Charge Acceleration and the Spatial Distribution of Radiation Emitted by Antennas and Scatterers
Given that charge acceleration is the cause of all electromagnetic radiation, the question arises about where such acceleration occurs on objects typically modelled and analysed by electromagnetic engineers. Charge acceleration, as the cause of radiation from these typical kinds of objects (antennas, radars etc) is examined in this book on a quantitative basis.
The book describes new ways of modelling the actual distribution of EM radiation waves from its various sources. Unlike other books on EM it focuses on radiation, a fundamental property of electromagnetic fields, it does not follow the usual analytical kind of approach to be found in a book on electromagnetics. Rather than developing and presenting a formal theoretical foundation of electromagnetic theory, this book instead focuses on various aspects of EM radiation from a variety of perspectives.
The goal is to provide the reader with computational tools for determining quantitatively why and where radiation is emitted by antennas and scatterers. This is a unique approach which is of wide interest to the EM theoretical community.
 Book DOI: 10.1049/SBEW567E
 Chapter DOI: 10.1049/SBEW567E
 ISBN: 9781839538131
 eISBN: 9781839538148
 Page count: 328
 Format: PDF

Front Matter
 + Show details  Hide details

p.
(1)

1 Overview
 + Show details  Hide details

p.
1
–20
(20)
Radiation is the fundamental physical property of electromagnetic fields from which everything else follows. The goal of the book is to explain why and where radiation occurs from simple perfectelectric conducting objects as exemplified by wire antennas and scatterers. Numerous examples to illustrate how radiation occurs and its relationship with the behavior of the current and charge on such objects are presented. The numerical results are primarily derived using two wellknown and wellvalidated computer models, TWTD (ThinWire Time Domain, described in Appendix A) and NEC (Numerical Electromagnetics Code, described in Appendix B) with which the author has been long associated.
Several different methods for determining why and where radiation originates from a perfect electric conductor are examined. While electromagnetic (EM) radiation is caused by acceleration of electric charge, this fact is rarely mentioned in engineering texts. In spite of that, computing the radiation patterns of complex, perfectelectric conductors (PEC) has been longestablished and validated using Maxwell's equations (ME). Although charge acceleration is not explicitly included for PEC objects in ME, they obviously contain this effect implicitly in farfield computations based on them. Typical physics texts do discuss charge acceleration as the basis of EM radiation, but in terms of free charge in space, rather than in connection with, for example, how a physical antenna operates.
The goal of this book is to demonstrate the relationship between charge acceleration and how PEC objects behave when excited by localized sources as antennas or by incident waves as scatterers. Various analytical and numerical techniques developed by the author address the question "Where and in what amount is the power (frequency domain) or energy (time domain) emitted by PEC objects for various representative geometries?" A method called FARS (Far field Analysis of Radiation Sources) is demonstrated to provide an answer to this question in both the frequency and time domains. It follows that also answered is where the charge acceleration that produces radiation occurs. FARS also applies to specified currents such as the sinusoidal current filament, long used as an approximation for a dipole antenna.
The techniques described and demonstrated can be incorporated into most computational electromagnetics models with little effort to provide those interested in investigating localized radiation behavior for various situations. Such techniques will be of value in a teaching setting since they will give students a learning tool and unique insight into a fundamental aspect of the electromagnetic discipline. A variety of examples throughout will demonstrate geometrical features that cause charge acceleration or radiation. As a specific example, various published observations that associate current decay along a straight wire with radiation are confirmed to be due to charge reflection, caused by a waveimpedance variation with distance.

2 The electricfield kink model of electromagnetic radiation
 + Show details  Hide details

p.
21
–36
(16)
The apparent mathematical complexity of Maxwell's equations may seem to obfuscate the beauty of the physical phenomena that they describe. Yet the defining fundamental property of electromagnetics, radiation, can be illustrated visually and qualitatively independent of its mathematical foundation. The purpose of this chapter is to present a way to do this called the ElectricField kink model. The Efield kink model relies on two basic properties of electromagnetics: (1) electromagnetic fields propagate at a finite speed, denoted by the symbol "c," the speed of light, that is 3 × 10^{8} m/sec in free space; and (2) electric field lines of force originate by convention from positive electric charge and terminate on negative electric charge.
These two facts make possible the development of graphical depictions of the fields radiated by charges whose speed and/or direction of motion change in time, i.e., when they are accelerated. This phenomenon is described in more detail below and illustrated graphically for a variety of charge motions. The goal is to provide a way to visualize how radiation is produced and so to gain an intuitive understanding of the physical process conveyed by Maxwell's equation. Also demonstrated is how the field lines close as they radiate away from a wire antenna in the frequency and time domains.

3 Chargeacceleration and radiation from a generic wire object
 + Show details  Hide details

p.
37
–58
(22)
The LienardWichert potentials show that radiation is caused by charge acceleration. The question arises about where charge acceleration occurs on the most basic of antennas, a centerfed, perfectly conducting dipole for which there are two obvious causes. One is the feedpoint exciting voltage that sets into motion an outwardpropagating charge and current wave at light speed c in the medium. A second is at the dipole ends where the outgoing wave is totally reflected producing a change in charge speed of 2c. A third, possibly lessobvious cause is the deceasing amplitude of the propagating wave with distance due to its partial reflection along the wire. That reflected charge also undergoes a speed change of 2c. This is the reason why the decay of current flowing along a straight wire antenna has been attributed as being due to radiation. Radiation caused by these and other kinds of charge acceleration due to resistive loads, rightangle bends, and radius steps are investigated.
These phenomena are examined primarily in the timedomain where they are more observably separable in time and space than in the frequency domain. The current and charge induced on an impulsively excited wire antenna and its broadside radiated Efield are computed using a timedomain, integralequation model, thinwire time domain (TWTD). The computed results are used to derive a numerical relationship between the amount of accelerated charge and its radiated field. This relationship is denoted as an acceleration factor (AF) and is derived for various chargeaccelerating features of a generic wire object. Their values are normalized to those of the exciting sources to standardize their respective values.
Footnote: This chapter is largely based on "The Proportionality between Charge Acceleration and Radiation from a Generic Wire Object," Progress In Electromagnetics Research, Vol. 162, 2018, 1529, by E. K. Miller, with some additions and deletions including correction of acceleration factors for resistanceloaded and bent wires that were too low by a factor of 2.

4 Timedomain electromagneticfield energy measures
 + Show details  Hide details

p.
59
–84
(26)
Among the options offered as outputs of the thinwire timedomain (TWTD) computer model are the current and charge distributions as a function of time over the wire object for which a numerical solution has been obtained. These quantities are useful in various ways, ranging from providing the frequency dependence of an antenna's input admittance to providing the near and far fields that the object produces as a function of time or frequency. Another benefit provided by the far fields is that they can reveal from where on the object that they originate, using TimeDomain Farfield Analysis of Radiation Sources (TDFARS) as will be discussed in Chapter 7. One disadvantage of FARS in either the time or frequency domain, however, is that it requires integrating the radiated fields over the farfield sphere, an exercise that can be computationally expensive for a large or complex object.
A simpler alternative to TDFARS is presented in this chapter, timedomain energy measures (TDEM). These involve using only the solvedfor current and charge spacetime variations, a concept that was introduced in [1] and expanded upon further in [2,3]. The total timedependent energy decays due to radiation loss over time, and its differentiation with respect to time yields the rate of energy loss. Furthermore, where the loss occurs is discernible from where the current and charge pulses are located at a particular time. The following discussion first summarizes the basic idea and then demonstrates this approach with a variety of applications. The advantage of TDEM is its computational efficiency compared with TDFARS, but it does have some limitations that are also addressed.

5 Radiationloss dependence of a circular loop antenna on its circumference and wire radius
 + Show details  Hide details

p.
85
–96
(12)
The LienardWiechert potentials show explicitly that charge acceleration, i.e. a change in charge velocity, causes radiation of an electromagnetic field. The goal of this chapter is to explore the rate of energy loss due to radiation from current and charge flowing on a circular loop as a function of the loop's curvature and wire radius. The results presented are obtained using a thinwire, timedomain (TWTD) computer model for Gaussianpulse excitation. Some results for a straight wire are also presented for comparison. Analytical estimates for the curvature and wireradius effects are developed from bestfit expressions to the computed results using modelbased parameter estimation (MBPE).
Footnote: This chapter is based on "The dependence of timedomain radiation loss on the circumference and wire radius of a circular loop antenna," Progress In Electromagnetics Research M, vol. 92, 2020, 19, by E. K. Miller.

6 Differentiating the onsurface Poynting vector of a wire to determine its radiation loss
 + Show details  Hide details

p.
97
–128
(32)
This chapter explores use of the Poynting vector (PV) computed from the surface current and charge distribution to investigate the power flow at the surface of various thin, perfect, electric conducting (PEC) wires excited as antennas or scatterers. By differentiating the axial Poynting vector at the wire's surface, the rate of change of power flow in the current and charge along a the wire can be determined. The idea to be explored is whether the loss in power flow along the wire can show where radiation occurs. The differentiated Poynting PV (DPV) results are compared with those obtained using Farfield Analysis of Radiation Sources (FARS), a method briefly introduced here and covered more thoroughly in Chapter 9.
Results are presented for two antennaexcitation models for a straightwire dipole, the usual tangential Efield model and a twowire transmissionline feed. Their comparison for a 10wavelength dipole shows them to agree to within 10% relative to end peaks in the distribution of spatial radiation except in the vicinity of the antenna feedpoint. Both show that radiation occurs not only near the feedpoint and ends of the antenna, but is distributed along its length. Results presented for other antennas such as a bentwire dipole, and circular and square loops, and for a straightwire scatterer further demonstrate the effect of shape and excitation on the distributed radiation obtained using the DPV.

7 Timedomain farfield analysis of radiation sources and TWTD
 + Show details  Hide details

p.
129
–155
(27)
The procedure called FARS (FarField Analysis of Radiation Sources ha been briefly introduced in earlier chapters of this book. It is a technique for determining the quantitative distribution of power or energy radiated from a perfect electric conductor. FARS is based on a sourceintegral expression for the fields of an object of interest for which both timedomain (TDFARS) and frequencydomain (FDFARS) versions have been developed. These two versions provide complementary perspectives of general electromagnetic phenomena. While a frequencydomain result explicitly demonstrates the effects of standing waves, for example, a timedomain result has the advantage of separating various contributions to the far field due to their different time delays. The motivation for both FDFARS and TDFARS is to provide information about radiation from a perfect electric conductor. A brief description of TDFARS is given here and demonstrated for some simple wire geometries.

8 Frequencydomain farfield analysis of radiation sources and NEC
 + Show details  Hide details

p.
157
–182
(26)
Timedomain far field analysis of radiation sources (TDFARS) were introduced in the previous chapter and its implementation is illustrated by a variety of results obtained using the computer code thinwire time domain (TWTD). This order of presentation has been used because initial discussion in this book was devoted to the time domain as a more intuitive way of introducing the physical basis for electromagnetic radiation. This following chapter introduces the complementary version of frequencydomain far field analysis of radiation sources (FDFARS), development of which actually came first. FDFARS was developed in an attempt to determine how much power is contributed to the far field from a PEC object on a perunitlength or perunitarea basis. Examples considered here include straight, curved, and bent wires, with the far field analysis of radiation sources (FARS) results appearing to be physically consistent with other expectations about radiation.

9 Timedomain FARS and frequencydomain FARS compared
 + Show details  Hide details

p.
183
–190
(8)
Timedomain far field analysis of radiation sources (TDFARS) and frequencydomain far field analysis of radiation sources (FDFARS) have been shown in Chapters 7 and 8 to determine the quantitative distribution of radiated power and radiated energy on a variety of wire objects. The FDFARS results reveal their frequency dependence through a series of lobes related to the wavelength. For antennas, there are nominally 2 lobes per wavelength with larger maxima at the feedpoint and ends. For scattering the lobe structure can vary from 1 to 2 lobes per wavelength. Similar lobe structure is found for other wire objects. The TDFARS results, on the other hand, are not lobed but vary smoothly over an object with maxima at the open ends of a wire and at the feedpoint as well as opposite the feedpoint of a circular or square loop. The absence of lobes is because the timedomain current and charge are not standing waves.
The comparisons included here are normalized to a 1W total power or 1J total energy on a persegment basis for a nominal spatial sampling density of 20 per m. Discussion is limited here to wires of several wavelengths so that physical features that may not be as pronounced for shorter objects are observable.

10 The radiation properties of some specified currents
 + Show details  Hide details

p.
191
–208
(18)
This chapter focuses on radiation from various specified current distributions, with an emphasis on the classic sinusoidal current filament (SCF). The SCF provided a basis for early attempts to predict the pattern and radiation characteristics of an elementary physical antenna, the wire dipole. This was because closedform, analytical expressions had been developed for its near and far fields and radiated power as a function of its length. The SCF made a good test case for FDFARS because the effective input power required to maintain the SCF can be determined from the Induced ElectroMotive Force (IEMF) method. As was shown in Chapter 8, the IEMF results for the SCF were instrumental in development of FDFARS.
The SCF is examined further in this chapter. One item discussed is establishing why the total power it radiates oscillates between maximum and minimum values as its increasing length, L, passes through even and oddnumber of half wavelengths. Radiatedpower maxima occur when its length is an even number of half wavelengths while minima occur for an odd number of half wavelengths. The reason why the average radiated power increases as the Log(kL) is shown to be due to radiation that takes place between the center feedpoint and its ends.
The distributions of radiated power derived from FDFARS and the IEMF method are presented for several other specified currents to provide further validation of both methods while also demonstrating the wide applicability of these procedures.

11 The incremental FARS (IFARS) and incremental IEMF (IIEMF) methods
 + Show details  Hide details

p.
209
–224
(16)
Incremental versions of farfield analysis of radiation sources (FARS) and the induced electromotive force (IEMF) method are implemented in this chapter in connection with momentmethod models for two reasons. One is to provide a more geometrically detailed way of determining the powerdensity distribution of radiation from over the surface of an object. A second is to make this possible without the need to integrate the power flow over the entire farfield sphere. The generalizations of these two methods are denoted here as incremental FARS (IFARS) and incremental IEMF (IIEMF). These incremental procedures are developed and their application demonstrated using various NEC models. Both involve determining the pairwise interaction between current samples on a PEC object. Mutual validation of both techniques is confirmed by the agreement shown between their numerical results in the following.

12 The SchelkunoffFeldman radiation resistance
 + Show details  Hide details

p.
225
–244
(20)
This chapter revisits the concept of a distributed radiation resistance developed by Schelkunoff and Feldman. Their article addressed the possibility of accounting for radiation from a wire antenna via a distributed resistance added to whatever dissipative resistance an imperfectly conducting wire might have.
In order to retain its complete development of this novel concept, their entire article is included here. This is followed by an extension of their development. While they limited the results of their analytical treatment to currents an even number of half wavelengths long their treatment is shown numerically here to be valid for an arbitrary length. This is demonstrated by using their distributed radiation resistance to determine the quantitative distribution of radiation from along the current. Results thus obtained are found to agree with the frequencydomain FARS and IEMF results discussed in previous chapters, providing validation for both approaches. Also, numerical computations from FARS are shown to provide an alternate way to evaluate the distributed radiation resistance.

13 Radiation from a nearzeroradius dipole and a sinusoidal current filament
 + Show details  Hide details

p.
245
–263
(19)
The electric field of a sinusoidal current filament (SCF) is one of the relatively few problems in electromagnetics whose solution can be developed in closed form. This is why the SCF was routinely used to approximate the radiation characteristics of the thinwire, centerfed, dipole antenna. This proved to be useful because the current on a perfect electric conductor (PEC) wire of nearzero radius (NZR) closely approximates a sinusoidal current as does its radiation patterns.
However, while the SCF and NZR dipole are very similar in some respects, they are quite different in others as will be show here. These similarities and differences are explored below and how these two sources actually produce a far radiation field is explained.

14 The pattern rank and spatial radiation distribution of radiation emitted by a sinusoidal current filament
 + Show details  Hide details

p.
265
–278
(14)
Two propositions are explored in this chapter that relate to the issue of where radiation originates from a specified current source. One is that if some incremental portion of a source distribution increases (changes) the total far field at any observation angle, then by definition radiation originates from that portion of the source distribution. The other is that the greater the number of degrees of freedom in a radiation pattern the greater will be the proportion of the source distribution that actually radiates. These issues are explored here in terms of the radiation from a sinusoidal current filament.
Footnote: Excerpted and rewritten from E. K. Miller, "The Incremental Far Field and Degrees of Freedom of the Sinusoidal Current Filament," IEEE Antennas and Propagation Society Magazine, 49 (4), pp. 1321, August, 2007.

Appendix A: The thinwire timedomain (TWTD) computer code
 + Show details  Hide details

p.
279
–284
(6)
A brief description of thinwire timedomain (TWTD) is presented together with a sampling of some of the results a timedomain model can generate. The code is based on a timedomain version of the electricfield integral equation specialized to thin wires. It originated in the late 1960s inspired by timedomain results reported at the 1968 IEEE APS conference. Its initial use was for simple wire antennas and scatterers and subsequently for ElectroMagnetic Pulse (EMP) applications. For the latter problems, a circuit capability was added to evaluate the damage that an EMP might do to electronic systems. This later feature was exploited in later research to design passive electronic tags for radiofrequency identification (RFID).

Appendix B: The Numerical Electromagnetics Code (NEC)
 + Show details  Hide details

p.
285
–292
(8)
The Numerical Electromagnetics Code is one of the longestlived computational electromagnetics code, having its origin in the 1960s. As NEC exists now it has little resemblance to its beginnings, benefiting from a changing team of contributors over time. Its primary managerdeveloper over most of those years was Jerry Burke. Various enhancements and features have been added from the original NEC to NEC4. Some problems that can arise when validating computer models are demonstrated as part of the process of validating NEC that has continued through various applications as illustrated by some additional examples.

Appendix C: Notation
 + Show details  Hide details

p.
293
–295
(3)
No Abstract available.

Back Matter
 + Show details  Hide details

p.
(1)