Electric Field Boundary Conditions Research Articles

Auroral ionospheric F region density cavity formation and evolution: MICA campaign results

Auroral ionospheric F region density depletions observed by PFISR (Poker Flat Incoherent Scatter Radar) during the MICA (Magnetosphere‐Ionosphere Coupling in the Alfvén Resonator) sounding rocket campaign are critically examined alongside complementary numerical simulations. Particular processes of interest include cavity formation due to intense frictional heating and Pedersen drifts, evolution in the presence of structured precipitation, and refilling due to impact ionization and downflows. Our analysis uses an ionospheric fluid model which solves conservation of mass, momentum, and energy equations for all major ionospheric species. These fluid equations are coupled to an electrostatic current continuity equation to self‐consistently describe auroral electric fields. Energetic electron precipitation inputs for the model are specified by inverting optical data, and electric field boundary conditions are obtained from direct PFISR measurements. Thus, the model is driven in as realistic a manner as possible. Both incoherent scatter radar (ISR) data and simulations indicate that the conversion of the F region plasma to molecular ions and subsequent recombination is the dominant process contributing to the formation of the observed cavities, all of which occur in conjunction with electric fields exceeding ∼90 mV/m. Furthermore, the cavities often persist several minutes past the point when the frictional heating stops. Impact ionization and field‐aligned plasma flows modulate the cavity depth in a significant way but are of secondary importance to the molecular generation process. Informal comparisons of the ISR density and temperature fits to the model verify that the simulations reproduce most of the observed cavity features to a reasonable level of detail.

The influence of the breakdown electric field in the configuration of lightning corona sheath on charge distribution in the channel

A model of corona sheath that surrounds the thin core of the lightning channel has been investigated by using a generalized traveling current source return stroke model. The lightning channel is modeled by a charged corona sheath that stretches around a highly conductive central core through which the main current flows. The channel core with the negatively charged outer channel sheath forms a strong electric field, with an overall radial orientation. The return stroke process is modeled as the negative leader charge in the corona sheath being discharged by the positive charge coming from the channel core. Expressions that describe how the corona sheath radius evolves during the return stroke are obtained from the corona sheath model, which predicts charge motion within the sheath. The corona sheath model, set forth by Maslowski and Rakov (2006), Tausanovic et al. (2010), Marjanovic and Cvetic (2009), Cvetic et al. (2011) and Cvetic et al. (2012), divides the sheath onto three zones: zone 1 (surrounding the channel core with net positive charge), zone 2 (surrounding zone 1 with negative charge) and zone 3 (the outer zone, representing uncharged virgin air). In the present study, we have assumed a constant electric field inside zone 1, as suggested by experimental research of corona discharges in coaxial geometry conducted by Cooray (2000). The present investigation builds upon previous studies by Tausanovic et al. (2010) and Cvetic et al. (2012) in several ways. The value of the breakdown electric field has been varied for probing its effect on channel charge distribution prior and during the return stroke. With the aim of investigating initial space charge distribution along the channel, total electric field at the outer surface of the channel corona sheath, just before the return stroke, is calculated and compared for various return stroke models. A self-consistent algorithm is applied to the generalized traveling current source return stroke model, so that the boundary condition for total electric field is fulfilled. The new density of space charge and the new radius of channel corona envelope, immediately before the return stroke stage, are calculated. The obtained results indicate a strong dependence of channel charge distribution on the breakdown electric field value. Among the compared return stroke models, transmission-line-type models have exhibited a good agreement with the predictions of the Gauss' law regarding total breakdown electric field on the corona sheath's outer surface. The generalized lightning traveling current source return stroke model gives similar results if the adjustment of the space charge density inside the corona sheath is performed.

Influence of Poisson equation boundary conditions and quantum corrections to carrier concentrations at material interfaces in TCAD process simulation

AbstractIn TCAD process simulation, the Poisson equation for electrostatic potential is usually solved in silicon and polysilicon regions, assuming a zero normal component of electric field (ZEF) boundary conditions (BCs) at material interfaces. This is correct for a free (or covered only with dielectric) flat surface of silicon, which is typical for 1D SIMS profile simulations. However, it is inaccurate in other important cases, in particular, under the gate of submicron MOS transistors, where more general BCs preserving the continuity of the flux of electric displacement should be applied. In a simulation, the choice of BCs changes the electrostatic potential near material interfaces and, thereby, impacts simulated dopant distributions and transistor characteristics. We introduced such general BCs in Sentaurus Process and applied them to the 2D simulation of CMOS transistors with polysilicon or metal gate. A noticeable (but moderate) increase of simulated threshold voltage in comparison to the ZEF BCs is demonstrated. In addition, the effect of carrier concentration reduction at silicon/dielectric interfaces due to quantum‐mechanical repulsion was introduced into a continuum process simulation using the modified local‐density approximation. This changes the dopant distributions in a nanometre thin layer in semiconductors at both sides of the gate oxide, resulting in a reduced concentration of the main dopant near the interface, which is most pronounced at high dopant concentrations. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Validation of single-fluid and two-fluid magnetohydrodynamic models of the helicity injected torus spheromak experiment with the NIMROD code

We present a comparison study of 3-D pressureless resistive MHD (rMHD) and 3-D presureless two-fluid MHD models of the Helicity Injected Torus with Steady Inductive helicity injection (HIT-SI). HIT-SI is a current drive experiment that uses two geometrically asymmetric helicity injectors to generate and sustain toroidal plasmas. The comparable size of the collisionless ion skin depth di to the resistive skin depth predicates the importance of the Hall term for HIT-SI. The simulations are run with NIMROD, an initial-value, 3-D extended MHD code. The modeled plasma density and temperature are assumed uniform and constant. The helicity injectors are modeled as oscillating normal magnetic and parallel electric field boundary conditions. The simulations use parameters that closely match those of the experiment. The simulation output is compared to the formation time, plasma current, and internal and surface magnetic fields. Results of the study indicate 2fl-MHD shows quantitative agreement with the experiment while rMHD only captures the qualitative features. The validity of each model is assessed based on how accurately it reproduces the global quantities as well as the temporal and spatial dependence of the measured magnetic fields. 2fl-MHD produces the current amplification ItorIinj and formation time τf demonstrated by HIT-SI with similar internal magnetic fields. rMHD underestimates ItorIinj and exhibits much a longer τf. Biorthogonal decomposition (BD), a powerful mathematical tool for reducing large data sets, is employed to quantify how well the simulations reproduce the measured surface magnetic fields without resorting to a probe-by-probe comparison. BD shows that 2fl-MHD captures the dominant surface magnetic structures and the temporal behavior of these features better than rMHD.

On the vibration behavior of functionally graded electrorheological sandwich beams

Dynamic behavior of adaptive sandwich beams is studied, where middle layer is electro-rheological fluid (ERF) and constraining layers are functionally graded materials (FGM). Despite various research regarding FGM or ERF composite beams, few studies are carried out on functionally graded electro-rheological (FGER) beams. To do this, finite element (FE) formulation of FGER beams is developed, and the FE model is validated by comparative studies in the literature. Due to the fact that complex shear modulus of the viscoelastic core has significant role in dynamic behavior of the beam, a dependable procedure is proposed to estimate this characteristic to ensure the reliability of the FE model for predicting the dynamic behavior of FGER beams. In this process that combines experimental and computational analysis, firstly, the complex shear modulus is roughly estimated using the ASTM E756 method. Secondly, the results are updated by means of particle swarm optimization (PSO). The optimized FE model is then utilized to investigate the effects of FGM volume fraction index, electric field and different boundary conditions on the dynamic response of adaptive sandwich beams.

Comparison of self‐consistent simulations with observed magnetic field and ion plasma parameters in the ring current during the 10 August 2000 magnetic storm

We assess whether magnetically and electrically self‐consistent ring current simulations can account simultaneously for in situ magnetic field and ion flux measurements in the inner magnetosphere during the large 10 August 2000 storm (min Dst = −107 nT). We use the Rice Convection Model–Equilibrium (RCM‐E) and drive it with time‐dependent magnetic field, electric field, and plasma boundary conditions that are guided by empirical and assimilative models. Comparisons of the simulated and observed magnetic field from Geostationary Operational Environmental Satellites (GOES) and observed proton differential flux spectra from Los Alamos National Laboratory (LANL) satellites are made at geosynchronous orbit (GEO). Similarly, simulated and observed magnetic field and proton density and temperature are compared along the orbit of Polar (r ∼ 1.8–9 RE) for the event. The simulated and observed magnetic field components agree reasonably well at GEO and along the orbit of Polar. However, since the effects of substorm dipolarizations are not explicitly modeled, the simulation fails to reproduce observed sawtooth fluctuations in the magnetic field. Over energies from 1 to 150 keV, the RCM‐E reproduced well the ion dispersion features in the LANL 1994‐084 ion differential flux spectra over energies at GEO and proton densities and temperatures calculated from Polar proton flux measurements. Thus, the RCM‐E simulations can account simultaneously for in situ magnetic field and ion flux measurements for the 10 August 2000 storm. This demonstrates that a self‐consistent model can produce realistic features of the storm time inner magnetosphere.

Electromechanical behavior of [001]-textured Pb(Mg1/3Nb2/3)O3-PbTiO3 ceramics

[001]-textured Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ceramics were synthesized by using templated grain growth method. Significantly high [001] texture degree corresponding to 0.98 Lotgering factor was achieved at 1 vol. % BaTiO3 template. Electromechanical properties for [001]-textured PMN-PT ceramics with 1 vol. % BaTiO3 were found to be d33 = 1000 pC/N, d31 = 371 pC/N, ɛr = 2591, and tanδ = ∼0.6%. Elastoelectric composite based modeling results showed that higher volume fraction of template reduces the overall dielectric constant and thus has adverse effect on the piezoelectric response. Clamping effect was modeled by deriving the changes in free energy as a function of applied electric field and microstructural boundary condition.

Storm-time ring current: model-dependent results

Abstract. The main point of the paper is to investigate how much the modeled ring current depends on the representations of magnetic and electric fields and boundary conditions used in simulations. Two storm events, one moderate (SymH minimum of −120 nT) on 6–7 November 1997 and one intense (SymH minimum of −230 nT) on 21–22 October 1999, are modeled. A rather simple ring current model is employed, namely, the Inner Magnetosphere Particle Transport and Acceleration model (IMPTAM), in order to make the results most evident. Four different magnetic field and two electric field representations and four boundary conditions are used. We find that different combinations of the magnetic and electric field configurations and boundary conditions result in very different modeled ring current, and, therefore, the physical conclusions based on simulation results can differ significantly. A time-dependent boundary outside of 6.6 RE gives a possibility to take into account the particles in the transition region (between dipole and stretched field lines) forming partial ring current and near-Earth tail current in that region. Calculating the model SymH* by Biot-Savart's law instead of the widely used Dessler-Parker-Sckopke (DPS) relation gives larger and more realistic values, since the currents are calculated in the regions with nondipolar magnetic field. Therefore, the boundary location and the method of SymH* calculation are of key importance for ring current data-model comparisons to be correctly interpreted.

Multilayer thin-film inspection through measurements of reflection coefficients

A vibration-insensitive interferometer is described to measure the thickness, refraction index and surface profile of thin-film stack at normal incidence. By satisfying the continuous boundary conditions of electric and magnetic fields at interfaces in a multilayer film stack, the reflection coefficient phase of the thin-film stack can be distinguished from the phase of spatial path difference, thus thickness and refraction index can be extracted. The experiment results showed that the measurement precision is significantly increased after the phase analysis was added into the reflectance analysis.

Comparison of Methods to Bias Fully Depleted SOI-Based MOSFET Nanoribbon pH Sensors

The potential and electric field boundary conditions for the Gouy-Chapman model of the electrolyte diffuse layer are used to properly couple the potentials in the silicon-on-insulator-based metal-oxide-semiconductor field-effect transistor to the electrolyte. This analysis is possible because the active silicon channel is fully depleted. Both the subthreshold and linear regimes are simulated. An operation with electrolyte floating and bias applied to the substrate is compared with the other methods of biasing the sensor.

A numerical matching technique for linear resistive magnetohydrodynamics modes

A new numerical matching technique for linear stability analysis of resistive magnetohydrodynamics (MHD) modes is developed. The solution to the resistive reduced MHD equations in an inner layer with a finite width is matched onto the solution to the inertialess ideal MHD or the Newcomb equation by imposing smooth disappearance of parallel electric field in addition to the continuity of perturbed magnetic field and its spatial gradient. The boundary condition for the parallel electric field is expressed as a boundary condition of the third kind for the stream function of the perturbed velocity field. This technique can be applied for the reversed magnetic shear plasmas of their minimum safety factors being rational numbers, for which the conventional asymptotic matching technique fails. In addition, this technique resolves practical difficulties in applying the conventional asymptotic matching technique, i.e., the sensitivity of the outer-region solution on the accuracy of the local equilibrium as well as the grid arrangements, even in normal magnetic shear plasmas. Successful applications are presented not only for the eigenvalue problem but also for the initial-value problem.

The drift-diffusion interpretation of the electron current within the organic semiconductor characterized by the bulk single energy trap level

The closed solution for the internal electric field and the total charge density derived in the drift-diffusion approximation for the model of a single layer organic semiconductor structure characterized by the bulk shallow single trap-charge energy level is presented. The solutions for two examples of electric field boundary conditions are tested on room temperature current density-voltage data of the electron conducting aluminum/tris(8-hydroxyquinoline aluminum/calcium structure [W. Brütting et al., Synth. Met. 122, 99 (2001)] for which jexp∝Va3.4, within the interval of bias 0.4 V≤Va≤7. In each case investigated the apparent electron mobility determined at given bias is distributed within a given, finite interval of values. The bias dependence of the logarithm of their lower limit, i.e., their minimum values, is found to be in each case, to a good approximation, proportional to the square root of the applied electric field. On account of the bias dependence as incorporated in the minimum value of the apparent electron mobility the spatial distribution of the organic bulk electric field as well as the total charge density turn out to be bias independent. The first case investigated is based on the boundary condition of zero electric field at the electron injection interface. It is shown that for minimum valued apparent mobilities, the strong but finite accumulation of electrons close to the anode is obtained, which characterize the inverted space charge limited current (SCLC) effect. The second example refers to the internal electric field allowing for self-adjustment of its boundary values. The total electron charge density is than found typically to be of U shape, which may, depending on the parameters, peak at both or at either Alq3 boundary. It is this example in which the proper SCLC effect is consequently predicted. In each of the above two cases, the calculations predict the minimum values of the electron apparent mobility, which substantially exceed the corresponding published measurements. For this reason the effect of the drift term alone is additionally investigated. On the basis of the published empirical electron mobilities and the diffusion term revoked, it is shown that the steady state electron current density within the Al/Alq3 (97 nm)/Ca single layer organic structure may well be pictured within the drift-only interpretation of the charge carriers within the Alq3 organic characterized by the single (shallow) trap energy level. In order to arrive at this result, it is necessary that the nonzero electric field, calculated to exist at the electron injecting Alq3/Ca boundary, is to be appropriately accounted for in the computation.

Transient source current formulation for the analysis of arbitrarily shaped dielectric/conducting composite structures

In this paper, a novel time-domain integral equation (TDIE) approach is presented to analyze the transient electromagnetic response from three-dimensional dielectric/conducting composite structures. The composite bodies with different materials and conductor structures are considered as autonomous scattering objects. The scattered electromagnetic field is derived by superposition of the individual scatterers. The principal method is based on the application of electric and magnetic field boundary conditions on the surfaces of dielectric and conducting objects while considering the electric currents as unknowns. Triangular patches as well as quadrangular patches model the surfaces of the combined structure. The scattered electromagnetic fields inside and outside the combined structure depend only on the electric surface currents. This improves the post-processing time and complexity as compared with other methods using both equivalent electric and magnetic surface currents. To solve the resultant integral equations, the implicit method of moments is used. In our approach, the internal fields are independent of external currents and vice-versa, reducing the number of the matrix elements by considering them as zero.

Dynamics of domain-wall motion in ferroelectric liquid crystals in an electric field

The director reorientation in smectic liquid crystals with ferroelectric properties has been considered in the case where the interaction of liquid-crystal molecules with the surface leads to a partial unwinding of the helical structure of the liquid crystal and the reorientation occurs as a result of the domain-wall motion. The dependences of the velocity of domain-wall motion on the electric field strength, electric field variation frequency, boundary conditions, spontaneous polarization, and viscosity of the liquid crystal have been determined. It has been demonstrated that an increase in the electric field variation frequency or the polar part of the anchoring energy and the spontaneous polarization of the liquid crystal at a constant field frequency results in an increase of the velocity of domain-wall motion. As a consequence, the time of the electro-optic response of the liquid crystal in weak electric fields (from 0.4 to 2.0 V/µm) decreases by a factor of more than three.

Nuclear physics of reverse electron flow at pulsar polar caps

Protons produced in electromagnetic showers formed by the reverse-electron flux are usually the largest component of the time-averaged polar-cap open magnetic flux-line current in neutron stars with positive corotational charge density. Although the electric-field boundary conditions in the corotating frame are time-independent, instabilities on both medium and short time-scales cause the current to alternate between states in which either protons or positrons and ions form the major component. These properties are briefly discussed in relation to nulling and microstructure in radio pulsars, pair production in an outer gap, and neutron stars with high surface temperatures.

An “exact” geometric-optics approach for computing the optical properties of large absorbing particles

Based on the principles of geometric optics, the ray-tracing technique has been extensively used to compute the single-scattering properties of particles whose sizes are much larger than the wavelength of the incident wave. However, the inhomogeneity characteristics of internal waves within an absorbing particle, which stem from a complex index of refraction, have not been fully taken into consideration in the geometric ray-tracing approaches reported in the literature for computing the scattering properties of absorbing particles. In this paper, we first demonstrate that electromagnetic fields associated with an absorbing particle can be decomposed into the TE and TM modes. Subsequently, on the basis of Maxwell's equations and electromagnetic boundary conditions for the TE-mode electric field and the TM-mode magnetic field, we derive generalized Fresnel reflection and refraction coefficients, which differ from conventional formulae and do not involve complex angles. Additionally, a recurrence formulism is developed for the computation of the scattering phase matrix of an absorbing particle within the framework of the conventional geometric ray-tracing method. We further present pertinent numerical examples for the phase function and the degree of linear polarization in conjunction with light scattering by individual absorbing spheres, and discuss the deviation of the geometric optics solutions from the exact Lorenz–Mie results with respect to size parameter and complex refractive index.

Ionospheric conductivity effects on electrostatic field penetration into the ionosphere

Abstract. The classic approach to calculate the electrostatic field penetration, from the Earth's surface into the ionosphere, is to consider the following equation ∇·(σ·∇Φ)=0 where σ and Φ are the electric conductivity and the potential of the electric field, respectively. The penetration characteristics strongly depend on the conductivities of atmosphere and ionosphere. To estimate the electrostatic field penetration up to the orbital height of DEMETER satellite (about 700 km) the role of the ionosphere must be analyzed. It is done with help of a special upper boundary condition for the atmospheric electric field. In this paper, we investigate the influence of the ionospheric conductivity on the electrostatic field penetration from the Earth's surface into the ionosphere. We show that the magnitude of the ionospheric electric field penetrated from the ground is inverse proportional to the value of the ionospheric Pedersen conductance. So its typical value in day-time is about hundred times less than in night-time.

Cover Picture: phys. stat. sol. (b) 245/1

AbstractThe cover picture of the current issue shows the local enhancement of the electric field magnitude in a gap plasmon–polariton resonator. This configuration consists of three silver strips of 20 nm thickness and 65 nm, 65 nm, and 130 nm width, respectively, all being illuminated by a p‐polarized plane wave with wavelength of ∼615 nm. The enhancement is particularly strong (∼26) in a 5 nm air gap between two strips. The picture relates to the Feature Article by T. Søndergaard and S. I. Bozhevolnyi (pp. 9–19) on optical resonators based on nm‐thin submicron‐wide metal strips in which resonances and strong near fields in narrow air‐gaps are obtained by utilizing plasmonic waves and the electric field boundary conditions. Thomas Søndergaard is presently working as a post‐doc at the Department of Physics and Nanotechnology, Aalborg University, Denmark, on the project “Plasmonic nanostructures for biomolecular spectroscopy and microscopy”.

An efficient nonequilibrium Green’s function formalism combined with density functional theory approach for calculating electron transport properties of molecular devices with quasi-one-dimensional electrodes

An efficient self-consistent approach combining the nonequilibrium Green's function formalism with density functional theory is developed to calculate electron transport properties of molecular devices with quasi-one-dimensional (1D) electrodes. Two problems associated with the low dimensionality of the 1D electrodes, i.e., the nonequilibrium state and the uncertain boundary conditions for the electrostatic potential, are circumvented by introducing the reflectionless boundary conditions at the electrode-contact interfaces and the zero electric field boundary conditions at the electrode-molecule interfaces. Three prototypical systems, respectively, an ideal ballistic conductor, a high resistance tunnel junction, and a molecular device, are investigated to illustrate the accuracy and efficiency of our approach.

Crack energy density in arbitrary direction for piezoelectrics and its characteristic features in electromechanical mixed mode crack

The concepts of crack energy density (CED) and its derivatives in arbitrary direction were established for piezoelectric material and, keeping their application to mixed mode fracture in mind, the characteristic features of them as fracture parameters were investigated based on the approximate equations for CED and its derivatives. That is, CED and its derivatives in arbitrary direction are defined first and separation into their each mode contribution is made. Subsequently, path independent integral expressions of them are derived, and then using them, approximate equations of each mode contribution of CED are obtained concretely for the case where linear singular solution is known. The resulting equations are then used to investigate the effects of electric field and electrical boundary condition on CED and its derivatives. An infinite piezoelectric plane with a crack inclined with respect to the poling direction is considered as a numerical example. Mode I contribution of mechanical CED is mainly employed as a possible fracture parameter for the study and it was shown that applied electric field significantly influences on fracture parameters especially for the impermeable crack perpendicular to the poling direction. The effect of electric field has the tendency to decrease as crack inclination angle increases. It was also found that, even for the impermeable crack perpendicular to the poling direction, crack propagation could be deviated from self-similar direction under a strong negative electric field, and this fact is qualitatively consistent with an existing experimental observation. For the ideally sharp crack with no width, impermeable and Hao and Shen type boundary conditions are admissible showing qualitative agreement with experimental results, but exact boundary condition is not suitable and finally consistent with permeable boundary condition.