Net Electric Field Research Articles

Simulated three‐dimensional branched lightning in a numerical thunderstorm model

Lightning discharges are simulated by using a stochastic dielectric breakdown model within a numerical thunderstorm model with extensive parameterizations of electrification mechanisms. The lightning model simulates the macroscopic bidirectional extension of discharges as a step‐by‐step stochastic process. Discharge channels are propagated on a uniform grid, and the direction of propagation (including diagonals) for a particular step is chosen randomly, with the probability for choosing a particular direction depending on the net electric field. After each propagation step the electric fields are recomputed via Poisson's equation to account for the effect of the conducting channel. The lightning parameterization produces realistic looking, three‐dimensional, branched lightning discharges. A variety of lightning types have been produced, including intracloud discharges, negative cloud‐to‐ground (CG) lightning, and positive CG lightning. The model simulations support the hypothesis that negative CG flashes occur only when a region of positive charge exists below the main negative charge region. Similarly, simulated positive CG flashes were found to occur only in regions of storms where the two significant charge layers closest to ground had roughly a “normal dipole” structure (i.e., positive charge above negative).

Spontaneous Ridge Formation and Its Effect on Field Emission of Heavily Si-Doped AlN

From the linear relation between the anode-sample distance and the voltage, we have accurately obtained the net electric field between the anode and the sample surface. When Si is doped heavily into AlN, ridge structures with nanometer-order sharpness form spontaneously due to the facet growth. We found that the net electric field decreased with Si-dopant density (N Si ). The highest field emission (FE) current density was 0.22 A/cm 2 . Numerical calculations show that a ridge lowers the energy barrier by about 1.5 eV, and this can explain well the ridge effect on FE.

Spontaneous Ridge Formation and Its Effect on Field Emission of Heavily Si-Doped AlN

From the linear relation between the anode–sample distance and the voltage, we have accurately obtained the net electric field between the anode and the sample surface. When Si is doped heavily into AlN, ridge structures with nanometer-order sharpness form spontaneously due to the facet growth. We found that the net electric field decreased with Si-dopant density (NSi). The highest field emission (FE) current density was 0.22 A/cm2. Numerical calculations show that a ridge lowers the energy barrier by about 1.5 eV, and this can explain well the ridge effect on FE.

Model Channel Ion Currents in NaCl-Extended Simple Point Charge Water Solution with Applied-Field Molecular Dynamics

Using periodic boundary conditions and a constant applied field, we have simulated current flow through an 8.125-Å internal diameter, rigid, atomistic channel with polar walls in a rigid membrane using explicit ions and extended simple point charge water. Channel and bath currents were computed from 10 10-ns trajectories for each of 10 different conditions of concentration and applied voltage. An electric field was applied uniformly throughout the system to all mobile atoms. On average, the resultant net electric field falls primarily across the membrane channel, as expected for two conductive baths separated by a membrane capacitance. The channel is rarely occupied by more than one ion. Current-voltage relations are concentration dependent and superlinear at high concentrations.

The close lightning electromagnetic environment: Dart‐leader electric field change versus distance

Net electric field changes due to dart leaders in triggered lightning from experiments conducted in 1997, 1998, and 1999 at the International Center for Lightning Research and Testing at Camp Blanding, Florida, are analyzed and compared with similar data obtained in 1993 at Camp Blanding and at Fort McClellan, Alabama. In 1997–1999 the fields were measured at 2–10 stations with distances from the lightning channel ranging from 10 to 621 m, while in 1993 the fields were measured at three distances, 30, 50, and 110 m, in Florida and at two distances, about 10 and 20 m, in Alabama. With a few exceptions, the 1997–1999 data indicate that the distance dependence of the leader electric field change is close to an inverse proportionality (r−1), in contrast to the 1993 data in which a somewhat weaker distance dependence was observed. The typically observed r−1 dependence is consistent with a uniform distribution of leader charge along the bottom kilometer or so of the channel.

A new nonlinear approach to the theory of E region irregularities

In the study of E region irregularities the standard procedure is to Fourier analyze the irregularities in both time and space, that is, to describe them as a superposition of plane waves. This introduces difficulties when the amplitude of the plane waves becomes large, thereby adding nonlinear terms to the original equations and forcing all the plane waves to become coupled to one another. In the present work we stay away from Fourier analysis and use the standard fluid description of the instabilities in the limit of perturbed electric fields that are strictly perpendicular to the geomagnetic field. We obtain a nonlinear generalization of the standard results whereby the diffusion‐like operator found in linear theory is now a function of the density itself. Therefore, as the structures grow, the net electric field seen by the ambient plasma inside the structures changes in time: it rotates and its amplitude decreases. Consequently, one possible saturation mechanism for the instabilities is a reduction in the net electric field inside the structures, which brings them to threshold velocity conditions. This being stated, other nonlinear saturation mechanisms remain possible if they require smaller saturation amplitudes than the present work. Either way, our work is consistent with intermittency and implies that the largest amplitude structures in the medium should be rotated away from zero flow angle conditions by a measurable amount. Finally, we show that when compared to an irregularity‐free situation, there should be a measurable reduction in the average Hall current carried by the plasma, while the average Pederseri current should not be affected.

Spectroscopy of O3 trapped in rare gas matrices. I. Theoretical model for low-lying vibrational levels

A theoretical model is elaborated which allows methods used in gas phase to be applied to calculate the vibrational energies and transition moments for low-lying levels of O3 trapped in rare gas matrices. The model used in a previous work allowed only one mode to be handled at a time. With the new approach, an overall treatment of low-lying levels is achieved. The trapping site, a single or double substitutional one is distorted to minimize the free energy of the molecule–matrix system. The molecule is considered to be submitted to the net electric field present in the site as the result of the distortion and polarization of the matrix atoms. New harmonic and anharmonic constants that lead to matrix dependent calculated energy levels and transition moments can then be determined. Besides confirmation of two trapping sites, a single (S1) and a double (S2) substitutional site in a distorted face-centered-cubic (fcc) lattice structure, two other S1 sites in argon and krypton in a distorted hexagonal-closed-packed (hcp) lattice structure are shown to be possible. A fit within experimental uncertainty is reached between observed and calculated frequencies for fundamental bands v1, v2, and v3.

Electroreflectance measurements of electric fields in ordered GaInP2

Ordered Ga0.52In0.48P alloys (GaInP2 for simplicity) grown on miscut [001] GaAs resemble monolayer superlattices with alternating Ga- and In-rich layers along either the [1̄11] or [11̄1] directions. Recent calculations suggest that, in fully ordered GaInP2, an intrinsic ordering-induced electric field of order 1600 kV/cm should exist. In partially ordered samples, as can actually be grown, the expected field is reduced to 400 kV/cm. For such a strong internal electric field, clear Franz–Keldysh Oscillations (FKOs) would be expected in an electroreflectance measurement. We report electroreflectance measurements of ordered GaInP2 layers measured at T=100 K. For all samples measured, no FKOs are observed in the absence of an additional external dc bias voltage. At the lowest bias voltages for which FKOs are seen, the internal electric field in the GaInP2 layer, determined from the FKOs, is ∼60 kV/cm along the [001] direction corresponding to ∼100 kV/cm along the ordering direction. Hence, we conclude that, at least in the organometallic vapor phase epitaxy grown samples studied here, any net macroscopic internal electric field in the GaInP2 layer is less than ∼100 kV/cm along the ordering direction.

Electron drift reversal caused by remaining holes in semiconductor superlattices due to effective-mass filtering.

Delayed photoluminescence from a GaAs cladding layer was observed in a GaAs/AlAs short-period super-lattice under high-intensity optical pulse excitation. This phenomenon is explained by a reverse transport process of electrons due to electric-field screening by remaining holes. Because of the influence of effective-mass difference in tunneling, electrons in a superlattice region can immediately be swept out, while holes are left behind. Consequently, a net electric field opposite to the applied field arises when the hole density is sufficiently high, and electrons that are pulled back and reinjected into the GaAs cladding layer recombine with remaining holes, causing the delayed photoluminescence.

Formation of osteoclast-like cells is suppressed by low frequency, low intensity electric fields.

With use of a solenoid to generate uniform time-varying electric fields, the effect of extremely low frequency electric fields on osteoclast-like cell formation stimulated by 1,25(OH)2D3 was studied in primary murine marrow culture. Recruitment of osteoclast-like cells was assessed by counting multinuclear, tartrate-resistant acid phosphatase positive cells on day 8 of culture. A solenoid was used to impose uniform time-varying electric fields on cells; sham exposures were performed with an identical solenoid with a null net electric field. During the experiments, both solenoids heated interiorly to approximately 1.5 degrees C above ambient incubator temperature. As a result of the heating, cultures in the sham solenoid formed more osteoclast-like cells than those on the incubator shelf (132 +/- 12%). For this reason, cells exposed to the sham solenoid were used for comparison with cultures exposed to the active coil. Marrow cells were plated at 1.4 x 10(6)/cm2 in square chamber dishes and exposed to 60 Hz electric fields at 9.6 muV/cm from days 1 to 8. Field exposure inhibited osteoclast-like cell recruitment by 17 +/- 3% as compared with sham exposure (p < 0.0001). Several variables, including initial cell plating density, addition of prostaglandin E2 to enhance osteoclast-like cell recruitment, and field parameters, were also assessed. In this secondary series, extremely low frequency fields inhibited osteoclast-like cell formation by 24 +/- 4% (p < 0.0001), with their inhibitory effect consistent throughout all variations in protocol. These experiments demonstrate that extremely low intensity, low frequency sinusoidal electric fields suppress the formation of osteoclast-like cells in marrow culture. The in vitro results support in vivo findings that demonstrate that electric fields inhibit the onset of osteopenia and the progression of osteonecrosis; this suggests that extremely low frequency fields may inhibit osteoclast recruitment in vivo.

Focusing of nonducted whistlers by the equatorial anomaly

Impulsive ELF/VLF electric field bursts observed by the vector electric field instrument (VEFI) on the Dynamics Explorer 2 (DE 2) satellite on almost every crossing of the geomagnetic equator in the evening hours are interpreted as originating in lightning discharges. These signals that peak in intensity near the magnetic equator are observed within 5‐20° latitude of the geomagnetic equator at altitudes of 300–500 km with amplitudes of the order of ∼ mV/m in the 512‐ to 1024‐Hz frequency band of the VEFI instrument. Whistler‐mode ELF/VLF wave propagation through a horizontally stratified ionosphere predicts strong attenuation of subionospheric signals reaching the equator at low altitudes. However, ray tracing analysis shows that the presence of the equatorial density anomaly, commonly observed in the upper ionosphere during evening hours, leads to the focusing of the wave energy from lightning near the geomagnetic equator at low altitudes, thus accounting for all observed aspects of the phenomenon. The observations presented here indicate that during certain hours in the evening, almost all the energy input from lightning discharges entering the ionosphere at &lt;30° latitude remains confined to a small region (in altitude and latitude) near the geomagnetic equator. The net wideband electric field, extrapolated from the observed electric field values in the 512‐ to 1024‐Hz band, can be ∼10 mV/m or higher. These strong electric fields generated in the ionosphere by lightning at local evening times may be important for the equatorial electrodynamics of the ionosphere.

Experimental studies of surface relief gratings on polymer Films

ABSTRACTWe report our investigation on the recording of surface relief gratings on azobenzene containing polymer films by laser beams with different polarizations. Experimental evidence shows that it is necessary to have spatial variations of both magnitude and direction of net electric field in the films to record surface relief gratings. Large surface modulation (&gt; 3500 Å) and high diffraction efficiency (about 30%) were obtained under optimized recording conditions. In addition, polarization dependent erasure of the gratings by a single laser beam has been studied.

On the assumption of the Earth's surface as a perfect conductor in atmospheric electricity

The assumption of considering the Earth's surface as a plane perfect conductor is examined. The electric field produced due to a point charge or a model thundercloud in the atmosphere and the field changes produced due to a leader in a lightning flash have been calculated if the Earth's surface, instead of a perfect conductor, is considered as a dielectric of finite dielectric constant and zero conductivity. It is shown that when the dielectric constant of the surface is &lt;10, the horizontal and vertical components of electric field may be comparable to each other at comparatively large distances from the charge. The net electric field in such a case may be inclined from the vertical by as much as 45° or even more. At different distances, the field changes caused due to the leader in a lightning flash change not only its magnitude but direction as well. Certain igneous and metamorphic rocks with low moisture contents, fine‐grained sand when it is dry or has a moisture content of &lt;1% or is at low temperatures, and ice at very low temperatures of &lt;−50°C or oriented such that its c axis is perpendicular to the direction of electric field have dielectric constant values &lt; 10 and conductivity &lt; 10−9 S/m. Therefore, for some regions, such as polar regions, high‐latitude regions covered with sea ice or dry sand, hot and dry regions covered with sand in the midst of vast deserts, and regions covered with hot and dry igneous and metamorphic rocks, the average representative values of dielectric constant and conductivity of the surface may be such that the Earth's surface at those places cannot be assumed as a perfect conductor. Consequently, the assumption of treating the Earth's surface as an insulating surface generally taken for fast field changes during a stepped leader in a lightning flash, may be extended for much slower field changes occurring even in fair weather. It needs to be mentioned, however, that thunderstorm activity is generally minimal in most of the regions mentioned above. It is proposed that instead of measuring only the vertical component of electric field, as is normally done, a measurement of the electric field vector will give a fifil description of the intensity of the electric field at some places.

Magnitude of the piezoelectric field in (111)B InyGa1−yAs strained-layer quantum wells

The relationship between the magnitude of the piezoelectric field and the degree of lattice constant mismatch is investigated via low-temperature photoluminescence measurements of the quantum-confined Stark effect for a series of (111)B Al0.15Ga0.85As-InyGa1−yAs pseudomorphic quantum well heterostructures. The experimental strain-induced electric field values agree well with theoretical calculations for indium mole fractions in the range 0.037≤y≤0.09. In addition, an anomalous saturation of the photoluminescence transition energy is observed at values of applied voltage greater than that required to nullify the piezoelectric field, despite the indication from separate electroreflectance measurements that the net electric field within the quantum well reverses polarity under similar electrical biasing conditions.

Structure and band bending at Si/GaAs(001)-(2 x 4) interfaces.

We have grown thin, epitaxial overlayers of undoped and As-doped Si on As-stabilized n- and p-type GaAs(001)-(2\ifmmode\times\else\texttimes\fi{}4) in order to investigate the influence such overlayers have on band bending in the surface depletion region. We have carried out structural, chemical, and electronic investigations of the resulting interfaces by means of x-ray photoemission spectroscopy, low-energy electron diffraction, and x-ray photoelectron diffraction. Strained, epitaxial overlayers of Si could be grown for thicknesses of up to 10\ifmmode\pm\else\textpm\fi{}1 \AA{} at a growth temperature of 400 \ifmmode^\circ\else\textdegree\fi{}C. The perpendicular lattice constant of the overlayer is estimated to be 5.32\ifmmode\pm\else\textpm\fi{}0.10 \AA{} in this coverage regime. An interface reaction between Si and Ga is observed for all coverages. Growth of undoped Si overlayers essentially conserves the band bending that exists on the free surface (\ensuremath{\sim}0.6 eV on n-type GaAs and \ensuremath{\sim}0.5 eV on p-type GaAs). However, the growth of heavily As-doped Si flattens the bands to \ensuremath{\sim}0.3 eV on n-type GaAs, but increases the band bending on p-type GaAs to \ensuremath{\sim}0.8 eV. The influences that undoped and ${\mathit{n}}^{+}$-doped Si overlayers have on the surface band bending are readily explained by a simple model in which it is recognized that (1) epitaxial Si does not unpin the Fermi level in the sense that interface states are eliminated, and (2) a decrease (increase) in the net electric field in the depletion region of n-type (p-type) GaAs is brought about by charge transfer from the ${\mathit{n}}^{+}$-doped Si epilayer to the near-surface region of the GaAs substrate.

On the assumption of the Earth's surface as a perfect conductor in atmospheric electricity

The assumption of considering the Earth's surface as a plane perfect conductor is examined. The electric field produced due to a point charge or a model thundercloud in the atmosphere and the field changes produced due to a leader in a lightning flash have been calculated if the Earth's surface, instead of a perfect conductor, is considered as a dielectric of finite dielectric constant and zero conductivity. It is shown that when the dielectric constant of the surface is <10, the horizontal and vertical components of electric field may be comparable to each other at comparatively large distances from the charge. The net electric field in such a case may be inclined from the vertical by as much as 45° or even more. At different distances, the field changes caused due to the leader in a lightning flash change not only its magnitude but direction as well. Certain igneous and metamorphic rocks with low moisture contents, fine-grained sand when it is dry or has a moisture content of <1% or is at low temperatures, and ice at very low temperatures of <−50°C or oriented such that its c axis is perpendicular to the direction of electric field have dielectric constant values < 10 and conductivity < 10−9 S/m. Therefore, for some regions, such as polar regions, high-latitude regions covered with sea ice or dry sand, hot and dry regions covered with sand in the midst of vast deserts, and regions covered with hot and dry igneous and metamorphic rocks, the average representative values of dielectric constant and conductivity of the surface may be such that the Earth's surface at those places cannot be assumed as a perfect conductor. Consequently, the assumption of treating the Earth's surface as an insulating surface generally taken for fast field changes during a stepped leader in a lightning flash, may be extended for much slower field changes occurring even in fair weather. It needs to be mentioned, however, that thunderstorm activity is generally minimal in most of the regions mentioned above. It is proposed that instead of measuring only the vertical component of electric field, as is normally done, a measurement of the electric field vector will give a fifil description of the intensity of the electric field at some places.

Turbulent acceleration of auroral electrons

It is shown that the characteristic peak in the auroral electron velocity distribution can be generated stochastically through resonant interactions with lower hybrid electrostatic turbulence. The peak itself is shown to be a direct consequence of restrictions imposed on reflection of electron velocities in the frame of reference of individual wave packets by the limitation in group velocity. A Monte‐Carlo model demonstrates how the various properties of the acceleration region are reflected in the resultant electron distribution. It is shown, in particular, that the width of the peak is governed by the amplitude of the turbulence, while the amplitude of the peak reflects the column density of wave energy. Electron distributions encountered within three auroral arcs are interpreted to yield order of magnitude estimates of the amplitude and rms electric field of lower hybrid wave packets. The velocities and frequencies of the resonant waves, the net electric field, the column density of wave energy, and the electric‐field energy density are also estimated. The results are found to be consistent with available electric‐field measurements. A general broadening of the electron distribution caused by less systematic interactions between electrons and wave packets is shown to have a negligible effect on the peak resulting from the reflection process; it does, though, lead to the creation of a characteristic high‐energy tail.

Ratio of leader to return stroke electric field change for first and subsequent lightning strokes

The ratio of leader to return stroke electric field change versus distance is presented as a function of stroke order for 218 first and subsequent strokes in 70 cloud‐to‐ground flashes which occurred near Tampa, Florida, in 1979. The measured leader to return stroke field ratio tended to be more negative as the stroke order increased, implying that the charge sources for successive strokes were, on average, progressively farther from both the observer and the ground strike point. Sixteen percent of all flashes analyzed contained at least one leader‐return stroke sequence with a negative net electric field change; that is, a ratio that is less than −1. These strokes were observed at distances from 2.5 to 11.6 km, with 56% farther than 8 km. They exhibited a strong tendency to occur late in a flash, with 89% occurring after the fourth stroke. The geometic mean initial electric field peak normalized to 100 km for strokes with a ratio less than −1 was found to be 1.1 V/m, 2.6 times lower than for all subsequent strokes in our data base.

Transient nonlinear optical properties of δ-doped asymmetric superlattices measured by picosecond electro-optic sampling

We have performed the first picosecond time-resolved measurements of the photorefractive and nonlinear absorptive properties of asymmetric GaAs doping superlattices. The lack of inversion symmetry in these structures results in a net photoinduced electric field and, therefore, photorefractive phenomena via the χ(2) of the material. Using the electro-optic sampling technique, the temporal behavior of the photorefractive, and nonlinear absorption effects are uniquely determined. We have observed peak refractive index changes of 3.8×10−4 at an energy density of 40 fJ/μm2.

Analysis of H − ion trajectories in a space-charge lens

The success of an electron, space-charge-corrected, solenoidal magnetic lens experiment encouraged the analysis of H − trajectories in a large model-corrected solenoid. With a confined distribution of low energy electrons, the solenoid magnetic flux surfaces define electric equipotential surfaces. The field contribution from trapped electrons cancel net axial electric fields. Negatively charged beam particles then experience a defocusing force which can alleviate spherical aberration. Regions of the magnetic field can be linked by individually biased potential rings to program the correcting electric field. Given a magnetic field distribution, the electric potential distribution required to numerically correct beam particle orbits can be used to determine these ring voltages.