Definitions Of Current Density Research Articles

Comparison of three formulations for eddy-current problems in a spiral coil electromagnetic acoustic transducer

Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density (TCD). Formulations II and III are based on incomplete and complete equations for source current density (SCD), respectively. Using the weak form of finite element method (FEM), three formulations were applied in a spiral coil electromagnetic acoustic transducer (EMAT) example to solve magnetic vector potential (MVP). The input impedances calculated by Formulation III are in excellent agreement with the experimental measurements. Results show that the errors for Formulations I & II vary with coil diameter, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin & proximity effects. And the current distribution across the coil conductor also follows the same trend. It is better to choose Formulation I instead of Formulation III to solve MVP when the coil diameter is less than twice the skin depth for Formulation I is a low cost and high efficiency calculation method.

Comparison of three formulations for eddy-current and skin and proximity problems in a meander coil electromagnetic acoustic transducer

Three differential equations based on different definitions of current density are compared. Formulation I is based on an incomplete equation for total current density (TCD). Formulations II and III are based on incomplete and complete equations for source current density (SCD), respectively. Using the weak form of Finite Element Method (FEM), the three formulations were applied in a meander coil Electromagnetic Acoustic Transducer (EMAT) example to solve magnetic vector potential (MVP). The FEM results from frequency domain and time domain models are in excellent agreement with previously published works. Results show that the errors for Formulations I and II vary with coil dimensions, coil spacing, lift-off distance and external excitation frequency, for the existence of eddy-current and skin and proximity effects. And the current distribution across the coil conductors also follows the same trend. It is better to choose Formulation I instead of Formulation III to solve MVP when the coil height or width are less than twice the skin depth, due to the low cost and high efficiency of Formulation I.

First-principles calculation of current density in molecular devices

Based on the single-particle nonequilibrium Green's function (NEGF) technique coupled with the density-functional theory (DFT), we investigate the current density distribution of a molecular device Al-${\mathrm{C}}_{60}$-Al from first principles. Due to the presence of nonlocal pseudopotential, the conventional definition of current density is not suitable to describe the correct current density profile inside the molecular device. By using the new definition of current density, which includes the contribution due to the nonlocal potential, our numerical results show that the new definition of current density $\mathbf{J}(\mathbf{r})$ conserves the current. In addition, the current obtained from the current density calculated inside the molecular device equals to that calculated from the Landauer-B\uttiker formula. Finally, for the molecular device Al-${\mathrm{C}}_{60}$-Al, loop currents were found, which confirms the result obtained from the tight-binding approach.

Comparison of three formulations for eddy-current and skin effect problems

Three finite-element formulations based on different definitions of current density are compared. Formulations I and II are based on incomplete equations for total and source current densities, respectively. Formulation III is based on a complete equation for source current density. To validate the third formulation, a one-dimensional test problem is solved analytically for the magnetic field intensity. The formulations are applied to a nondestructive testing example and a three-phase bus-bar example. Results show that errors due to the use of incomplete equations for current densities increase with frequency and conductor dimensions.

Currents, kinetic energy, and molecular magnetism

Definitions of current density and kinetic energy density, for a general many-electron system in the presence of an external magnetic field, are carefully discussed and various results are established. In particular, the electronic energy expression has a purely classical interpretation in which every element of the ‘charge cloud’ behaves like a small magnet, the magnetization depending on the circulation of the induced currents.