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The finite-difference time-domain (FDTD) method is a widespread numerical tool for full-wave analysis of electromagnetic fields in complex media and for detailed geometries. Applications of the FDTD method cover a range of time and spatial scales, extending from subatomic to galactic lengths and from classical to quantum physics. Technology areas that benefit from the FDTD method include biomedicine — bioimaging, biophotonics, bioelectronics and biosensors; geophysics — remote sensing, communications, space weather hazards and geolocation; metamaterials — sub-wavelength focusing lenses, electromagnetic cloaks and continuously scanning leaky-wave antennas; optics — diffractive optical elements, photonic bandgap structures, photonic crystal waveguides and ring-resonator devices; plasmonics — plasmonic waveguides and antennas; and quantum applications — quantum devices and quantum radar. This Primer summarizes the main features of the FDTD method, along with key extensions that enable accurate solutions to be obtained for different research questions. Additionally, hardware considerations are discussed, plus examples of how to extract magnitude and phase data, Brillouin diagrams and scattering parameters from the output of an FDTD model. The Primer ends with a discussion of ongoing challenges and opportunities to further enhance the FDTD method for current and future applications. 

Space weather can affect the Earth over time spans of hours and days. However, time-stepping increments for FDTD models are typically on the order of a fraction of a second. This paper introduces a means of increasing the time stepping increment’s upper limit by artificially slowing down the speed of light. Numerically slowing down the speed of light is achieved by appropriately modifying the permittivity, permeability, and conductivity values in the model. Proof-of-concept results are provided to show that the method works well for homogeneous media. 

The historical record indicates the possibility of intense coronal mass ejections (CMEs). Energized particles and magnetic fields ejected by coronal mass ejections (CMEs) towards the Earth may disrupt the Earth’s magnetosphere and generate a geomagnetic storm. During a geomagnetic storm, the induced geoelectric field can drive geomagnetically-induced currents (GICs) that flow through ground-based conductors. These GICs have the potential to damage high voltage power transmission systems and cause blackouts. As part of the NSF-funded Comprehensive Hazard Analysis for Resilience to Geomagnetic Extreme Disturbances (CHARGED) project, a solar-wind-to-lithosphere numerical model of the geoelectric field is being developed. The purpose of this new tool is to drive a new generation of GIC forecasting. As a part of that work, Maxwell’s equations, finite-difference time-domain (FDTD) models of the last stage of the Sun-to-Earth propagation path is being coupled to output generated by the Block Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) magnetohydrodynamics model and the Ridley Ionosphere Model (RIM) of ionospheric dynamics. Specifically, three-dimensional (3-D) BATS-R-US and RIM-predicted ionospheric currents occurring in the lower ionosphere during and around the time of the March 17, 2015 storm are modeled in 3-D FDTD models of North America. These models start at a depth of 150 km, and they account for ionospheric currents occurring up to an altitude of 115 km. The resolution of the FDTD models is 22 km (East-West) x 11 km (North-South) x 5 km (radially), and they account for 3-D lithosphere conductivities provided by the U.S. Geological Survey. The FDTD-calculated results are compared with surface magnetic fields measured in the region by SuperMAG and INTERMAGNET magnetometers. The FDTD results are also compared with virtual magnetometer data, which calculates the perturbation of the surface magnetic field using output from the BATS-R-US magnetohydrodynamics model. Comparison plots and an analysis of the results will be provided.