Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method

Shahid Ahmed

• Publisher: Wiley
• Year: 2021
• ISBN:
  9781119526223
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Electromagnetism

Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method

Discover the utility of the FDTD approach to solving electromagnetic problems with this powerful new resource

Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method delivers a comprehensive overview of the generation and propagation of ultra-wideband electromagnetic pulses. The book provides a broad cross-section of studies of electromagnetic waves and their propagation in free space, dielectric media, complex media, and within guiding structures, like waveguide lines, transmission lines, and antennae.

The distinguished author offers readers a fresh new approach for analyzing electromagnetic modes for pulsed electromagnetic systems designed to improve the reader's understanding of the electromagnetic modes responsible for radiating far-fields. The book also provides a wide variety of computer programs, data analysis techniques, and visualization tools with state-of-the-art packages in MATLAB ® and Octave.

Following an introduction and clarification of basic electromagnetics and the frequency and time domain approach, the book delivers explanations of different numerical methods frequently used in computational electromagnetics and the necessity for the time domain treatment. In addition to a discussion of the Finite-difference Time-domain (FDTD) approach, readers will also enjoy:

• A thorough introduction to electromagnetic pulses (EMPs) and basic electromagnetics, including common applications of electromagnetics and EMP coupling and its effects
• An exploration of time and frequency domain analysis in electromagnetics, including Maxwell's equations and their practical implications
• A discussion of electromagnetic waves and propagation, including waves in free space, dielectric mediums, complex mediums, and guiding structures
• A treatment of computational electromagnetics, including an explanation of why we need modeling and simulations

Perfect for undergraduate and graduate students taking courses in physics and electrical and electronic engineering, Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method will also earn a place in the libraries of scientists and engineers working in electromagnetic research, RF and microwave design, and electromagnetic interference.

1
Electromagnetic Pulse

Various natural and artificial processes, such as lightning discharges and nuclear explosions, can produce a strong pulse of broad‐band electromagnetic radiation called an electromagnetic pulse (EMP). EMP has been the subject of research since World War II, as Fermi anticipated the electromagnetic effects resulting from a nuclear explosion [1]. The large electric fields in such a pulse can cause damage to electronic and control equipment. The generation of EMP during nuclear tests was first observed in the 1950s, where it sometimes resulted in instrumentation failure [2]. EMP occurring in lightning discharges, and during fast switching of high‐voltage circuits, is also known to cause damage to electrical and electronics systems. The experimental and theoretical study of different sources of EMP, and their effects on systems, is an active field of study around the world [2].

1.1 Sources of EMP

There are various natural and artificial sources of EMP. A common natural source is lightning. Artificial sources include high‐voltage fast switches, power stations and distribution systems, nuclear explosions, ultra‐wideband radar, etc. EMP generated by lightning is called lightning electromagnetic pulse (LEMP), while that due to nuclear explosions is called nuclear electromagnetic pulse (NEMP). More details are available in [3].

Figure 1.1 illustrates the basic mechanism of NEMP generation. A nuclear detonation releases a stream of energetic gamma‐ray photons. This primary gamma,

, produces Compton electrons

following a collision with free electrons available in the atmosphere. The current channel formed by the Compton electrons gives rise to a large d

, producing NEMP [1].

Figure 1.2 shows the temporal as well as spectral waveforms of LEMP and NEMP. This figure is adapted from [4]. The electromagnetic fields in a NEMP follow a double‐exponential temporal waveform given by [5]:

where

,

and

are constants that govern the amplitude, inverse of rise and fall times, respectively. The rise‐time and pulse‐width of NEMP are of the order of nanoseconds and microseconds. For LEMP, these parameters are typically microsecond and

millisecond, respectively. Both have an ultra‐wideband nature.

Figure 1.1 Schematic of basic mechanism for NEMP generation.

Figure 1.2 Temporal and spectral waveform of different kinds of EMP [4].

1.2 EMP Coupling and its Effects

We have seen that EMP from different sources covers a broad range of the electromagnetic spectrum, with frequencies ranging from a few hertz to hundreds of megahertz. This corresponds to a wide range of free‐space wavelengths. The longer wavelengths can couple to large objects such as overhead transmission lines, while small wavelengths couple to small objects such as control equipment and semiconductor devices. The coupling mechanism can be divided into two broad types, viz. “front door” and “back door” coupling. Front door coupling refers to energy that enters through the antennas of systems containing a receiver or transmitter. Back door coupling denotes energy that leaks into systems through apertures and seams in their enclosures [6].

The amount of front‐door coupling depends upon the design frequency of the antenna and is maximum around its bandwidth. Back‐door coupling through apertures and vents is maximum for wavelengths of the order of the aperture size and falls off steadily with increase in the wavelength. Figure 1.3 shows a schematic of front‐ and back‐ door coupling of EMP generated following a nuclear detonation, to electronic and electrical equipment [3]. EMP can enter the enclosure through overhead and underground transmission lines, telephone lines, windows, as well as utility ducts.

The high‐intensity transient voltages and currents induced in electrical/electronic appliances can cause damage. The damage can be either temporary or permanent, depending upon the intensity of the incident pulse and the hardness of the exposed system [3].

1.3 EMP Simulators

A number of laboratories around the world have developed EMP simulators that can produce pulses of different types, with the objective of testing the susceptibility of systems exposed to EMP [7]. These are generally driven by a high‐voltage pulsed‐power source, e.g. a Marx capacitor bank. These simulators are used in two ways. The first is for assessing the effects of EMP on systems. The second is for testing the effectiveness of shielding (“hardening”) of these systems.

Simulators can be divided into two broad categories: bounded‐wave (closed) and radiate‐wave (open). In a radiate‐wave simulator, an ultra‐wideband antenna, e.g. transverse electro‐magnetic (TEM) horn, is used to radiate the electromagnetic field. This type of EMP simulator is used when systems to be tested are spread over a wide area [8]. Bounded‐wave type simulators, with which this study is concerned, concentrate energy within the workspace of the system itself [9].

Figure 1.3 Schematic showing EMP coupling to electrical and electronics. This schematic is taken from [3].

(Source: Ghose [3]. 1984, Don White Consultants.)

A bounded‐wave EMP simulator, in its simplest form, consists of two electrically conducting triangular plates, making up a TEM structure, separated by a parallel plate region [10]. This is illustrated schematically in Figure 1.4.

The front plate, which displays a near‐constant impedance over a wide frequency range, plays a significant role in determining the EMP waveform, while the middle and rear plates serve to guide the signal [10]. The object to be tested is mounted in the bounded volume of the parallel‐plate region.

There are several variants of the geometry shown in Figure 1.4. Some simulators do not have the rear plate, while others dispense with the parallel‐plate section as well. The tapered section could also have some other shape, e.g. conical.

Figure 1.5 shows the setup of a bounded‐wave EMP simulator, details of which have been reported in Ref. [9]. Only the tapered section of the simulator is shown here – the test section consists of a parallel‐plate section, several meters in length.

Figure 1.4 Schematic of parallel‐plate transmission‐line type of EMP simulator.

(Source: Adapted from Giri et al. [11].)

Figure 1.5 Experimental setup of a bounded‐wave EMP simulator.

(Source: Adapted from Schilling et al. [9].)

1.4 Review of Earlier Work

In this section, we examine earlier work in different areas relevant to modeling of EMP simulators.

We first consider earlier work involving overall analysis of bounded‐wave simulator performance. Several time‐ and frequency‐domain models have been reported. However, these analyses are based on several simplifying assumptions. For example, the conducting plates of a simulator have been approximated by wire grids or meshes. The current induced on the wires has been solved in the time‐domain using a space–time‐domain technique [12]. It has also been solved in the frequency domain using the method‐of‐moments (MOM) [13].

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