Electromagnetic Diffusion Research Articles

Fractional order inductive phenomena based on the skin effect

The Maxwell equations play a fundamental role in the electromagnetic theory and lead to models useful in physics and engineering. This formalism involves integer-order differential calculus, but the electromagnetic diffusion points towards the adoption of a fractional calculus approach. This study addresses the skin effect and develops a new method for implementing fractional-order inductive elements. Two genetic algorithms are adopted, one for the system numerical evaluation and another for the parameter identification, both with good results.

3D controlled-source electromagnetic edge-based finite element modeling of conductive and permeable heterogeneities

A new 3D controlled-source electromagnetic finite element (FE) modeling algorithm is presented which is capable of handling local inhomogeneities in the magnetic permeability and electrical conductivity distribution of buried geologic and anthropogenic structures. An ungauged, coupled-potential formulation of the governing electromagnetic vector diffusion and scalar continuity equations is used. The formulation introduces magnetic reluctivity, the inverse of magnetic permeability, to facilitate a separation of secondary and primary potentials. The governing equations are solved using a tetrahedral edge-based FE method. The postprocessing steps to obtain electromagnetic fields are outlined. The code is validated for non-magnetic and permeable conductive structures by comparisons against analytic and previously published numerical solutions. Some limitations of the implementation are explored and directions are proposed for its further development.

Research on TEM Pulse Compression Technique

There is a mathematical relationship between the transient electromagnetic diffusion equation in electric media and the wave equation. Thus, pseudo-seismic migration imaging is possible. However, the pseudo-seismic wavelets associated with the transformed data show a broaden waveform for increasing physical times. This phenomenon causes the resolution of the subsurface image to degrade and consequently limit the arrears of application for the Transient Electromagnetic Method (TEM). Horizontal resolution can be improved, certainly, through the technique of synthetic aperture algorithm. We developed a TEM pulse compression technique based on previous research in order to improve the vertical resolution. The result of synthetic model shows that the vertical resolution is improved after processing the synthetic aperture data with the pulse compression technique.

Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction

We consider sparse linear systems, where a set of “interior” degrees of freedom have been eliminated in order to reduce the problem size. This elimination is assumed to be local, so the “interior” principal submatrix is block-diagonal, and the resulting Schur complement is still sparse. For it to be beneficial, the elimination process should lead to reduced memory requirements, but equally importantly, it should also result in an algebraic problem that can be solved efficiently. In this paper we propose a general element reduction approach and show how the elimination process can exploit a particular “subzonal” discretization to maintain the sparsity of the Schur complement. We also investigate algebraic multigrid (AMG) solution algorithms applied to the reduced problem, and we discuss the influence of the local elimination on solver-related properties of the matrix, such as near-nullspace preservation and the availability of stable subspace decompositions. We focus on BoomerAMG, a parallel variant of classical Ruge–Stüben AMG, applied to scalar diffusion problems [V. Henson and U. Yang, Appl. Numer. Math., 41 (2002), pp. 155–177], and the auxiliary-space Maxwell solver (AMS) for electromagnetic diffusion applications [T. Kolev and P. Vassilevski, J. Comput. Math., 27 (2009), pp. 604–623]. In the electromagnetic case, we establish algebraically a reduced version of the Hiptmair–Xu decomposition from [R. Hiptmair and J. Xu, SIAM J. Numer. Anal., 45 (2007), pp. 2483–2509] and consider a modification of the reduction process that targets the singular problems arising in simulations with pure void (zero conductivity) regions. For scalar diffusion problems, our particular stencil analysis shows that the reduction has a positive effect on meshes with stretched elements. We present a number of two-dimensional, three-dimensional, and axisymmetric numerical experiments, which demonstrate that the combination of an appropriately chosen local elimination with the use of the BoomerAMG and AMS solvers can lead to significant improvements in the overall solution time.

3D time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach

We present a finite-element time-domain (FETD) approach for the simulation of 3D electromagnetic (EM) diffusion phenomena. The finite-element algorithm efficiently simulates transient electric fields and the time derivatives of magnetic fields in general anisotropic earth media excited by multiple arbitrarily configured electric dipoles with various signal waveforms. To compute transient electromagnetic fields, the electric field diffusion equation is transformed into a system of differential equations via Galerkin’s method with homogeneous Dirichlet boundary conditions. To ensure numerical stability and an efficient time step, the system of the differential equations is discretized in time using an implicit backward Euler scheme. The resultant FETD matrix-vector equation is solved using a sparse direct solver along with a fill-in reduced ordering technique. When advancing the solution in time, the FETD algorithm adjusts the time step by examining whether or not the current step size can be doubled without unacceptably affecting the accuracy of the solution. To simulate a step-off source waveform, the 3D FETD algorithm also incorporates a 3D finite-element direct current (FEDC) algorithm that solves Poisson’s equation using a secondary potential method for a general anisotropic earth model. Examples of controlled-source FETD simulations are compared with analytic and/or 3D finite-difference time-domain solutions and are used to confirm the accuracy and efficiency of the 3D FETD algorithm.

Stability of nonlinear iteration in diffusion problems

In this paper, a one dimensional electromagnetic diffusion problem is considered in a half space filled with nonlinear hysteretic media. The material is fed with sinusoidal alternating magnetic field. For the numerical solution of the resulting second order nonlinear partial differential equation, a Finite Difference Time Domain (FDTD) method (the Yee-algorithm) combined with the material Limiting Loop Proximity Hysteresis (LLPH) characteristic is introduced. Stability problems of the numerical method is examined on the basis of the resulted attractor of the iterative map, which exhibits period-doubling bifurcations and chaotic behavior under certain parameter values. The stability analysis based on this attractor is focusing on the reasons behind the instability of the implicit inner iteration.

A Novel Split-Domain Iteration Scheme for Solution of Electromagnetic Diffusion Problems Modeled by the Hybrid Finite-Element–Boundary-Element Formulation

The hybrid finite-element (FE)-boundary-element (BE) formulation for electromagnetic diffusion problems provides some advantages in modeling including the following: 1) no truncation error; 2) ease of model generation; and 3) ease in solving problems involving moving conductors. However, the resulting matrix from this formulation loses its symmetry and is not banded, unlike the FE method. This results in significantly lower convergence rates in iterative solution schemes. A novel split-domain iteration scheme was developed to reduce computation times. The new scheme splits the domain into FE and BE subdomains. Only the matrix associated with the FE subdomain is solved subject to initial guessed potentials along the interface of two subdomains. The BE equation is then used as the corrector to update the prescribed interface potentials. The iteration scheme proceeds with these newly corrected interface potentials until the solution converges within the required prescribed error tolerances. In this paper, detailed descriptions of the newly developed scheme and performance comparisons are presented with a sample railgun problem.

Optimization of electromagnetic coupling in induction heating systems excited by solenoidal and axial windings

A dimensionless analysis of eddy current distribution on massive conductors was undertaken, using configurations for two excitation sources co-axial to a cylindrical induction device: a solenoidal type, as found in most coreless furnaces, and an axial type, similar to that used in induction motors. The mathematical model is based on a one-dimension solution of the electromagnetic diffusion equation in an infinitely long cylinder utilizing the Newton shooting method. The simulated electromagnetic performance is compared for both configurations for a minimum in either the operational frequency or the size of a given induction heating system. The theoretical results show that workpieces powered by single-phase axial winding, featuring one pair of magnetic poles, release ohmic losses equivalent to the solenoidal counterpart using half of its frequency or the square root of its radius.

Multiphysics Technologies

Currently available tools can help establish a common interface for various problem solvers in different fields. By integrating these tools, researchers can start bringing together the best work in science and engineering, perhaps forging an entirely new field. The multiphysics systems available today concentrate on physics problems commonly found in industrial and commercial applications. The focus is on including classical physics, such as electromagnetic wave propagation, fluid dynamics, and thermal diffusion, but we can look forward to these environments including quantum physics. As areas such as quantum optics, low-temperature condensed fluids, and quantum computing become part of the multiphysics systems, they'll become environments that join all kinds of physics into single computational packages.

Considerable rise in the stability of combined superconductors doped by intermetallic compounds with an extremely high low-temperature specific heat

The influence of doping intermetallics based on rare-earth elements and ceramics with an extremely high low-temperature specific heat on the stability of combined NbTi superconductors against electromagnetic disturbances is studied experimentally and theoretically. The objects of investigation are standard NbTi conductors (0.85 mm in diameter) in a copper matrix that are soldered to copper wires containing high-specific-heat dopants. CeCu6, HoCu2, CeAl2, and PrB6 intermetallics (at 4.2 K, their specific heat is on average 150 times that of copper) or Cd2O2S ceramics (at 4.2 K, its specific heat is higher than that of copper by 600 times) are introduced into combined superconductor samples in the form of fine powder. The powder is placed into the copper wire either as one thick (0.6 mm in diameter) strand or as 19 thin (0.1 mm in diameter) strands. An undoped reference sample contains a solid conductor. Samples with a transport current placed in an external transverse magnetic field are subjected to longitudinal magnetic disturbances causing pulsed heating of the samples by eddy currents. The disturbance time is varied in a wide range: from 50 μs to 1.2 ms. To compare the critical energy densities of the disturbances in differently shaped samples, a mathematical technique is developed that is based on analytical solution of the equation of electromagnetic diffusion into the sample. It is found that the critical energy density of doped samples is much higher (by several times) than that of the reference sample. Upon direct cooling of the samples by liquid helium in a vertical channel (the most intense heat removal under steady-state conditions), the effect of stability improvement for the doped samples persists. Moreover, it is shown that the high-specific-heat dopants, raising the heat needed to warm the sample, restrict the heat flux into the liquid and thereby increase the energy removed by the coolant during unsteady heat transfer.

Anomalous diffusion of electromagnetic eddy currents in geological formations

Controlled‐source electromagnetic (EM) induction in some geological formations is shown here to be compactly described by an anomalous subdiffusion process. Such a process, which is not universal, is governed by a fractional diffusion equation or alternatively the convolutional form of Ohm's law. A subdiffusing eddy current vortex, or electromagnetic smoke ring, propagates in such a way that its position of median intensity overruns its position of peak intensity. This behavior is not allowed in classical diffusion but is a simple consequence of diffusion within a stationary fractal medium. A similar analysis has been applied to understand heavy‐tailed traveltime distributions that appear in certain hydrological time series. The tell‐tale signature of anomalous electromagnetic diffusion is a slope β of the magnetic zero‐crossing moveout curve that is constant with transmitter‐receiver (RX) offset and significantly different from unity. Neither lateral heterogeneity nor unixial anisotropy can generate such a constant‐slope moveout curve with an economy of model parameters. Controlled‐source EM data from two sites in Texas and one in New Mexico are used in this study to test the eddy current subdiffusion hypothesis.

An arbitrary Lagrangian–Eulerian discretization of MHD on 3D unstructured grids

We present an arbitrary Lagrangian–Eulerian (ALE) discretization of the equations of resistive magnetohydrodynamics (MHD) on unstructured hexahedral grids. The method is formulated using an operator-split approach with three distinct phases: electromagnetic diffusion, Lagrangian motion, and Eulerian advection. The resistive magnetic induction equation is discretized using a compatible mixed finite element method with a second order accurate implicit time differencing scheme which preserves the divergence-free nature of the magnetic field. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations to compute the Lagrangian motion of the conducting materials. By virtue of the compatible discretization method used, the invariants of Lagrangian MHD motion are preserved in a discrete sense. When the Lagrangian motion of the mesh causes significant distortion, that distortion is corrected with a relaxation of the mesh, followed by a second order monotonic remap of the electromagnetic state variables. The remap is equivalent to Eulerian advection of the magnetic flux density with a fictitious mesh relaxation velocity. The magnetic advection is performed using a novel variant of constrained transport (CT) that is valid for unstructured hexahedral grids with arbitrary mesh velocities. The advection method maintains the divergence-free nature of the magnetic field and is second order accurate in regions where the solution is sufficiently smooth. For regions in which the magnetic field is discontinuous (e.g. MHD shocks) the method is limited using a novel variant of algebraic flux correction (AFC) which is local extremum diminishing (LED) and divergence preserving. Finally, we verify each stage of the discretization via a set of numerical experiments.

Modeling analysis of the electromagnetic braking action on rotating solid cylinders

The electromagnetic diffusion and the electromechanical phenomena arising in a solid cylinder rotating inside a magnetic field are here analyzed. The study is developed through a time stepping Finite Element voltage-driven formulation, employing the sliding mesh technique for handling the cylinder motion. The influence on the dynamic behavior and energy dissipation of the material electric and magnetic properties, the geometrical parameters and the supply conditions is investigated considering a model problem.

Simulating radial diffusion of energetic (MeV) electrons through a model of fluctuating electric and magnetic fields

Abstract. In the present work, a test particle simulation is performed in a model of analytic Ultra Low Frequency, ULF, perturbations in the electric and magnetic fields of the Earth's magnetosphere. The goal of this work is to examine if the radial transport of energetic particles in quiet-time ULF magnetospheric perturbations of various azimuthal mode numbers can be described as a diffusive process and be approximated by theoretically derived radial diffusion coefficients. In the model realistic compressional electromagnetic field perturbations are constructed by a superposition of a large number of propagating electric and consistent magnetic pulses. The diffusion rates of the electrons under the effect of the fluctuating fields are calculated numerically through the test-particle simulation as a function of the radial coordinate L in a dipolar magnetosphere; these calculations are then compared to the symmetric, electromagnetic radial diffusion coefficients for compressional, poloidal perturbations in the Earth's magnetosphere. In the model the amplitude of the perturbation fields can be adjusted to represent realistic states of magnetospheric activity. Similarly, the azimuthal modulation of the fields can be adjusted to represent different azimuthal modes of fluctuations and the contribution to radial diffusion from each mode can be quantified. Two simulations of quiet-time magnetospheric variability are performed: in the first simulation, diffusion due to poloidal perturbations of mode number m=1 is calculated; in the second, the diffusion rates from multiple-mode (m=0 to m=8) perturbations are calculated. The numerical calculations of the diffusion coefficients derived from the particle orbits are found to agree with the corresponding theoretical estimates of the diffusion coefficient within a factor of two.

Arbitrary Lagrangian Eulerian Electromechanics in 3D

We present results from an effort to couple the equations of electromagnetic diffusion with the equations of arbitrary Lagrangian-Eulerian (ALE) hydrodynamics. The electromagnetic diffusion equations are discretized using a novel mixed finite element method coupled with a generalized Crank-Nicholson time differencing scheme. At each discrete time step, electromagnetic force and heat terms are calculated and coupled to the hydrodynamic equations in an operator split approach. We present preliminary results from a fully coupled electromechanical simulation as well as results concerning advection techniques for electromagnetic quantities.

Verification of high-order mixed finite-element solution of transient magnetic diffusion problems

We develop and present high-order mixed finite-element discretizations of the time-dependent electromagnetic diffusion equations for solving eddy-current problems on three-dimensional unstructured grids. The discretizations are based on high-order H(Grad), H(Curl), and H(Div) conforming finite-element spaces combined with an implicit and unconditionally stable generalized Crank-Nicholson time differencing method. We develop three separate electromagnetic diffusion formulations, namely the E (electric field), H(magnetic field), and the A-/spl phi/ (potential) formulations. For each formulation, we also provide a consistent procedure for computing the secondary variables J(current flux density) and B(magnetic flux density), as these fields are required for the computation of electromagnetic force and heating terms. We verify the error convergence properties of each formulation via a series of numerical experiments on canonical problems with known analytic solutions. The key result is that the different formulations are equally accurate, even for the secondary variables J and B, and hence the choice of which formulation to use depends mostly on relevance of the natural and essential boundary conditions to the problem of interest. In addition, we highlight issues with numerical verification of finite-element methods that can lead to false conclusions on the accuracy of the methods.

A Finite Difference Thermal Model of a Cylindrical Microwave Heating Applicator Using Locally Conformal Overlapping Grids: Part I-Theoretical Formulation

In this paper, we present a versatile mathematical formulation of a newly developed 3-D locally conformal Finite Difference (FD) thermal algorithm developed specifically for coupled electromagnetic (EM) and heat diffusion simulations utilizing Overlapping Grids (OGFD) in the Cartesian and cylindrical coordinate systems. The motivation for this research arises from an attempt to characterize the dominant thermal transport phenomena typically encountered during the process cycle of a high-power, microwave-assisted material processing system employing a geometrically composite cylindrical multimode heating furnace. The cylindrical FD scheme is only applied to the outer shell of the housing cavity whereas the Cartesian FD scheme is used to advance the temperature elsewhere including top and bottom walls, and most of the inner region of the cavity volume. The temperature dependency of the EM constitutive and thermo-physical parameters of the material being processed is readily accommodated into the OGFD update equations. The time increment, which satisfies the stability constraint of the explicit OGFD time-marching scheme, is derived. In a departure from prior work, the salient features of the proposed algorithm are first, the locally conformal discretization scheme accurately describes the diffusion of heat and second, significant heat-loss mechanisms usually encountered in microwave heating problems at the interfacial boundary temperature nodes have been considered. These include convection and radiation between the surface of the workload and air inside the cavity, heat convection and radiation between the inner cavity walls and interior cavity volume, and free cooling of the outermost cavity walls.

Investigation of degradation mechanisms in CICCs

The performance of cable-in-conduit conductors often does not meet the anticipation extrapolated from the data of single strands. Various mechanisms are currently discussed as potential causes of this degradation. However, their quantitative influence in real-scale conductors remains to be determined. We investigated several mechanisms such as self-field effect, joint resistance scatter, and local strand degradation (e.g., by a local strain maximum in Nb/sub 3/Sn strands), using a recently presented model for the coupled electromagnetic and thermo-hydraulic analysis of forced-flow cooled multi-strand conductors. The significance of the electromagnetic diffusion length for the current distribution processes in multi-strand conductors is emphasized.

Stable FDITD formulation for electromagnetic field diffusion in soft magnetic materials

In this paper, a stable finite difference discretization is defined for problems of electromagnetic field diffusion in nonlinear hysteretic media. More precisely, the numerical formulation consists of a Crank-Nicolson-like algorithm applied to a space-centered finite difference scheme for nonuniform point distribution. Following the von Neumann analysis, the unconditional stability of this implicit two-level/three-point scheme is established. Moreover, the good behavior of this formulation has been numerically verified for very critical soft material like ferrites and irons.

Parametric short-circuit force analysis of three-phase busbars-a fully automated finite element approach

A three-phase busbar arrangement with straight rigid conductors carrying short-circuit currents is investigated. Calculations are made assuming steady-state AC current with a peak value equal to the peak value of the short-circuit current. The electromagnetic forces are calculated by solving the electromagnetic field diffusion equation numerically, using finite elements. The results are compared with results calculated according to the IEC Standard 865/93. A large number of arrangements have been examined, covering a wide variety of cases, as used in AC indoor installations of medium and low voltage. For this purpose, the finite element procedure has been fully automated to a degree of minimal human intervention. A let-it-grow artificial neural network (ANN) has been utilized for the automatic mesh generation. The forces calculated were in all cases in excellent agreement with the IEC Standard 865/93.