Lightning Electromagnetics, Volume 2: Return Electrical processes and effects

Cover
Contents
About the editors
Acknowledgements
1 Basic discharge processes in the atmosphere
	1.1 Introduction
	1.2 Electron avalanche
	1.3 Streamer discharges
	1.4 Corona discharges
	1.5 Thermalization or heating of air by a discharge
	1.6 Low-pressure electrical discharges
	1.7 Leader discharges
	1.8 Some features of mathematical modelling of positive leader discharges
	1.9 Leader inception based on thermalization of the discharge channel
	References
2 Modelling of charging processes in clouds
	2.1 Introduction
	2.2 Definitions of some model descriptors
		2.2.1 Basic terminology
		2.2.2 Terms related to microphysics
		2.2.3 Categories of electrification mechanisms
		2.2.4 Other categorizations of cloud models
	2.3 Brief history of electrification modelling
	2.4 Parameterization of electrical processes
		2.4.1 Calculating the electric field
		2.4.2 Charge continuity
		2.4.3 The non-inductive graupel–ice collision mechanism
		2.4.4 The inductive charging mechanism
		2.4.5 Small ion processes
	2.5 Lightning parameterizations
		2.5.1 Stochastic lightning model
		2.5.2 Pseudo-fractal lightning
	2.6 Some applications of models
		2.6.1 Ion and inductive mechanisms
		2.6.2 Non-inductive graupel–ice sensitivity
		2.6.3 Charge structure and lightning type
		2.6.4 Concluding remarks
	References
3 Numerical simulations of non-thermal electrical discharges in air
	3.1 Introduction
	3.2 Outline of electro-physical processes in gaseous medium under electric fields
		3.2.1 Generation of charged species in gas
		3.2.2 Losses of charged species in gas
		3.2.3 Dynamics of densities of charge carriers in discharge plasma
		3.2.4 Concepts of electron avalanche and streamer
	3.3 Hydrodynamic description of gas discharge plasma
	3.4 Solving gas discharge problems
		3.4.1 Simulations of corona in air
		3.4.2 Computer implementation of corona model
		3.4.3 Study case: positive corona between coaxial cylinders
		3.4.4 Study case: positive corona in rod-plane electrode system
	3.5 Simulations of streamer discharges in air
		3.5.1 Study case: positive streamer in a weak homogeneous background field
		3.5.2 Study case: negative streamer in weak homogeneous background fields
	References
4 Attachment of lightning flashes to grounded structures
	4.1 Introduction
	4.2 Striking distance
	4.3 Leader inception models
		4.3.1 Critical radius and critical streamer length concepts
		4.3.2 Rizk’s generalized leader inception equation
		4.3.3 Lalande’s stabilization field equation
		4.3.4 Leader inception model of Becerra and Cooray (SLIM)
	4.4 Leader progression and attachment models
	4.5 The potential of the stepped leader channel and the striking distance
		4.5.1 Armstrong and Whitehead
		4.5.2 Leader potential extracted from the charge neutralized by the return stroke
		4.5.3 Striking distance based on the leader tip potential
	4.6 Comparison of EGM against SLIM
	4.7 Points where more investigations are needed
		4.7.1 Orientation of the stepped leader
		4.7.2 The orientation of the connecting leader
		4.7.3 The connection between the leader potential and the return stroke current
		4.7.4 Inclination of the leader channel
		4.7.5 Main assumptions of SLIM
	4.8 Concluding remarks
	References
5 Modeling lightning strikes to tall towers
	5.1 Introduction
	5.2 Modeling lightning strikes to tall structures
		5.2.1 Engineering models
		5.2.2 Electromagnetic models
		5.2.3 Hybrid electromagnetic model (HEM)
	5.3 Electromagnetic field computation
		5.3.1 Electromagnetic field expressions for a perfectly conducting ground
		5.3.2 Electromagnetic field computation for a finitely conducting ground
	5.4 Review of lightning current data and associated electromagnetic fields
		5.4.1 Experimental data
		5.4.2 Data from short towers
		5.4.3 Summary of Berger’s data
		5.4.4 Other data obtained using short towers (≤100 m)
		5.4.5 Data from tall towers
	5.5 Summary
	References
6 Lightning electromagnetic field calculations in the presence of a conducting ground: the numerical treatment of Sommerfeld’s integrals
	6.1 Introduction
	6.2 Lightning electromagnetic field calculation in presence of a lossy ground with constant electrical parameters
		6.2.1 Over-ground electromagnetic field
		6.2.2 Underground electromagnetic field
	6.3 Lightning electromagnetic field calculation in presence of a lossy ground with frequency-dependent electrical parameters
		6.3.1 The dependence of soil conductivity and permittivity on the frequency
		6.3.2 Numerical simulation of over-ground and underground lightning electromagnetic field
	6.4 Lightning electromagnetic field calculation in presence of a lossy and horizontally stratified ground
		6.4.1 Statement of the problem and derivation of the Green’s functions for the electromagnetic field
		6.4.2 Derivation of the lightning electromagnetic field
		6.4.3 The reflection coefficient R
	6.5 Conclusions
	References
7 Lightning electromagnetic field propagation: a survey on the available approximate expressions
	7.1 Lightning electromagnetic fields over a homogeneous soil
		7.1.1 Horizontal electric field – Cooray–Rubinstein (CR) formula
		7.1.2 Vertical electric field and azimuthal magnetic field
		7.1.3 Lightning electromagnetic fields under the groundCooray formula
	7.2 Electromagnetic fields propagation along a horizontally stratified ground
		7.2.1 Lightning electromagnetic fields for a two-layer horizontally stratified ground: a simplified formulation
		7.2.2 Validation of the simplified formula
	7.3 Electromagnetic fields propagation along a vertically stratified ground
		7.3.1 Lightning electromagnetic fields for a two-layer vertically stratified ground: a simplified formulation
		7.3.2 Validation of the simplified formula
	7.4 Summary
	References
8 Interaction of lightning-generated electromagnetic fields with overhead and underground cables
	8.1 Introduction
	8.2 Transmission line theory
	8.3 Electromagnetic field interaction with overhead lines
		8.3.1 Single-wire line above a perfectly conducting ground
		8.3.2 Taylor, Satterwhite, and Harrison model
		8.3.3 Agrawal, Price, and Gurbaxani model
		8.3.4 Rachidi model
		8.3.5 Rusck model and its extensions
		8.3.6 Inclusion of losses
		8.3.7 Multiconductor lines
		8.3.8 Coupling to complex networks
		8.3.9 Frequency-domain solutions
		8.3.10 Time-domain solutions
		8.3.11 Analytical solutions
		8.3.12 Application to lightning-induced voltages
	8.4 Electromagnetic field interaction with buried cables
		8.4.1 Field-to-buried cables coupling equations
		8.4.2 Frequency-domain solutions
		8.4.3 Time-domain solutions
		8.4.4 Lightning-induced disturbances in a buried cable
	8.5 Conclusions
	Acknowledgments
	References
9 Application of scale models to the study of lightning transients in power transmission and distribution systems
	9.1 Introduction
	9.2 Basis of scale modeling
	9.3 Simulation of the electromagnetic environment
		9.3.1 Lightning channel
		9.3.2 Ground
		9.3.3 Overhead lines
		9.3.4 Transformers
		9.3.5 Surge arresters
		9.3.6 Buildings
		9.3.7 Transmission line towers
	9.4 Evaluation of lightning surges in power lines
		9.4.1 Investigations associated with direct strokes
		9.4.2 Investigations associated with indirect strokes
	9.5 Conclusions
	Acknowledgments
	References
10 Lightning interaction with the ionosphere
	10.1 Introduction
	10.2 The full-wave FDTD model of lightning EMPs interaction with the D-region ionosphere
		10.2.1 The parameterization of the lower D-region ionosphere
		10.2.2 3D spherical model
		10.2.3 2D symmetric polar model
	10.3 VLF/LF signal of lightning EM fields propagation through the EIWG
		10.3.1 The effect of Earth’s curvature
		10.3.2 The effect of the ground conductivity
		10.3.3 The effect of different D-region ionospheric profiles
	10.4 Application to the propagation of NBEs at different distances in the EIWG
	10.5 Application to lightning EM field propagation over a mountainous terrain
	10.6 Application to the optical emissions of lightninginduced transient luminous events in the nonlinear D-region ionosphere
	10.7 Summary
	References
11 Lightning effects in the mesosphere
	11.1 Introduction
	11.2 Sprites
		11.2.1 Basic properties and morphology of sprites
		11.2.2 Mechanism of the sprite nucleation
		11.2.3 Sprite development
		11.2.4 Sprite models
		11.2.5 Inner structure and color of sprites
		11.2.6 ELF/VLF electromagnetic fields produced by sprites
		11.2.7 Effects of sprites on the ionosphere
	11.3 Blue jet, blue starter, and gigantic jet
		11.3.1 Basic properties and morphology of blue and gigantic jets
		11.3.2 Development of gigantic jet
		11.3.3 Models of gigantic jet
	11.4 Elves
	11.5 Other transient atmospheric phenomena possibly related to lightning activity
		11.5.1 Gnomes and Pixies
		11.5.2 Transient atmospheric events
		11.5.3 Terrestrial gamma-ray flashes
	References
12 The effects of lightning on the ionosphere/magnetosphere: whistlers and ionospheric Alfven resonator
	12.1 Introduction
	12.2 Lightning-induced whistlers in the ionosphere/ magnetosphere
		12.2.1 General description of whistlers
		12.2.2 Theoretical background of plasma waves
		12.2.3 Use of whistlers as a diagnostic tool of the ionosphere/magnetosphere
	12.3 Ionospheric Alfve´n resonator (IAR)
		12.3.1 Brief history and general introduction of IAR
		12.3.2 Ground-based observations of IARs at middle latitude
		12.3.3 Generation mechanisms of IAR
		12.3.4 Excitation of IAR by nearby thunderstorms
	12.4 Summary of lightning effects on the ionosphere/ magnetosphere
	References
13 On the NOx generation in corona, streamer and low-pressure electrical discharges
	13.1 Introduction
	13.2 Testing the theory using corona discharges
	13.3 NOx generation in electron avalanches and its relationship to energy dissipation
	13.4 NOx production in streamer discharges
	13.5 Discussion and conclusions
	References
14 On the NOx production by laboratory electrical discharges and lightning
	14.1 Introduction
	14.2 NOx production by laboratory sparks
		14.2.1 Radius of spark channels
		14.2.2 The volume of air heated in a spark channel and its internal energy
		14.2.3 NOx production in spark channels
		14.2.4 Efficiency of NOx production in sparks with different current wave-shapes
		14.2.5 NOx production in sparks as a function of energy
	14.3 NOx production in discharges containing long-duration currents
	14.4 NOx production in streamer discharges
	14.5 NOx production in ground lightning flashes
		14.5.1 The model of a ground lightning flash
		14.5.2 NOx production in different processes in ground flashes
	14.6 NOx production by cloud flashes
	14.7 Global production of NOx by lightning flashes
	14.8 Conclusions
	Appendix 1
	References
15 Lightning and climate change
	15.1 Introduction
	15.2 Basics of thunderstorm electrification and lightning
	15.3 Thermodynamic control on lightning activity
		15.3.1 Temperature
		15.3.2 Dew point temperature
		15.3.3 Water vapor and the Clausius–Clapeyron relationship
		15.3.4 Convective available potential energy and its temperature dependence
		15.3.5 Cloud base height and its influence on cloud microphysics
		15.3.6 Balance level considerations in deep convection
		15.3.7 Baroclinicity
	15.4 Global lightning response to temperature on different time scales
		15.4.1 Diurnal variation
		15.4.2 Semiannual variation
		15.4.3 Annual variation
		15.4.4 ENSO
		15.4.5 Decadal time scale
		15.4.6 Multi-decadal time scale
		15.4.7 Hiatus in global warming and “warming hole”
	15.5 Aerosol influence on moist convection and lightning activity
		15.5.1 Basic concepts
		15.5.2 Observational support
		15.5.3 Lightning response to the COVID-19 pandemic
		15.5.4 Work of Wang et al. (2018) on the global aerosollightning relationship
	15.6 Lightning as a climate variable
	15.7 Lightning activity at high latitude
		15.7.1 The Arctic
		15.7.2 Alaska
	15.8 Winter-type thunderstorms and lightning
		15.8.1 Effects of global warming on winter thunderstorms
	15.9 Storms at the mesoscale
	15.10 Tropical cyclones
	15.11 Cloud-to-ocean lightning
	15.12 Lightning superbolts and megaflashes
	15.13 Nocturnal thunderstorms
	15.14 Meteorological control on lightning type
	15.15 The global circuits as monitors for destructive lightning and climate change
	15.16 Expectations for the future
	References
Index
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