Inhomogeneous Current Density Research Articles

2+1D modelling of a polymer electrolyte fuel cell with glassy-carbon microstructures

A computationally efficient model of a polymer electrolyte fuel cell (PEFC) is presented, based on a 2+1D FEM modelling approach. This approach is suitable to take the high aspect ratio between the in-plane and the through-plane dimensions of fuel cells into account, and to avoid expensive 3D calculations. The anode and cathode are described by 2D transport models. The coupling between the anode and cathode side is established by a nonlinear point-to-point 1D model representing the membrane electrode assembly (MEA). This 1D boundary value problem is formulated using the computer algebra software Mathematica. The approach is based on the symbolic weak form expressions of a nonlinear system of PDEs. The integrands of the tangential element stiffness matrix and the element residual vector of the coupled FEM problem are computed analytically. These integrands are converted to C code automatically. The model is applied to simulate a micro PEFC without gas diffusion layers (GDLs). The simulations reveal an inhomogeneous in-plane electric current density. Further, neutron radiography data obtained with the micro fuel cell is compared to the calculated water flux between the 1D MEA model and the 2D domains. The model is used to explain the locations where water condensation is found.

Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices

In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. To demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions is proposed and hydrodynamic equations for electron density, electric field and the complex amplitude of the Bloch oscillations are derived by singular perturbation methods. For appropriate parameter ranges, numerical solutions of these equations show stable Bloch oscillations with spatially inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short. For sufficiently low lattice temperatures, Bloch and Gunn type oscillations mediated by electric field, current and energy domains coexist for a range of voltages. For larger lattice temperatures (300 K), there are only Bloch oscillations with stationary amplitude and electric field profiles.

Design and FEM Analysis of a New Distributed Vernier Traveling Wave Induction Heater for Heating Moving Thin Strips

A new traveling wave induction heating system with distributed windings and vernier structure (DV-TWIH) is proposed. That system is specially designed to address the inhomogeneous eddy current density problem that dominates the pattern of thermal distribution on the surface of work. The typical traveling wave induction heating (TWIH) system is replaced by double-layer vernier combined ones, which enables the magnetic fluxes generated by each phase to interact and complement each other to compensate for local weak magnetic fluxes in order to generate more uniform and concentrated eddy current density and temperature distribution in the work piece. In order to study the performance of the proposed DV-TWIH system, an interpolative FEA modeling method is introduced in this paper. Calculation results of the proposed systems are compared to those of typical TWIH and the traveling wave induction heating system with distributed windings but without vernier structure (D-TWIH) devices. Analytical analysis shows the attractive performance of the proposed system.

Magnetotransport in nanostructures: The role of inhomogeneous currents

In the study of electronic transport in nanostructures, electric current is commonly considered homogeneous along the sample. We use a method to calculate the magnetoresistance of magnetic nanostructures where the current density may vary in space. The current distribution is numerically calculated by combining micromagnetic simulations with an associated resistor network and by solving the latter with a relaxation method. As an example, we consider a Permalloy disk exhibiting a vortex-like magnetization profile. We find that the current density is inhomogeneous along the disk, and that during the core magnetization reversal it is concentrated toward the center of the vortex and is repelled by the antivortex. We then consider the effects of the inhomogeneous current density on spin-torque transfer. The numerical value of the critical current density necessary to produce a vortex core reversal is smaller than the one that does not take the inhomogeneity into account.

An advanced double-layer combined windings transverse flux system for thin strip induction heating

A novel double-layer (DL) combined windings transverse flux induction heating (TFIH) system is used to address the inhomogeneous eddy current density problem which dominates the thermal distribution on the surface of work strips. The single-phase winding of a typical TFIH system is replaced by a double-layer combined one, which enables the magnetic fluxes generated by each phase to interact and complement each other to compensate for the weak magnetic areas that otherwise would generate more uniform and concentrated eddy current density and temperature distribution. In order to attain the performance of the proposed DL-TFIH system, an interpolative finite element analysis modeling method is introduced in this paper. Simulation results of the proposed systems are compared with a typical TFIH device.

Inversion mechanism for the transport current in type-II superconductors

The longitudinal transport problem (the current is applied parallel to some bias magnetic field) in type-II superconductors is analyzed theoretically. Based on analytical results for simplified configurations, and relying on numerical studies for general scenarios, it is shown that a remarkable inversion of the current flow in a surface layer may be predicted under a wide set of experimental conditions. Strongly inhomogeneous current density profiles, characterized by enhanced transport toward the center and reduced, or even negative, values at the periphery of the conductor, are expected when the physical mechanisms of flux depinning and consumption (via line cutting) are recalled. A number of striking collateral effects, such as local and global paramagnetic behavior, are predicted. Our geometrical description of the macroscopic material laws allows a pictorial interpretation of the physical phenomena underlying the transport backflow.

Study on the Anode-to-Cathode Distance in an Aluminum Reduction Cell

A two-dimensional (2D) finite element model (FEM) of an anode immersed in an aluminum reduction cell was developed to study the initial current distribution in the anode as a function of anode geometry and electrical anode conductivity gradients. The numerical results of the initial state of the anode electrical current were used to describe analytically how this will affect the variation in the anode-to-cathode distance (ACD) in a steady-state scenario after several hours in the electrolysis bath. The electrical power loss in the anode has also been studied at different anode geometries and material properties. The slot positioning, slot depths, and stub hole dimensions have been considered in the FEM. The anode is implemented as an inhomogeneous orthotropic material with a defined six-parameter equation. The degree of initial inhomogeneous anode current density, which is expressed with a defined parameter k 0, can reach values to cause variations in the ACD typically measured in the aluminum industry. To avoid a variation in the ACD for this case, the defined bath conductivity relation n should be within certain limits for the analyzed industrial reduction cell. The lowest degree of initial inhomogeneous current in the anode is achieved with deeper slots closer to each other and with an electrical current entering the anode in the bottom of the anode stub hole.

Asymmetric Long Josephson Junction Acting as a Ratchet for a Quantum Field

We study the escape rate of flux quanta in a long Josephson junction having an asymmetric spatial inhomogeneous critical current density. Such a junction can behave as a ratchet when driven by an ac current in the presence of a magnetic field. This rectification gives rise to a dc voltage V(dc) across the junction. The usual approach of particlelike tunneling cannot describe this rectification, and a quantum field theory description is required. We also show that, under specific conditions, the rectification direction, and consequently V(dc), can change its sign when varying the temperature T near the crossover temperature T* between the quantum and classical regimes.

Investigation of Locally Resolved Current Density Distribution of Segmented PEM Fuel Cells to Detect Malfunctions

With the aid of PCB technology, current density distribution could be achieved by measuring the local current density inside the fuel cell, which would be more precisely reflecting the local electrochemical reaction. An important application of segmented cell technology was used for in-situ error detection of the evolution of membrane leakage. From the evolution of current density distributions, starting locations of membrane leakages and their spreading could be detected. The effect of operation conditions could be found: the steeply decreased pressure and the fast cooling of the local membrane was the main reason for the degradation of the membrane. It caused large temperature gradient in different local membranes, which resulted in inhomogeneous current density distribution and mechanical strain and stress. With the aid of segmented cell, malfunction could be detected at an early stage and thereby catastrophic failure of the whole stack may be avoided.

On the origin of horizontal counter-rotating electrolyte flow during copper magnetoelectrolysis

The understanding of electrolyte flow (convection) during metal magnetoelectrolysis can help towards a better quantitative understanding of the magnetohydrodynamic (MHD) effect. This paper summarizes numerical simulations of copper electrolysis in cuboid cells with vertical wall electrodes under the influence of homogeneous external magnetic fields. Horizontal counter-rotation in the top and bottom region is found in cuboid cells exposed to vertical magnetic fields as well as in tall cells exposed to electrode-normal magnetic fields. The main reason for this characteristic convection type induced by the Lorentz force is the vertical thickness variation of the concentration boundary layer along anode and cathode due to natural convection which results in an inhomogeneous current density distribution. Then, in both cases, the magnetic field and the corresponding normal component of the current density create a rotational Lorentz force which drives the horizontal counter-rotating flow.

Quasi-radial basis functions applied to boundary element solutions for the Grad–Shafranov equation

The Grad–Shafranov equation for axisymmetric fusion plasma has been transformed into a boundary integral equation by expanding the inhomogeneous current density term into a set of ‘quasi’-radial basis functions (RBFs). These quasi-RBFs are derived in such a way that a particular solution for the Grad–Shafranov equation will be a simple Gaussian function. Two or three stages of eigenvalue iterations are required together with a nonlinear optimization to update the scaling factor of each quasi-RBF. It has been found that excellent accuracy of the boundary element solution can be realized with a small number of quasi-RBFs when adopting RBF-dependent scaling factors.

Electric-field control of electron interference effects in 2D semiconductor nanostructures with parabolic quantum wells

The possibility of the influence of a constant electric field on spatial reproduction effects for quantum-mechanical current density, which arise during interference of electron waves in 2D semiconductor nanostructures, is studied theoretically. It is found that, in structures comprising a narrow rectangular quantum well and a wide parabolic quantum well placed successively in the direction of propagation of an electron wave, the transverse current density distribution existing at the input of the wide quantum well is reproduced in this well with a certain accuracy in periodically repeated cross sections. The inhomogeneous current density distribution arises because of the interference of electron waves propagating in the wide quantum well simultaneously in different quantum-dimensional subbands. It is shown that it is possible to control these effects via the use of a constant electric field perpendicular to the axis of the structure in the region of the wide quantum well.

Impact of the Meissner effect on magnetic microtraps for neutral atoms near superconducting thin films

We theoretically evaluate changes in the magnetic potential arising from the magnetic field near superconducting thin films. An example of an atom chip based on a three-wire configuration has been simulated in the superconducting and the normal conducting state. Inhomogeneous current densities within the superconducting wires were calculated using an energy-minimization routine based on the London theory. The Meissner effect causes changes to both trap position and oscillation frequencies at short distances from the superconducting surface. Superconducting wires produce much shallower microtraps than normal conducting wires. The results presented in this paper demonstrate the importance of taking the Meissner effect into account when designing and carrying out experiments on magnetically trapped neutral atoms near superconducting surfaces.

Investigation of Locally Resolved SOFC with Respect to Flow Configuration and Gas Composition

In this contribution the usefulness of spatially resolved measurements for the optimization of operating strategies for SOFC is demonstrated. First the influence of the flow configuration on power density and temperature is discussed. Increasing fuel utilization results in an inhomogeneous gas and current density distribution. The investigation of the locally resolved gas composition is important for the understanding of critical operating conditions, their avoidance and for elucidating degradation effects. It is found that a counter flow configuration has a more homogeneous temperature dependence compared to a co-flow arrangement. With reformate operation carbon deposition may occur at low water levels which might endanger long-term operation.

Formation of an ion beam in an elementary cell with inhomogeneous emission current density

A well-known Pierce solution that allows focusing a beam of charged particles using properly shaped electrodes outside the beam aperture is generalized to the case of an accelerating system with inhomogeneous emission current density. It is shown that the defocusing effect of the space charge can, in principle, be evenly compensated over the entire cross section of the beam. In contrast to the beam with a uniform emission current density, both the electric potential and the transverse electric field must be controlled along the beam boundary in order to eliminate the angular divergence. However, eliminating the angular spread evenly across the beam constitutes a mathematically ill-posed problem which needs to be solved with the use of one or another method of regularization. An alternative way of diminishing beam emittance is proposed for the beam where the emission current is uniform across the entire aperture except for a narrow beam edge layer and a simple formula for the Pierce electrodes is derived. Numerical simulation has proved the reasonable accuracy of our analytical theory.

An Impact of a Low Voltage Steady Electrical Current on the Solidification of a Binary Metal Alloy: A Numerical Study

This paper numerically studies the influence of a low voltage direct electrical current (LVDC) on the macroscale fluid, heat and mass transfer phenomena during unidirectional solidification of a binary metal alloy, Sn15wt%Pb. The numerical results show that in the case of an inhomogeneous electrical current density an electromagnetic Lorentz force (Pinch force) appears. This Pinch force induces a fluid flow in the melt responsible for the macrosegregation in the solidified alloy. Furthermore, an upper bound for the electric potential above which the Joule heating becomes significant was obtained analytically and confirmed numerically.

Magnetization, Magnetotransport and Ferromagnetic Resonance in A Permalloy Antidot Array with Square Holes

ABSTRACTA Permalloy antidot array with square hole size 800?800 nm2 has been fabricated by the means of electron-beam lithography and lift-off techniques. An out-of-plane anisotropy was found in both the reference film of Permalloy and the antidot array with the thickness of 100 nm. Inhomogeneous current-density distribution and complex domain structures in the antidot nanostructure result in unique behavior of the magnetoresistance. Quantized standing spin-wave modes originating from the lateral confinement of the antidot nanostructure were clearly observed for the magnetic field applied normal to the array plane. Two uniform precession resonance modes occurred when the field deviated more than 30 degrees from the normal to the plane. These two resonances originate from different regions of the array having distinct dipolar field patterns with different orientation and magnitude of magnetostatic field. The easy axes of the anisotropy in these regions are in-plane and orthogonal to each other.

Plasma localization in an extended hollow cathode of the plasma source of a ribbon electron beam

The plasma density distributions in the slit aperture of the extended rectangular hollow cathode of the source of a ribbon electron beam are investigated experimentally. It is found that a local maximum whose parameters are determined by the discharge current appears in the density distribution when the slot width is less than a certain threshold value. This maximum results in an inhomogeneous current density distribution in the beam. It is shown that the appearance of the local maximum in the plasma density is related to the overlapping of the ion sheaths in the slit aperture of the hollow cathode.

Modeling Lateral Parasitic Transistors in Smart Power ICs

Negative voltages in power stages of junction-isolated Smart Power ICs turn on parasitic bipolar transistors and inject minority carriers into the substrate, which can affect the functionality of the chip. In order to indicate inadmissible substrate currents and to evaluate protection measures, these parasitic transistors have to be included into a postlayout simulation. A methodology has been developed for automatically generating Verilog-A models for these parasites from layout data. These models account for an inhomogeneous current flow and high electron densities in the substrate. A reasonable tradeoff between convergence behavior and accuracy of the model has been found

Calculated E-I characteristics of HTS pancakes and coils exposed to inhomogeneous magnetic fields

The upper limit of the operating current of LTS solenoids can be estimated as the coordinate of the crossing point of its load line with IC (B) line of the superconductor. For HTS coils this approach seems to underestimate the allowable operating current of the coil. A better approach is to obtain a full electric field distribution over the coil and to use it as the base for a more sophisticated coil design criteria. We developed an algorithm and a Matlab program for calculating distributions of the current density, magnetic field and electric field in HTS solenoids made of pancakes, considering the inhomogeneous current density distribution inside the anisotropic tape. I-V curves of several Bi-2223 coils are calculated and good agreeement of the calculated and measured critical currents, IC, and indexes, n, are attained. One can utilize the program in the coil design choosing his own criteria of coil's critical current, e.g., 1) The average electric field 10−4 V/m over the coil, 2) The electric field 10−4 V/m at the weak point of the coil, 3) The energy dissipation in the entire coil, 4) Distribution of local energy dissipation.