Dc Limit Research Articles

Scalar-based finite element modelling of 3D eddy currents in thin moving conducting sheets

A number of electromagnetic devices contain geometries which prove to be challenging when modelled using finite elements. One type of complexity may be a physical dimension which is significantly smaller than the others. For example, a design of maglev coil-track systems may involve the use of relatively thin track sheets of finite widths and extensive lengths. A new set of formulations is presented for the 3D eddy current finite element analysis of thin moving conducting sheets. The conducting sheet, moving at a constant linear velocity in the direction of the sheet plane, is modelled using two scalar quantities, T and the normal component of the magnetic flux density. The second scalar, B/spl middot/n, is introduced to maintain a second order partial differential equation system. Scalar potentials are used to model the nonconducting regions. This scheme, implemented for time-harmonic cases, is compared with the more usual A-/spl psi/ method using a computer model, and force predictions agree favourably. In the DC limit, it is possible to eliminate the T variable, thereby retaining only the B/spl middot/n scalar in the sheet description. Two experimental test problems serve to illustrate drag and lift force predictions obtained using the two new schemes, T-B/spl middot/n-/spl psi/ and B/spl middot/n-/spl psi/, and the more usual moving A-/spl psi/ formulation.

Correlation length and time in the vortex-glass critical regime in YBa 2Cu 3O 7−x films

We report on the complex conductivity of a YBa 2Cu 3O 7−x microbridge in the presence of magnetic field 0.5 ≤B≤6.5 T applied parallel to the c-axis. A broad range of frequences 10 ≤ f ≤ 2 × 10 6 Hz for the transport current passing through the bridge allows us to explore the ac dynamical response of the vortices where conflicting results have been reported, in addition to the static characteristics of the vortex system ( dc limit). In consistency with the concept of a correlation length and a correlation time that diverge at the transition temperature T g(B), we demostrate that a single value for T g(B) can be identified in both the static and dynamical measurements, within an experimental uncertainty of 1 K. In conflict to previous reports, the real and imaginary components of the ac-linear voltage at T=T g (B) were found to follow the same power law V i ∝ V o ∝ f α, with α=0.82±0.05. Finally, as T→T g +, the critical scaling laws break down when the diverging vortex correlation length matches the film thickness of our sample and the correlation time exceeds 10 μs.

Direct measurement of partial ionic conductivity of Co 1−δO via impedence spectroscopy combined with dc relaxation

For an electron-blocking cell ZrO 2(+8m/0Y 2O 3)/Co 1−δO/ZrO 2(+8m/0Y 2O 3), a full impedance spectrum has been comstructed for a wide frequency range comprising diffusion, electrode and bulk by combining impedance data directly measured using a commercial impedance analyzer and the Fourier-Laplace transform of the dc relaxation into the frequency domain which carries the (ionic) information in the low frequency range including the dc limit. The ionic conductivity of Co 1−δO was then extracted from the finite length Warbung impedance at the low end of the full impedance spectrum, which was in a good agreement with the literature. Disturbing artifacts associated with gas/solid reactions and the limitation of the method are discussed.

Dynamical conductivity of a two-layered structure with electron-acoustic phonon coupling

The frequency-dependent conductivity (resistivity) of two isolated parallel electron layers is calculated. The authors take into account both the direct electron-electron interaction and the coupling between electrons through phonon exchange. It is found that the interlayer momentum relaxation due to the direct Coulomb interaction and the phonon exchange interaction has the same dependence on the layer separation. The results for the conductivity rests on the Kubo formula for conductivity and the Green function formalism. The numerical results for the temperature dependence of sigma 12 in the DC limit is presented. Furthermore, they have calculated the frequency dependence of sigma 12 in the zero-temperature limit.

Theory of laser-induced free-electron heating and impact ionization in wide-band-gap solids.

A microscopic theory for the interaction of intense laser radiation at visible and near-infrared wavelengths with free electrons in a wide-band-gap solid is presented. We calculate the free-electron mediated energy transfer from the laser field to the solid and the electron-multiplication rate due to band-to-band ionization as a function of laser intensity at wavelengths in the range 250 nm10 \ensuremath{\mu}m, using ${\mathrm{SiO}}_{2}$ as an example. The formalism is based on a Monte Carlo integration of the Boltzmann transport equation. The electron interaction with the lattice is described in terms of polar and acoustic-phonon scattering. Band-to-band impact ionization is included using an empirical, Keldysh-type impact ionization rate. The interaction of the laser radiation with the free electrons is treated both within the standard classical approximation and quantum mechanically using second-order perturbation theory. We find that the classical approach to the electron-laser field interaction is valid for \ensuremath{\lambda}>2 \ensuremath{\mu}m, while reliable results for short wavelengths, \ensuremath{\lambda}1 \ensuremath{\mu}m, can only be obtained by using the quantum approach. Second-order perturbation theory is found to fail at long wavelengths, \ensuremath{\lambda}>1 \ensuremath{\mu}m. Both methods are inaccurate for \ensuremath{\lambda}\ensuremath{\simeq}1 \ensuremath{\mu}m, yielding only upper and lower bounds for calculated quantities. For \ensuremath{\lambda}>2 \ensuremath{\mu}m the calculated quantities are found to be close to the values obtained in the dc limit, using a dc field equal to the rms value of the ac field. For \ensuremath{\lambda}1 \ensuremath{\mu}m the electron-multiplication rates decrease dramatically as wavelengths become shorter indicating that multiphoton absorption becomes the dominant mechanism for free-electron generation at visible wavelengths. At all wavelengths the theory predicts efficient free-electron mediated energy transfer from the laser field to the lattice. It is therefore possible to observe significant lattice heating caused by free electrons generated via multiphoton absorption in the prebreakdown regime. These findings are shown to be consistent with recent laser experiments [S. Jones, P. Braunlich, R. Casper, X. Shen, and P. Kelly, Opt. Eng. 28, 1039 (1989)].

Zero-temperature Hall coefficient of an insulator.

We prove that for noninteracting electrons at zero temperature, an insulator exhibits finite Hall resistivity in the dc limit. More generally, we present simple macroscopic arguments that this behavior is generic for all insulators. We therefore conclude that the zero-temperature Hall coefficient is not a measure of the number of mobile carriers.

Wigner-function formulation of nonlinear electron-hole transport in a quantum well and analysis of the linear transient and steady state.

This work is concerned with the determination of nonlinear coupled quasi-two-dimensional transport equations for the electron and hole Wigner functions of a quantum well subject to a time-dependent electric field, based upon our earlier development of a generalized shielded-potential approximation for the corresponding nonequilibrium Green's functions and the application of the generalized Kadanoff-Baym ansatz. In this work we take account of the electron-hole interaction, electron-phonon, and hole-phonon interactions, as well as treating impurity-scattering effects. Furthermore, the electron-electron and hole-hole Coulomb repulsions and associated dynamic, nonlocal screening effects are also incorporated. This formal development is applied to a linear analysis of electron-hole drag effects in a GaAs-${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ga}}_{\mathit{x}}$As quantum well, treating both the transient and steady-state regimes. We examine the electron and hole mobilities in the ballistic regime, followed in time by their overshoot phenomena and ultimately saturation. At low temperature, our computations trace out in detail the time development of negative absolute minority electron mobility for this system. In the steady-state dc limit, we find that a phonon-mediated electron-hole interaction induces a small irregularity or oscillation in the knee of the electron-mobility curve as a function of temperature at about 60 K, which nicely parallels the data of H\"opfel, Wolff, and Gossard.

Frequency-dependent response and dynamic disorder

This paper discusses selected aspects of the application of dynamic percolation models to ionic transport in mixed-ion superionic conductors. The discussion is based on an AB lattice gas model with hard-core repulsions and a ratio of τ, 0 ⩽ τ ⩽ ∞, between the transition rates of particles A and B. The frequency-dependent conductivity for a tracer particle is calculated within an effective-medium theory. The motion of the background B-particles is regarded as providing a fluctuating disordered environment for the tracer particles A. A crossover frequency separating high-frequency and low-frequency response is found which scales with τ as ω c ∼ τ 1 2 . The results for the dc limit are compared with simulations and are found to be in very good agreement.

Practical Applications of the Kramers-Kronig Relations

Abstract A technique is presented for using the Kramers-Kronig (KK) relations to evaluate the consistency of impedance data that do not exhibit a DC limit. The approach presented here differs from ...

Photodetachment-threshold shifts in two-frequency radiation fields

The one-dimensional Schrödinger equation was solved numerically to observe the effects of a strong radiation field on the photodetachment-threshold behavior of a model negative ion. The negative ion is exposed to a near-threshold single-photon detaching radiation pulse while in the presence of a second, constant-intensity, low-frequency field. As the second field frequency is increased from zero to the photodetachment threshold, we observe a gradual transition from the interference effects found for detachment into a static field (dc limit) to the increased energy required to detach an electron into a strong oscillatory field (ac limit). The detachment-threshold shift occurs because the second field drags temporarily detached low-energy electrons back across the potential, where they are reattached. This detachment, excursion, and reattachment process is quite fragile, particularly in three dimensions, and will lead to leakage detachment below the shifted threshold.

On thin‐layer telluric modeling of magnetotelluric responses

Modeling of three‐dimensional (3-D) thin‐sheet telluric anomalies has been a popular means of estimating the distortions of magnetotelluric (MT) response functions in the vicinity of an upper crustal resistivity inhomogeneity (Kaikkonen, 1986) because structures with an arbitrary 3-D shape in plan view can be simulated with modest computational effort. In the class of thin‐layer problems of this note, the sheet structure overlies an infinitely resistive basement; and anomalous fields are computed in the long‐period or zero‐frequency (dc) limit (e.g., Hermance, 1982). Under the assumption of no vertical current flow into the basement, this 3-D problem reduces to a two‐dimensional (2-D) dc solution across the sheet. Since only the long‐period limit is considered, however, the conclusions that can be drawn about the effects of general 3-D structures are restricted. The purpose of this note is to clarify restrictions on the use of 2-D MT interpretations in 3-D areas based on just thin‐sheet telluric modeling.

Reply by the authors to R. S. Smith

We appreciate the interest Richard Smith has shown in our paper and welcome the opportunity to respond. The main thrust of Smith’s comments is aimed at our choice of using a dc limit in the Cole‐Cole impedance model. Unlike the high‐frequency limit, the dc limit is not affected by the inductive limit of the conductor and so is by far the most logical choice. Any inherent increase in the TEM response at early time, because of the decrease in resistivity to [Formula: see text], is part of the IP effect and should not be discounted as mathematically spurious.

Response by Richard Smith to the authors’ reply

I would like to thank Marcus Flis and Gregory Newman for acknowledging that that there is more than one way of decomposing the total current into polarization and fundamental (EM) parts, although they have failed to establish that the Flis et al. (1989) decomposition is preferable to that previously suggested by Smith et al. (1988). The choice of a dc limit in the Cole‐Cole impedance model was not my main criticism; work cited as confirming the Smith et al. decomposition uses the dc limit also (Smith and West, 1988).

Threshold shifts in strong radiation fields: The connection between dc and ac effects.

We have studied near-threshold single-photon detachment of a model negative ion, in the presence of a second, intense radiation field. We find a simple, continuous connection between detachment in strong static fields (dc limit) and the increased energy needed to detach an electron into an intense optical field (ac limit). Below this shifted threshold energy, net detachment is suppressed because parent systems reabsorb electrons that have been temporarily emitted. This fragile emission-absorption process is easily upset, leading to leakage detachment below the shifted threshold.

Possible quantumelectrochemical effects on high Tc superconductors

Low-temperature electrochemical measurements were carried out on interfaces between different polycrystalline high T c superconductors (YBa 2Cu 3O 7−δ with 0 ⩽ δ ⩽ 0.5, YBa 2Cu 3(1 − x) Zn 3 x O 7−δ with 0 ⩽ x ⩽ 0.06, Tl 2Ba 2CaCu 2O 8, Tl 2Ba 2Ca 2Cu 3O 10) and Ag β″-alumina as a solid electrolyte. By using a special transient routine, cell currents were measured vs. time at a constant potential. From the dc limits of the transients, a small increase of the current is observed around T c which can not simply be explained by a specific property of the solid electrolyte. This effect must rather be correlated to the superconducting state of the HTSC and the formation of Cooper pairs changing the electrochemical double layer structure and possibly penetrating the energy barrier at the interface HTSC-solid electrolyte. The results are interpreted by quantumelectrochemical effects, ie either by an enhancement of the electrode kinetics or by a proximity effect.

Generalized Master Equations and Boltzmann-like transport in solids

Solution of the linearized Generalized Master Equations and that of the linearized Boltzmann equation are compared in the vicinity of the dc limit. In addition to straightforward higher-order corrections, the former solution is shown to differ from the latter by an additional term which is made explicit for the dc conductivity to the lowest order in coupling to static random short-range impurities. Numerical estimate shows that this term (proportional to the first power of impurity concentration) may become non-negligible in realistic situations.

Concerning the use of the Kramers-Kronig transforms for the validation of impedance data

The application of the Kramers-Kronig transforms to a number of typical corrosion systems has shown that severe problems exist with their use for validation of experimental impedance data. Even for theoretical data no agreement with the transforms is observed if the impedance data have not reached their dc limit within the frequency range used for the transform.

Generalized master equations and the phonon-assisted hopping

Time-convulution as well as time-convolutionless Generalized Master Equations are solved for the dc phonon-assisted hopping conductivity in disordered semiconductors, avoiding usual unphysical expansions in powers of the electron-phonon coupling before performing the dc limit. The explicit result obtained contradicts that of the lowest-order standard markovian rate equations but agrees to that based on rigorous methods avoiding approximate kinetic equations. Very good correspondence with experiment is discussed. With the above mentioned expansions, standard markovian-rate-equation results leading to the Miller and Abrahams network are reproduced.

Grain shape effects on dielectric and electrical properties of rocks

Recently there has been a considerable interest in the effect of anisotropy in the grain shape in the electrical and dielectrical properties of rocks and other inhomogeneous media (Sen 1981a, b; Sen et al, 1981; Mendelson and Cohen, 1982; and Kenyon, 1983). In this note I point out that equation (34) of Mendelson and Cohen (MC) is incorrect. The dc limit of MC equation (34) for the conductivity of rock σ, in terms of porosity ϕ and water conductivity [Formula: see text], gives [Formula: see text] or [Formula: see text] where [Formula: see text] L is the depolarization factor along the principal axis of spheroidal grain and 〈 〉 denotes an average over the distribution in L. This value of [Formula: see text] is in disagreement with the correct value of m in equation (28) of MC [equation (6) below]. [When the sign mistakes in equations MC (33)–(34) are corrected, [Formula: see text]. This agrees with equation (6) below for the case when L has a single value and averaging is redundant.] This inconsistency arises from an incorrect replacement of the inverse of an average in MC equation (33) by an average of inverses. The corrected form of MC equation (33) is [Formula: see text] where ε and [Formula: see text] are the dielectric constants of the mixture and of the matrix, respectively. The dielectric constant [Formula: see text] is complex, [Formula: see text] is real, [Formula: see text] is the permittivity of vacuum, σ the conductivity, ω the angular frequency. The last factor in the right‐hand side of the equation was replaced incorrectly by the average of the inverse, which is incorrect in general. Note that in the dc limit equation (4) above gives [Formula: see text] and, by integration, [Formula: see text] where [Formula: see text] is the dc conductivity of water, σ(0) is the dc conductivity of formation, and [Formula: see text]

Spin-fluctuation contribution to the high-frequency electrical conductivity of nearly magnetic transition metals

The high-frequency limit of the electrical conductivity of nonmagnetic transition metals is calculated. The conduction electrons are assumed to be scattered by the spin fluctuations in the partially filled $d$ bands. The frequency-dependent conductivity has a Drude-type form, in which the scattering rate is itself frequency dependent. The scattering rate is increased as the magnetic susceptibility is enhanced by the spin fluctuations. The scattering rate exhibits a complicated frequency and temperature dependence. However, in the dc limit it does follow the low-temperature ${T}^{2}$ law of electron-electron collisions followed at higher temperatures by a linear dependence on $T$. On the other hand, at $T=0$, the scattering rate is proportional to ${\ensuremath{\omega}}^{2}$ for low frequency.