The goal of this chapter is to provide a summary of the basic concepts of electro- magnetic theory as a complement to the subject matter, most of which is related to electromagnetism, discussed in this book. The chapter covers only the concepts that are necessary to understand the electromagnetics of lightning flashes.

The main constituents of air in the Earth's atmosphere are nitrogen (78%), oxygen (20%), noble gases (1%), water vapour (0.03%), carbon dioxide (0.97%) and other trace gas species. In general, air is a good insulator and it can maintain its insulating properties until the applied electric field exceeds about 2.8 x 104 V/cm at standard atmospheric conditions (i.e. T= 293 K and P =1 atm). When the background electric field exceeds this critical value, the free electrons in air generated mainly by the high energetic radiation of cosmic rays and radio active gases generated from the Earth start accelerating in this electric field and gain enough energy between collisions with atoms and molecules to ionize other atoms. This cumulative ionization leads to an increase in the number of electrons initiating the electrical breakdown of air. The threshold electric field necessary for electrical breakdown of air is a function of atmospheric density. When the leaders reach an electrode of opposite polarity or a region of opposite charge density, a rapid neutralization of the charge on the leader takes place. This neutralization process is called a return stroke. The exact mechanism of the return stroke is not yet known, but different types of models have been developed to describe them. These models are described in several chapters of this book. Here, we will concentrate on the four discharge processes mentioned above. Some parts of this chapter are adopted and summarized from Reference 1 where an extensive description of basic physics of discharges is given.

Our goal in this chapter is to introduce the treatments of electrical processes used by numerical cloud models that integrate dynamic, microphysical, thermodynamic and electric processes to track what happens to several classes of water particles as they move through the cloud and interact with each other and with the environment as the cloud evolves. We consider primarily models that treat ice particles, as well as liquid water, because ice is now commonly recognized as a necessary ingredient for strong electrification. We ignore models whose winds or particle spectra are unchanging and models that treat electrification as interactions of electric circuit elements driven by a current, charge or voltage source unrelated to microphysics and dynamics.

In this chapter, we will describe and discuss several engineering models that can be utilized either to evaluate electromagnetic fields from lightning flashes or to study the direct effects of lightning attachment to various structures including tall towers. We will start by describing the basic concepts of engineering return stroke models. This discussion will be followed by a description of various return stroke models and the equations necessary for the evaluation of electromagnetic fields using these return stroke models.

Lightning is a transient, high-current electric discharge with the height in kilometre range. Cloud-to-ground lightning is less common than the other kinds of lightning (i.e. cloud-to-cloud and interclub lightning), but they are more important for protection studies of electric and electronic apparatus used in power systems, information technology systems, etc. The complete discharge, known as flash, has a time duration of about 0.5 s and is made up of various components, including stepped leader, return-strokes and dart leaders. The part of a flash, which has been of great interest for protection purposes, is the return-stroke phase.

The exact solution to the electromagnetic fields generated by electric dipoles located above a finitely conducting ground plane was obtained by Sommerfeld. He presented his results in the form of a set of integrals. Since the numerical solutions of these integrals are time-consuming, attempts have been made to find approximate solutions to these integrals. In this chapter, various approximate solutions and procedures that have been used to calculate electromagnetic fields of return strokes over finitely conducting ground will be presented together with their limits of validity.

The chapter is organized as follows. The ground parameters will be considered constant; under such assumption both the derivation and the calculation of the lightning electromagnetic field components will be presented together with some guidelines to discover the cases in which the well-known approximate approaches provide accurate results. Next, the influence of the frequency-dependent behaviour of the ground electrical parameters will be studied. Finally, the problem of the derivation of the lightning electromagnetic fields over a stratified conducting ground will be faced and the effect of the stratification on the field waveforms will be analysed.

The Schumann resonances (SR) are global electromagnetic resonances excited within the Earth-ionosphere waveguide, primarily by lightning discharges. These resonances occur in the extremely low frequency (ELF) range, with resonant frequencies around 8, 14, 20, 26, . . . Hz. This Chapter is dedicated to the theory, phenomenology, and measurements of Schumann resonances.

This chapter will deal with the effect of lightning onto the upper atmosphere such as the ionosphere and magnetosphere. There are a few possible effects of lightning on the ionosphere/magnetosphere, but we restrict our attention to the following two phenomena: (1) lightning-induced whistlers and (2) ionospheric Alfven resonators (IARs). The former well-known whistlers are defined generally by signals in the extremely low frequency (ELF) and very low frequency (VLF) bands of causative lightning discharges that travel through the ionospheric/magnetospheric plasma along the Earth's magnetic field. IARs are characterized by the resonance phenomena in the frequency range below the conventional Schumann resonance. Their morphological characteristics and their interpretation in terms of lightning discharges are presented in this chapter.

This chapter presents, initially, the theory of scale models. Then, methods for simulating the electromagnetic environment, as well as various power system components, namely overhead lines, transformers and surge arresters are described, and details are given on the reduced system implemented at the University of Sao Paulo, Brazil. The last part of the chapter is dedicated to the application of the technique for the evaluation of lightning transients, with emphasis on the analysis of lightning-induced voltages on overhead power distribution lines. The versatility of the scale model technique is demonstrated and examples are presented that illustrate its usefulness in the analysis of complex phenomena, either for enabling the evaluation of situations that are not worthwhile to be treated theoretically or for giving adequate support for the validation of theoretical models and relevant computer codes.

An assessment of the global distribution of nitrogen oxides (NOx) is required for a satisfactory description of tropospheric chemistry and in the evaluation of the global impact of increasing anthropogenic emissions of NOx. In the mathematical models utilized for this purpose, it is necessary to have the natural as well as man-made sources of NOx in the atmosphere as inputs. Thunderstorms are a main natural source of NOx in the atmosphere and it may be the dominant source of NOx in the troposphere in equatorial and tropical South Pacific.

Great progress has been made in the last 10 years both measuring the energetic radiation from thunderclouds and lightning, and developing theory and models to explain these emissions. To date, four basic mechanisms have been used to describe the production of runaway electrons and the resulting energetic radiation: Wilson runaway electrons; RREA, RF and cold runaway. Although all four share some features and some underlying physics, their behaviour and the regimes of applicability are sufficiently different that it is useful to treat them independently when describing the production of energetic radiation in our atmosphere.

In this chapter, we present a review of recent progress in the modelling of lightning strikes to tall structures. Since some tall structures are struck by lightning several tens of time per year, they can be used as ground-truth to measure and calibrate the location accuracy of lightning location systems. In addition, knowledge of the transient processes in tall objects when they are subjected to a lightning strike allows us to use them to calibrate the lightning return-stroke currents reported by lightning detection and location systems. Tall objects constitute also a primary source of data from which channel-base lightning current statistics are obtained. These statistics are in turn used to improve the design of lightning protection devices and systems.