Haksu Moon

An Extremely Low-Profile Ferrite-Loaded Wideband VHF Antenna Design

A novel, very low-profile wideband antenna operating from 30 to 300 MHz is presented. The maximum diameter and height of this antenna is only 60.96 and 5.08 cm, respectively. This design is composed of a fat grounded metallic plate placed 5.08 cm over a ground plane. Several ferrite bars strategically placed between the plate and ground plane play a critical role in improving the low frequencies gain and pattern at high frequencies. Minimal amount of ferrite was used to keep the antennas weight below 9.07 kg. Several antenna prototypes were fabricated and tested at an outdoor range with their gain and patterns agreeing well with simulation results.

Local, Explicit, and Charge-Conserving Electromagnetic Particle-In-Cell Algorithm on Unstructured Grids

We present a charge-conserving electromagnetic particle-in-cell (EM-PIC) algorithm on unstructured grids based on a finite element (FE) time-domain methodology with explicit field update, i.e., requiring no linear solver. The proposed explicit EM-PIC algorithm attains charge conservation from first principles by representing fields, currents, and charges by differential forms of various degrees, following the methodology put forth in reference [25]. The need for a linear solver is obviated by constructing a sparse approximate inverse (SPAI) for the FE system matrix, which also preserves the locality (sparsity) of the algorithm. We analyze in detail the residual error caused by SPAI on the motions of charged particles and beam trajectories and show that this error is several orders of magnitude smaller than the inherent error caused by the spatial and temporal discretizations.

Stable evaluation of Green's functions in cylindrically stratified regions with uniaxial anisotropic layers

We present a robust algorithm for the computation of electromagnetic fields radiated by point sources (Hertzian dipoles) in cylindrically stratified media where each layer may exhibit material properties (permittivity, permeability, and conductivity) with uniaxial anisotropy. Analytical expressions are obtained based on the spectral representation of the tensor Greens function based on cylindrical Bessel and Hankel eigenfunctions, and extended for layered uniaxial media. Due to the poor scaling of these eigenfunctions for extreme arguments and/or orders, direct numerical evaluation of such expressions can produce numerical instability, i.e., underflow, overflow, and/or round-off errors under finite precision arithmetic. To circumvent these problems, we develop a numerically stable formulation through suitable rescaling of various expressions involved in the computational chain, to yield a robust algorithm for all parameter ranges. Numerical results are presented to illustrate the robustness of the formulation including cases of practical interest.

Computation of potentials from current electrodes in cylindrically stratified media

We present an efficient and robust semi-analytical formulation to compute the electric potential due to arbitrary-located point electrodes in three-dimensional cylindrically stratified media, where the radial thickness and the medium resistivity of each cylindrical layer can vary by many orders of magnitude. A basic roadblock for robust potential computations in such scenarios is the poor scaling of modified-Bessel functions used for computation of the semi-analytical solution, for extreme arguments and/or orders. To accommodate this, we construct a set of rescaled versions of modified-Bessel functions, which avoids underflows and overflows in finite precision arithmetic, and minimizes round-off errors. In addition, several extrapolation methods are applied and compared to expedite the numerical evaluation of the (otherwise slowly convergent) associated Sommerfeld-type integrals. The proposed algorithm is verified in a number of scenarios relevant to geophysical exploration, but the general formulation presented is also applicable to other problems governed by Poisson equation such as Newtonian gravity, heat flow, and potential flow in fluid mechanics, involving cylindrically stratified environments.

Trade-Offs for Unconditional Stability in the Finite-Element Time-Domain Method

We discuss basic trade-offs in the application of unconditionally-stable time-updating schemes for the finite-element time-domain solution of Maxwells equations. Particular attention is given to the case of large Courant-Friedrichs-Lewy number, where the conventional thought holds that unconditionally stable schemes provide marked advantage over conditionally stable ones.

Relativistic extension of a charge-conservative finite element solver for time-dependent Maxwell-Vlasov equations

In many problems involving particle accelerators and relativistic plasmas, the accurate modeling of relativistic particle motion is essential for accurate physical predictions. Here, we extend a charge-conserving finite element time-domain (FETD) particle-in-cell (PIC) algorithm for the time-dependent Maxwell-Vlasov equations on irregular (unstructured) meshes to the relativistic regime by implementing and comparing three particle pushers: (relativistic) Boris, Vay, and Higuera-Cary. We illustrate the application of the proposed relativistic FETD-PIC algorithm for the analysis of particle cyclotron motion at relativistic speeds, harmonic particle oscillation in the Lorentz-boosted frame, and relativistic Bernstein modes in magnetized charge-neutral (pair) plasmas.

Charge-conserving relativistic PIC algorithm on unstructured grids

We discuss the extension of an exact charge-conserving particle-in-cell (PIC) algorithm based on unstructured grids to the relativistic regime. The present PIC algorithm is based on the representation of grid-based variables such as fields, currents, and (nodal) charges as discrete differential forms of various degrees. In gather and scatter steps, Whitney functions are used as spatial interpolators from grid-based variables to kinetic variables. In the push step, Boris method is adopted to efficiently incorporate relativistic effects into the particle updates. Computational example of a plasma ball expansion and synchrotron charge acceleration are used to illustrate the proposed algorithm in the relativistic regime.

Full-wave FETD-based PIC algorithm with local explicit update

We present a full-wave, finite-element time-domain (FETD)-based electromagnetic particle-in-cell (PIC) algorithm for unstructured grids with explicit field update. Charge conservation is attained from first principles by utilizing scatter and gather steps based on the representation of fields, currents, and charges by differential forms of various degrees. A sparse approximation inverse (SPAI) is employed for the mass (Hodge) matrix so that a linear solver is obviated during time-stepping and the field update becomes explicit. Since sparsity is preserved, the field update remains local. We investigate the effect of the approximate inverse on particle motion by comparing the proposed SPAI-based PIC algorithm versus a conventional (implicit) PIC algorithm based on LU decomposition.

Full-wave EM modeling in tilted cylindrically-layered media

We propose a Transformation Optics-based (T.O) methodology to rigorously (full-wave) model interactions of electromagnetic (EM) waves with tilted cylindrical interfaces, i.e., where the (locally) cylindrical interfaces exhibit tiltin relative to each other. Antennas radiating in such tilted-layer environments arise (for example) in geophysical prospection scenarios characterized by relative deviation between the exploration borehole and invastion zone. We introduce flexibly-defined, T.O.-based annular slabs coating each vertically-oriented interface so that the fields interact with the interfaces as if the latter were in fact tilted, while satisfying the appropriate boundary conditions. Numerical results illustrate teh proposed modeling method, assessing the perturbation on the EM fields versus the relative interface tilting angle.

Efficient particle locator for unstructured-grid PIC simulations

An efficient particle locator for particle-in-cell simulations on unstructured grids is presented. It is inspired by computational efficiency when particle attributes such as position and velocity are updated during the particle push step of the simulations. It requires minimal computing resources particularly when particles travel near any nodes (vertices) of the grids. In addition, all connectivity information among grid elements is stored into the so-called intelligent mesh (i-mesh) in order to facilitate locating particles. The i-mesh is motivated by the need for instant giving of the adjacent cells. The new algorithm for the particle locator together with the i-mesh can result in efficient computation.