetic pulsations: A case study using multipoint measurements

Abstract Pc5 pulsations with a latitude-independent frequency of ∼2.8 mHz (period ∼6 min) were observed with ground-based magnetometers in the morning sector (0700–1000 local time) from 0730 to 0810 UT, April 29, 2001. The pulsations exhibited an amplitude peak and a ∼180° phase change at ∼67° geomagnetic latitude. A vortex structure of the equivalent ionospheric current system was also observed centered at the geomagnetic latitude between 67° and 71°. During the Pc5 event, the Polar spacecraft was located near the morningside magnetic equator and crossed magnetic field lines conjugate to the ground stations at which the pulsations were strong. Polar observed ∼2.8 mHz pulsations in the radial electric field and compressional magnetic field components. Since toroidal mode Alfvén waves in the magnetosphere are characterized by an electric field perturbation in the radial direction, the simultaneous presence of pulsations in both components indicates that a field line resonance (FLR) was driven by compressional pulsations. The ground H component at the station conjugate to Polar and the radial electric field perturbation at Polar oscillated with a great similarity without a phase delay. From an analysis of the ground-satellite data, we suggest that the ground perturbations are associated with toroidal mode Alfvén waves rather than compressional mode propagating across magnetic field lines. In addition, we discuss the source of the compressional perturbations observed at Polar using solar wind and geosynchronous data.

Axisymmetric Alfvén resonances in a multi-component plasma at finite ion gyrofrequency

Abstract. This paper deals with the spatial structure of zero azimuthal wave number ULF oscillations in a 1-D inhomogeneous multi-component plasma when a finite ion gyrofrequency is taken into account. Such oscillations may occur in the terrestrial magnetosphere as Pc1-3 waves or in the magnetosphere of the planet Mercury. The wave field was found to have a sharp peak on some magnetic surfaces, an analogy of the Alfvén (field line) resonance in one-fluid MHD theory. The resonance can only take place for waves with frequencies in the intervals ω&lt;ωch or Ω0&lt;ω&lt; ωcp, where ωch and ωcp are heavy and light ions gyrofrequencies, and Ω0 is a kind of hybrid frequency. Contrary to ordinary Alfvén resonance, the wave resonance under consideration takes place even at the zero azimuthal wave number. The radial component of the wave electric field has a pole-type singularity, while the azimuthal component is finite but has a branching point singularity on the resonance surface. The later singularity can disappear at some frequencies. In the region adjacent to the resonant surface the mode is standing across the magnetic shells.

Impact of toroidal ULF waves on the outer radiation belt electrons

Relativistic electron fluxes in the outer radiation belt exhibit highly variable complex behavior. Previous studies have established a strong correlation of electron fluxes and the inner magnetospheric ULF waves in the Pc 3–5 frequency range. Resonant interaction of ULF waves with the drift motion of radiation belt electrons violates their third adiabatic invariant and consequently leads to their radial transport. If the wave‐particle interaction has a stochastic character, then the electron transport is diffusive. The goal of this paper is to analyze the impact of toroidal ULF waves on radiation belt electrons. The study is based on direct measurements of ULF electric fields on the CRRES spacecraft. We show that the electric fields of inner magnetospheric toroidal ULF waves exhibit high asymmetry in magnetic local time and have narrow‐band frequency spectra. Such narrow‐band waves can induce radial diffusion of energetic electrons, if an extrinsic stochasticity is introduced in the system. The quasi‐periodic variations in the solar wind dynamic pressure are identified as a possible source of extrinsic stochasticity. In the asymmetric magnetic field, drifting electrons can interact with both azimuthal and radial electric field components. We derive analytically and then calculate numerically the diffusion rates associated with azimuthal and radial electric field components of the waves. It is shown that even under highly disturbed geomagnetic conditions, when the background field asymmetry is large, the diffusion rates due to the radial field component are small. At the same time, the resonant scattering of energetic electrons by the azimuthal electric field of the waves provides an efficient form of radial diffusion and therefore can play an important role in the dynamics of the outer radiation belt.

Satellite observations of electric fields in the South Atlantic anomaly region during the July 2000 magnetic storm

During the great magnetic storm of 15 July 2000 the ROCSAT‐1 low Earth‐orbiting satellite detected an unusually large region of density depletion at low latitudes (&lt;35°) in the ionosphere in corotation with the South Atlantic anomaly (SAA). Adjacent to the region of density dropout was a region of density enhancement with irregularities. We report characteristics of convective electric fields deduced from analyzing measurements of ROCSAT‐1 drift meters and a retarding potential analyzer in the region of ion density structures during the event. Specifically, the ROCSAT‐1 satellite observed penetration of large convective electric fields at apex height below 5000 km (L = 1.78) in the low‐latitude nightside ionosphere. The zonal electric field component was eastward, corresponding to outward convection, and the radial electric field component on the magnetic meridian plane was outward, corresponding to westward convection. In general, both components of the observed convective electric fields were reduced and characterized with wave structures or fluctuations with a wavelength of the order of 100 km in the density enhancement region. In the density depletion region, electric fields increased steadily as density decreased. Distinctly, the observed electric field had a peak near the apex height of the magnetic field line connected to the boundary between ion density dropout and enhancement. The magnitude of the peak electric field was largest in the beginning of the storm main phase and decayed with time. We have conducted a modeling calculation to demonstrate that energetic electron precipitation in the SAA region could increase Hall conductivities in the E region. We have theoretically examined electric field patterns for a circular region of enhanced conductivity in the ionosphere in the presence of a background electric field. Theoretically, electric fields are reduced inside the high‐conductance region but are enhanced immediately outside the conductive region with radial decay from the conductive boundary. It is interpreted that the localized electric field signatures observed by ROCSAT‐1 are produced when ionospheric conductivities are enhanced in the density enhancement region and reduced in the density depletion region. On the basis of modeling results we speculate that energetic particle precipitation might occur in the density enhancement region near the SAA during magnetic superstorms. The obtained results suggest that ionospheric density variation in the SAA region during intense magnetic disturbances might play an important role in the low‐latitude ionosphere electrodynamics.

Calculation of the surface charge on a circular type-II superconducting wire carrying transport current

A normal uniform conductor, such as a copper wire, which carries a dc or ac transport current is subject to a surface charge consisting at a given time of a constant term plus a term which varies linearly along the conductor length. For a circular type-II superconducting wire carrying an ac transport current a similar surface charge is computed (for a dc current such a surface charge is not expected unless the critical current is exceeded). In both cases the variation of surface charge along the length produces an electric field inside the wire that allows transport current to flow through the wire. Also it is shown that in a superconducting wire obeying a Bean model the electric field distribution in the wire demanded by the model results from the electric field of the surface charge canceling part of the electric field due to the time rate of change of the vector potential. The surface charge does not change previous expressions for the ac loss but it does change the electric field outside the wire. For a circular wire a radial component of electric field exists, and a measurement of this component of external electric field can be used to investigate the current distribution inside the wire. In particular, one can examine how closely the Bean model is obeyed.