Filamentary Ion Flow E-Book

Francesco Lattarulo

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 352

Veröffentlichungsjahr: 2014

Beschreibung

Presents all-new laboratory-tested theory for calculating more accurate ionized electric fields to aid in designing high-voltage devices and its components Understanding and accurately calculating corona originated electric fields are important issues for scientists who are involved in electromagnetic and electrostatic studies. High-voltage dc lines and equipment, in particular, can generate ion flows that can give rise to environmental inconveniences. Filamentary Ion Flow: Theory and Experiments provides interdisciplinary theoretical arguments to attain a final model for computational electrostatics in the presence of flowing space charge. Based on years of extensive lab tests pertaining to the physical performance of unipolar corona ion flows, the book covers the enlarging of conventional electrostatic applications, which allows for some emerging and uncharted interests to be explored. Filamentary Ion Flow: * Examines the theoretical discussions for creating a model of computational electrostatics involved with flowing space charges * Presents new theory and experimental data based on extensive testing * Offers potential design applications utilizing the theory * Helps scientists who are involved in electromagnetic and electrostatic studies understand and accurately calculate corona originated ion flow fields Filamentary Ion Flow: Theory and Experiments is ideal for electrical engineers and research scientists interested in high-voltage technology, computational electrostatics, and electromagnetic theory.

Leseprobe

CONTENTS

Cover

Series Page

Title Page

Copyright

Dedication

Preface

Acknowledgments

Introduction

Principal Symbols

Chapter 1: Fundamentals of Electrical Discharges

1.1 Introduction

1.2 Ionization Processes in Gases

1.3 Deionization Processes in Gases

1.4 Ionization and Attachment Coefficients

1.5 Electrical Breakdown of Gases

1.6 Streamer Mechanism

1.7 Breakdown in Nonuniform DC Field

1.8 Other Streamer Criteria

1.9 Corona Discharge in Air

1.10 AC Corona

1.11 Kaptzov's Hypothesis

Chapter 2: Ion-Flow Models: A Review

2.1 Introduction

2.2 The Unipolar Space-Charge Flow Problem

2.3 Deutsch's Hypotheses (DH)

2.4 Some Unipolar Ion-Flow Field Problems

2.5 Special Models

2.6 More on DH and Concluding Remarks

Appendix 2.A: Warburg's Law (WL)

Appendix 2.B: Bipolar Ionized Field

Chapter 3: Introductory Survey on Fluid Dynamics

3.1 Introduction

3.2 Continuum Motion of a Fluid

3.3 Fluid Particle

3.4 Field Quantities

3.5 Conservation Laws in Differential Form

3.6 Stokesian and Newtonian Fluids

3.7 The Navier–Stokes Equation

3.8 Deterministic Formulation for et

3.9 Incompressible (Isochoric) Flow

3.10 Incompressible and Irrotational Flows

3.11 Describing the Velocity Field

3.12 Variational Interpretation in Short

Appendix 3.A

Chapter 4: Electrohydrodynamics of Unipolar Ion Flows

4.1 Introduction

4.2 Reduced Mass-Charge

4.3 Unified Governing Laws

4.4 Discontinuous Ion-Flow Parameters

4.5 Departures from Previous Theories

4.6 Concluding Remarks on the Laplacian Structure of Ion Flows

Appendix 4.A

Appendix 4.B

Appendix 4.C

Appendix 4.D

Chapter 5: Experimental Investigation on Unipolar Ion Flows

5.1 Introduction

5.2 V-Shaped Wire Above Plane

5.3 Two-Wire Bundle

5.4 Inclined Rod

5.5 Partially Covered Wire

5.6 Pointed-Pole Sphere

5.7 Straight Wedge

5.8 Discussion

5.9 Generalization According to Invariance Principles

Appendix 5.A

References

Index

End User License Agreement

List of Tables

Table 2.1

Table 2.2

Table 5.1

List of Illustrations

Figure 2.1

Figure 2.2

Figure 2.3

Figure 2.4

Figure 2.5

Figure 2.6

Figure 2.7

Figure 2.8

Figure 2.9

Figure 2.10

Figure 2.11

Figure 2.12

Figure 2.13

Figure 2.14

Figure 4.1

Figure 4.2

Figure 4.3

Figure 5.1

Figure 5.2

Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Figure 5.7

Figure 5.8

Figure 5.9

Figure 5.10

Figure 5.11

Figure 5.12

Figure 5.13

Figure 5.14

Figure 5.15

Figure 5.16

Figure 5.17

Figure 5.18

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Figure 5.24

Figure 5.25

Figure 5.26

Figure 5.27

Figure 5.A.1

Guide

Cover

Table of Contents

Introduction

Preface

Chapter 1

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IEEE Press445 Hoes LanePiscataway, NJ 08854

IEEE Press Editorial BoardTariq Samad, Editor in Chief

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Filamentary Ion Flow

Theory and Experiments

Francesco Lattarulo

Vitantonio Amoruso

Copyright © 2014 by The Institute of Electrical and Electronics Engineers, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey. All rights reserved.

Published simultaneously in Canada.

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LibraryofCongressCataloging-in-PublicationData:

Lattarulo, Francesco.

Filamentary ion flow : theory and experiments / Francesco Lattarulo, Vitantonio Amoruso.

pages cm

ISBN 978-1-118-16812-7 (cloth)

1. Ion flow dynamics. 2. Electrostatics. I. Amoruso, Vitantonio, 1955- II. Title.

QC717.L38 2013

537′.2–dc23

2013029213

Dedication

There is nothing more uncommon than common sense.

Anonymous author

Because, up there, in heaven, isn't paradise an immense library?

Gaston Bachelard (La Poétique de la rêverie)

Preface

The arguments put forward by this book offer a coupled theoretical framework for an appropriate description and treatment of unipolar ion flows subject to electric fields. Several mechanisms can be adopted to generate ion flows, but exclusive reference is made here to those typical charge-injecting sources that are confined to overstressed (in an electrostatic sense) surface areas of conductors under direct current corona. The rationale for this choice is that a pair of main requirements for the physical phenomenon to be investigated, namely, generating ions and then setting them in motion by an impressed force, are met at once. The ion source identifies with an ionization region that occupies a restricted volume of space in contact with a conductor raised at a potential exceeding the corona onset level. Therefore, it could be said that the far broader drift region, where the repelled ions can slowly flow toward a collecting counterelectrode, covers the entire electrode gap. Under the described circumstances, and with special reference to the ion flow crossing the drift region, the governing electromagnetic and fluid dynamic laws form that special body of knowledge preferentially referred to as electrohydrodynamics (EHD). Given that there is a large amount of traditional and emerging practical applications somehow involving EHD applied to drifting ions (see later on), urgent improvements to available theoretical resources need to be made. Before going straight to the heart of the matter, it is positive to say a few preliminary words on the difficult task of finding a way of moving forward in the world of interdisciplinary investigations, where the present one is a prominent example. Any skillful and prudent researcher is aware of the fact that carefully putting together a set of governing equations under the described complex situations could result in a very hard undertaking, sometimes exposed to misinterpretations and inconsistencies. The excuse for this difficulty resides in the need of getting, at first, information from broken up sections of physics before attaining a final joint model. It has been argued at times that a physical problem appears to be far too involved not owing to the true attributes of the overall system, but to the mathematical aspects of the defective model being profiled. Note further that a good grounding in reasoning on composite problems could in principle allow the emergence of some still submerged relationships between parameters that are traditionally pertaining to different areas of physics. Unfortunately, that is not really the case because when the departure between theory and experiment becomes a matter of some importance, the improving efforts often adopted by trial and error consist in supplementing the starting model with a number of higher-order terms. Such a commendable intention could result in a frustrating, unfruitful exercise because first-order interactions between parameters distinct from and usually handled in different compartments of physics still remain overlooked. These disappointing circumstances seem to characterize previous EHD approaches because the electromagnetic and fluid dynamic laws, somehow involved in the description of unipolar ion flows, are kept substantially decoupled. Very specifically, this is the case for the electric and velocity fields, enlivened in the ion-drift region, which are usually assumed to respectively exhibit divergence and circulation both different from zero. The real value of the present treatment essentially consists in highlighting the deficiencies commonly compromising EHD models and opposing them with a reformulated modeling that carefully takes into account mutual influences between the involved field laws. This revised approach distinctively applies in the drift regions because of the subsonic velocity of the ions flowing there. Indeed, all it requires is to only overcome some conceptual drawbacks resisting the explored hybridization. This will ultimately be expressed by the solenoidal and irrotational vector properties that, of necessity, the respective electric and velocity fields simultaneously should gain. Surprisingly and paradoxically, there is an added value to the given coupling: The complete governing formulation looks quite unsophisticated and eloquent to the benefit of physical interpretation. Especially in view of engineering applications, a recommended finishing touch is that of cautiously using Occam's razor to cut out the often useless, confounding, and oversophisticated higher-order terms mentioned above. Consider that long-lasting laboratory tests and mature reflection on the supplied databases ultimately persuaded this investigator on the validity of the claimed hybrid model. The adopted theoretical scheme has been derived imparting, after R. E. Kalman, in that lucid advice that reads “get the physics right, the rest is mathematics,”* which is thus rather against the largely complied with and competitive advice that could read “get the mathematics right, the rest is physics.” The compelling attraction exerted by the latter approach is, in general, questionable since the adopted mathematical structures invariably work well only in the confined domains of physics where they were conceived. Instead, a correct mathematical approach to an integral reality needs to be founded on a common theoretical substrate whose specialized aspects are permissible to the extent that it holds unbroken.

Perhaps the more striking aspect of the present coupled treatment is that a subsonic ion drift is instead seen to assume the discontinued configuration of a filamentary flow guided by a Laplacian-field pattern. This issue is in contrast with previous uncoupled theories according to which a space-filling ion flow is claimed to cross the drift region under the action of a Poissonian electric field. The raised difference is, in this author's opinion, the very cause of the commonly perceived departure between observables and theoretical predictions. This drawback is becoming increasingly unacceptable in view of the latest breakthroughs into avionics and turbomachinery, in relation to levitation or air propulsion by plasma actuators, and into geophysics and electromagnetic compatibility, in relation to ionosphere and pre-stroke mechanisms, to name just a few. Parenthetically, everything still remains to be done in evaluating whether this multichanneled corona-driven flow can be either fruitfully exploited in microfluidics—that is to say, as a substitute for diffusion-driven flow in microfluidic channels—or play a role in those geoelectric phenomena, classifiable as earthquake by-products, interfering with grounded sensitive systems. Even more traditional applications related to charge transfer—thus involving HVDC line environment, electrostatic precipitators, lightning protection systems, electrophotography, dry powder coating, ESD, ignition hazard, surface treatments of materials (fabric, etc.), and ozonizers—must be able to reap the benefits of research that has been carried out and reported in this book.

Several years ago, taking advantage of the sympathetic disposition of my collaborator Vitantonio Amoruso, I decided to bring together our experimental efforts to carefully understand the phenomenological aspects of the raised difficult problem. To this end, a patrimony of data, resulting from a three-decade activity developed in an ad hoc arranged department high-voltage laboratory, has organically been supplied. This has been made feasible by the special use of some unusual electrode assemblies. As a result, unexpected, submerged, or obliterated phenomena have been discovered and carefully taken into account in order for this unprecedented theory to be substantiated by convincing arguments. Therefore, the content of the book is preferentially addressed to all those who are employed in the forefront of research or are always willing to question currently available design paradigms.

The monograph is subdivided into five chapters, the first two and the remaining three separately authored, respectively, by my colleague Vitantonio Amoruso and the undersigned. Chapter 1 and 2 are written in the form of cursory commentaries on the basic phenomenology of corona activity (Chapter 1) and ion-drift theories (Chapter 2), whereas underlying principles of fluid dynamics are found in Chapter 3. The arguments treated in Chapter 1–3 are preliminary to the pair of key Chapter 4 and 5, the former providing deep insights into the physics of ion flows crossing drift regions by a joined theory, and the latter giving the necessary experimental support. It is suggested that the reader should take a look at the Introduction, where a more extended presentation of the chapter content is furnished in two respects: The reader will be able to better understand the scope and rationale of the book and comfortably discern those issues that might be of most interest to him or her.

Francesco Lattarulo

Note

*

Opening lecture IFAC World Congress—Prague, July 4, 2005.

Acknowledgments

On behalf of my coauthor, I would like to thank all the students who worked on their graduation theses on this subject and collected essential databases for the figures of Chapter 5 to be traced. In particular, I am grateful to F. V. Ambrico, R. Bronzino, G. Bulzis, D. De Luca, C. Florio, M. Rubini, and P. C. Schiavone for providing Figures 5.21; 5.27; 5.22–5.25; 5.6 and 5.7a; 5.17–5.19; 5.7b, 5.11, 5.14; and 5.10 and 5.13, respectively. Often reference is made to his/her life partner for help in checking the written material. This is not the case for my wife Gabri, merely because our common mother tongue is not English. Notwithstanding this, I have the good fortune of experiencing how she successfully contributes to achieving any objective in a mysterious way. Last, I owe a great debt of gratitude to Mary Hatcher, Associate Editor at John Wiley & Sons, for having commendably committed herself to the preparation of this book.

F. L.

Introduction

This book is divided into five chapters, (four of) which include one or more Appendices. The complexity of the subject matter accounts for the number of sections in each chapter. It is important to clarify that the purpose of this Introduction is not merely to summarize the separate items in an orderly fashion, but to provide an appropriate framework to enable the student to learn. Therefore, directly following a description of the content, the reader will find a brief comment about the reasoning behind the order of the material presented. The authors are confident that creating logical links among individual arguments in different sections of the book is the best way to present them as a whole. It is hoped that this will lead to improvements in technological applications traditionally accommodated in the wide realm of applied electrostatics, namely, wherever the notion of charge transfer applies to some extent. But that does not alter the fact that the book is especially tailored to the needs of individuals who are prone to examine the past with a critical eye and to create innovative ideas. Therefore, at the end of this Introduction, some suggestions are made that look far enough ahead at recent or unfamiliar applications where the theory can be appreciated.

Chapter 1 provides the reader with essential information about gas discharges, with special attention paid to different corona modes. These manifest when the designated active conductor is raised at a stationary potential with assigned magnitude and polarity. Several kinds of ionization processes and streamer mechanisms are addressed. The important role that photoelectrons and photoionization of gas molecules assume surrounding avalanches for self-propagating streamers to develop is stressed. Also, a description of Kaptzov's hypothesis applied to the electric field on the surface of active conductors is presented.

Chapter 2 is devoted to theoretical results, often achieved by experimental tests, derived from a collection of investigations on corona-originated unipolar ion flows and related effects. Usually, the Poissonian electric-field strength, charge density, and current density are taken as individual or collective surrogates in describing the electrical properties of ionized flows. The investigation is performed inside the drift region and, more often, on the inactive electrode because this has to play the dual role of collector for the impacting ions and measuring surface for the three parameters mentioned above. It is stressed that dealing with computational electrostatics of steady ion flows would imply resolving a homogeneous, fully nonlinear third-order partial differential equation. Apart from the difficulty in appropriately assigning all the boundary conditions to which the calculation is subject, the solution is an impossible task. This explains why it has not been concluded, because this survey makes it quite clear that the already long list of those that were and even currently are involved in attempting computational strategies—all invariably debatable for some reason—has been aimed at circumventing insuperable theoretical difficulties. As will be shown, use is basically made of the charge-drift formula and/or simplifying hypotheses applied to the boundary (notably, Kaptzov's hypothesis already introduced at the end of Chapter 1), to the ion trajectory pattern (this is the case for the familiar Deutsch's hypothesis conveniently introduced here), to the physical properties of the gaseous medium (extensively discussed in Chapter 3 and 4), and so on. Even more advanced computational resources, devised to do something about the far more difficult problem of waiving the above facilities, are often represented by arbitrary derivation of some boundary conditions.

Chapter 3 describes the basic notions of fluid dynamics that qualify as functional to the joined model that is being formulated. Conservation laws for mass, momentum, and energy, along with related ones, are conveniently expressed in differential form. The key notion of subsonic flow is introduced and, hence, due account is taken of enforcing the velocity field of the fluid particle to become solenoidal (a source-free one). This condition is then accomplished, for the reasons that will be explained in the next chapter, while also imposing a curl-less character on the flow. Combining the above pair of properties for the flow velocity is proved to be consistent with ionized particles slowly moving along preestablished Laplacian-field streamlines toward the collector. A reading of such a specialized dynamics is given, and identification of the constant energy density of the bulk motion with the kinetic energy is stressed. This issue is fully consistent with ionized particles flowing with zero conservative body forces, namely, as a result of some momentum transfer, by molecular collision, to the springing up ions before being injected into the field domain. It will be clear that in the end the above circumstances are equivalently interpreted as giving the gaseous fluid that fills the drift space excitation-field-independent properties, an issue of paramount importance exactly in view of the present application.

Chapter 4 describes an original coupled model for corona-originated unicharge flows. Starting from the primal, combinative notion of reduced mass-charge applied to the totality of gas particles forming the fluid, the common justification for classifying conduction in gases (this is the case for ion drift) and convection of charged molecules into two groups is then removed. As an overwhelming consequence, a kind of mutual influence between ion-drift velocity v and electric field E may occur, and that would explain their reciprocal identification. This is permitted to within a trivial factor, standing for ion mobility k, since a widely adopted low-field approximation pertaining to this investigation allows the physical relationship v = kE to hold. As extensively illustrated, the filamentary structure so given for the ionized flow is the logical consequence of the combined solenoidal and irrotational nature of the individual v- and E-fields that are about to be joined. In brief, any elemental current-carrying channel of the given multichanneled flow model behaves as a filamentary conductor along which the electrodynamic E-field and the ion velocity v-field are unidimensional and uniform. This appealing picture clashes with previous theories on ion drift and related arguments, even though some commendable attempts are also made here to regain them somehow. The raised disagreement is entirely expressed through those remarkable differences of a morphological nature that this coupled flow model shows in comparison to counterparts available to a large extent, all of them suffering from being uncoupled. In fact, the ion flow is enforced in the former model to become discontinued (in a filamentary sense) while being guided by a Laplacian-field pattern, whereas a continuous (in a space-filling sense) Poissonian-field pattern invariably derives from the latter. The treatment points out how uncoupled models have come under criticism since, even as they do not query the validity of the relationship v = kE, they actually contradict this equality. In fact, admission is made in uncoupled models for E = v/k to be a nonzero-divergence field, an attribute inconsistent with the subsonic classification of ion drifts invariably subject to solenoidal v-fields. In particular, this chapter offers opportunities for both (a) wide-ranging discussions on the very good reasons to finally substantiate Deutsch's hypothesis (DH) and (b) properly addressing the question of ion wind's source and blowing.

Chapter 5 gives substantiation to the cardinal equation [Eq. (4.25)] on which the filamentary ion-flow theory is founded. The experimental approach has been made possible by using some uncommon electrode assemblies and adopting ad hoc performed remote monitoring for suitable databases to be furnished. After these have been collected and carefully examined, a connection between the ion injecting mechanism and overall structure of the Laplacian field in the drift region is proved. As pointed out, even with the assistance of invariance principles, this discovery has been the deciding factor in safely claiming a filamentous nature for the category of ion flows.

Each chapter, with the exception of Chapter 1, is supplemented with Appendices treating the specific subjects summarized as follows:

Appendix 2.A—Warburg's cosine law customarily applied to the rod-plane corona.

Appendix 2.B—Bipolar ionized field, for the sake of completeness (bear in mind that monopolar ion flow is the main subject of the book).

Appendix 3.A—Thermodynamic quantities irrespective of the gaseous medium's (namely, at rest or subsonically moving) status.

Appendix 4.A—Emitter–collector relationships, involving ionized field parameters, through the key definition of channel density applied to the multi channeled flow model at hand.

Appendix 4.B—Governing equations for diffusional effects and related influence on the boundary conditions.

Appendix 4.C—Viscosity–mobility relationship for gases, after Walden's rule applied to liquids, an issue consistent with the coupled model.

Appendix 4.D—Substantial derivatives involved to theoretically show inherent consistency of the relationship

v

=

k

E

with the expected

v

- and

E

-fields' potential distributions.

Appendix 5.A—Subsidiary theoretical arguments to sustain generalization of Warburg's law (see also before Section 2.4.1 and Appendix 2.A). Accordingly, exponent

n

of the common cosine law is proved to assume specific integers, at least for the 2D cases studies listed in

Table 2.1

.

For the reader's convenience, some links are made according to the following outline:

Owing to the interdisciplinary character of the treated subject, those who are familiar with electromagnetism but have no knowledge of fluid dynamics may be surprised to find some terminological differences in describing common vector properties. This is especially the case in reading

Chapter 3

, where use of the locution “vorticity” of an unspecified vector

F

in the substitution of “circulation” of

F

, both to mean rot

F

. Additionally, an isochoric flow is nothing but a solenoidal (or source-free) flow in the

v

-field, for which div

v

= 0 (

v

stands for flow velocity).

The set of potentials applied, in particular, to the partially covered wire (Section 5.5) allow photoionization-promoted initiatory phenomena (Section 1.2.4) occurring in some receded locations external to and all around the cover to be neglected. This permission cannot be denied against a comparison with that strong activity concentrated on the uncovered fractional amount of the entire wire surface corresponding to the slot. Such an observation is made as an attempt to focus, by elimination, on a tangential spreadout of ions from the slot, a phenomenon supposedly dominated by an initially strong diffusional thrust prior to their outward injection (Sections 4.3.1, 4.4.2, and 4.6 and Appendix 4.B).

In spite of a pulsative corona activity (Sections 1.9.2 and 1.9.3), the elementary pulses may be assumed to merge in time (Appendix 4.B), compatibly with the applied voltage. Provided that this remains unchanged, the ion flow appears substantially steady, as the corona current does even at lower voltages (here and there in Sections 4.3, 4.4.2, and 4.5.2). This implies that time-independent governing equations for the potential of the electric field in the presence of space charge (Sections 2.2.1 and 4.3), and related parameters, are adopted. Even admitting that unsteady dynamics can occur, the contribution of the variable magnetic field is expected to be comparatively unimportant for the present class of problems (Section 4.3.5).

The otherwise tested and widely adopted low-field assumption (Sections 4.2 and 4.3.7) for the equality

v

=

k

E,

with

k

denoting a constant mobility (Section 2.1), tacitly gives arguments to substantiate the coupled model subject to rot

E

and div

E

both dropping to zero (Section 4.5.2 and Appendix 4.D). It is common knowledge that the first condition is distinctive of electric fields, whereas it is quite disregarded elsewhere that even the second condition legitimately applies. This by virtue of the novel definition of reduced mass-charge (Sections 4.1–4.3), which leads to div

E

= 0 for the electric field in an ion-drift region. Here, the velocity is notoriously subsonic, whereby div

v

= 0 and, in turn, div

E

= 0 simultaneously apply (Sections 3.2, 3.9.2, 3.10, 3.11.3, 3.12.1, and 3.12.2 and Appendix 3.A).

As previously mentioned, ion flows rigidly guided by Laplacian fluxlines (this is a prominent feature in the present treatment) are in fact fully responsive to DH, an argument around which ion-flow models procrastinated for far too long (Sections 2.3 and 2.6). An in-depth analysis now enables us (Section 4.3.8) to pursue the penultimate aim of incidentally proving its definitive validity and the ultimate aim of giving further arguments in favor of the filamentary model. Overall, this object has been achieved in an articulate manner, first remembering that real gases under ordinary ambient conditions can be safely treated as being ideal and then verifying that the thermodynamic quantities associated with the flow hold constant in practice (Appendix 3.A). As can be seen, the inquiry into the cause of DH has to progress through a series of arguments involving fluid dynamics as well (additionally, see Sections 3.5.3 and 3.7). This turns out to be the prerequisite for a self-consistent final formulation of the coupled ion-flow model.

Those who are aware of the difficulties that arise in attempting direct detection of the injection mechanism and consequent low-energy ion-swarm scenario know full well the value of indirect laboratory tests. These have been profitably performed to ultimately sustain the hard inverse problem of reconstructing distribution laws at the emitter (Appendix 4.A) by distanced measurements at the collector (Sections 5.2–5.7).

As already mentioned in the Preface, prominent importance could be currently ascribed to prototyping some devices for avionic applications. The spotlight is now on the electrostatic levitator and plasma actuator—the former presumably, the latter surely, based on the ionic wind for air propulsion. In addition, usually performed performance surrogates, as with pressure ratio, efficiency, and rotor power for some rotating engine studies, are also theoretically evaluated in understanding how the flow control actuation can be exploited in the best possible way. A reference is reported here, in the presentation of Chapter 4, toward the end, regarding the byproduct of corona activity represented by the ionic wind. Briefly, we have to look at the whole question that there is a need to differentiate the motion of the charge carriers under examination, whether it is subsonic or sonic/supersonic. With particular reference to levitation, it is a key point that should give rise to a more thorough study of the ion wind's genesis and blowing. Putting it bluntly, this is about being aware of the fact that as soon as the supersonic ion velocity switches to subsonic, namely, when recently formed (in the ionization region) unicharges with the same polarity of the active conductor are injected into the wider drift region, then the ion wind is predicted here to be generated only at the interface between those regions. This as a result of a type of momentum-transfer mechanism concentrated in close proximity to the active electrode because of the short dimensions of the ionization region. Therefore, such a description conflicts with previous expectations according to which levitation forces are instead permitted to enliven ion wind inside the drift region, throughout. As an immediate consequence, even cutting-edge 3D packages implemented for a theoretical simulation of device attributes cannot be immune to criticism and, hence, cannot prevent concerted design paradigms from being revisited. Currently, this is a cause for concern since the above computational codes show limitations in capturing the effects under examination. As regards the efficiency of a type of plasma actuator, the abrupt passage from the ionization to drift region could be separated by the ionic wind flow by constructional artifices. But the fact remains that carefully describing the morphology of the ionization region can importantly contribute to efficiency estimations even when the actuation is essentially due to an alternative electric field causing a dielectric-barrier discharge plasma. To this end, the subject matter treated in this book can be complemented with the electron component for the active zone to be theoretically analyzed. In any case, the model gets insights into the strong dependence of the plasma performances on some key factors for which the designer must have due regard. For instance, reference could be made to the role that diffusion can play in steadily shaping the peripheral region of the plasma. Additionally, it may be that some unwanted subsonic flows of charges, embedded somewhere in that region presumably occupied above all else by supersonic flows, can as such significantly modify the overall performances of the prototype. Passing now to a different problem, consider that electromagnetic interferences involving sensitive components could also be those caused by geophysical phenomena in the atmosphere, even those occurring at the Earth's level. The victims are on-board and on-ground electric power and communication systems that happen to be installed where a thunderstorm or tectonic activity is taking place, or thereabouts. The most important effect connected to the former activity is lightning and related preliminary phenomena. In particular, appropriately addressing pre-stroke models is a crucial exercise finalized to estimate the expected preventing or intercepting features of air terminals usually adopted as lightning protection systems. Of course, the same models can be used to predict preliminary mechanisms involving inadvertent interceptors. Interpreting the active head of the descending leader as the endpoint of a current impressed slanting filament could be useful in better investigating the intercepting attributes of intentional and unintentional structures. Therefore, the investigation cannot be performed without relying upon a suitable ion-drift model. With special interest in the second case study, which is an unexplored one, let the upper half space be exceedingly ionized by radon efflux presumably accompanying earthquake episodes, and let a background electric field be simultaneously present. Under these circumstances, ion flows formed in the atmosphere can induce an Earth-surface potential. Spurious currents are permitted to carry down the length of lines where mutually distanced and grounded susceptible equipments can be connected. Even though the extent and severity of this interfering mechanism vary considerably, the subject may be of interest for electromagnetic compatibility investigations. Because geoelectric phenomenology is quite similar, in a qualitative sense, to that determined by exceptional geomagnetic storms, it deserves attention.

Principal Symbols

a

electrode spacing; emitter elevation (unless otherwise specified)

a

p

characteristic length of a fluid particle

A

action

A

0

neutral gas atom in the normal state

A

T

Townsend formula constant

A

*

atom in the excited state

A

**

metastable

b

inter-axis distance between parallel cylinders

b

coordinate

B

magnetic flux density

B

0

neutral gas atom in the normal state

B

T

Townsend formula constant

c

speed of light in free space

c

m

dimensionless coefficient

c

s

local speed of sound

d

diameter

d

cathode-to-anode distance

d

x

coordinate

dA

streamtube or fluxtube cross-sectional area

dA

m

molecule surface area

dV

m

molecule volume

D

diffusion coefficient

D

rate-of-strain tensor; electric displacement

substantial (or material) derivative

e

i

specific internal energy

e

k

kinetic energy per unit mass of the bulk motion

e

t

total kinetic energy per unit mass

E

electric field strength

E

electric field

E

L

Laplacian electric field

E

0

detected corona onset electric field

f

m

body force

F

force

h

sphere center suspension; emitter elevation (in some cases, instead of

a

)

h

Planck's constant

h

f

focal length of confocal ellipsoids

h

0

height of a spherical equipotential with short radius

h

s

height of the center of a spherical electrode

h

ν

photon quantum of energy

H

magnetic field

i

c

steady current carrying a thin wire

I

channel carrying electric current; corona current

I

unit tensor

IP

injection point

J

current density

K

B

Boltzmann's constant

k

ion mobility

K

dimensionless constant

K

′

dimensionless constant

K

n

Knudsen's number

l

dimensionless scalar function of position

scalar function of position

L

fluxtube median line length; streamline, fluxline, or ion trajectory length

L

Lagrange function

L

D

diffusion distance

L

-

longitudinal-type

m

roughness factor

m

c

ion mass

m

0

mass of a single molecule

M

Mach number; mass of neutrals

M

e

number of secondary electrons released at the cathode per emitted primary electron

n

number density

n

outwardly directed unit vector

n

c

number of electrons emitted from the cathode surface; ion number density

n

0

initial number of electrons emitted from the cathode

number of electrons emitted by secondary ionization processes

n

x

increased number of electrons at distance

x

from the cathode

N

total number of channels

N

c

total number of primary ionizing collisions in the gas per primary electron emitted from the cathode; critical size of an avalanche

p

thermodynamic pressure

P

e

Péclet's number

q

c

ion's charge

heat flux density vector

r

radius

r

particle position

r

0

short radius of a spherical equipotential

r

s

radius of a spherical electrode

R

radius

R

i

ionic recombination coefficient

RSP

referential source point

S

surface

S

tensor

t

time

fluid absolute temperature

T

Cauchy stress tensor

T

k

total kinetic energy

T-

transversal-type

u

force unit vector

U

constant energy density of the bulk motion

v

velocity (modulus

v

)

v

D

diffusion velocity

v

m

gas velocity

vv

dyadic

V

volume

V

b

breakdown voltage

V

0

potential of a spherical equipotential with short radius

V

T

corona onset voltage

w

temperature-dependent average speed of a molecule

w

wind speed

w

e

atom excitation energy

w

i

atom ionization energy

w

k

average kinetic energy acquired by a particle carrying a charge

q

W

potential energy per unit volume

W

E

electrostatic potential energy density; work of charging

W

t

total positional energy density

W

**

energy of a metastable

x

coordinate

x

0

coordinate

x

ξ

coordinate

y

coordinate

α

isothermal compressibility coefficient

primary ionization coefficient

α

e

number of ionizing collision per unit length made by an electron

α

i

injection angle

α

j

cone angle

α

t

tilting angle

α

v

inclination angle

effective ionization coefficient

β

bulk expansion coefficient; azimuthal angle

γ

angular deviation

γ

efficiency of secondary electrons' emission process (Townsend secondary coefficient)

Γ

streamline, fluxline, or ion trajectory length

Γ

generic tensor

δ

l

oriented segment of a linear particle

medium permittivity

ζ

collision period; dimensionless factor labeling a circular fieldline

η

attachment coefficient

θ

semi-vertical cone or wedge angle of discharge

λ

mean free path

λ

p

radiated photon wavelength

μ

viscosity; medium permeability

μ′

second coefficient of viscosity

ν

kinematic viscosity

ξ

angular deviation

ξ

a

dimensionless factor

ρ

reduced-charge density

ρ

c

ion charge density

ρ

m

mass density; reduced-mass density

σ

T

fluid heat conductivity

τ

tangential shear stress; time-of-flight

τ

D

diffusion time

τ

external force per unit surface

υ

proportionality factor

Φ

unspecified agent

Ψ

unspecified agent

φ

E

Poissonian electrostatic potential

Laplacian electrostatic potential

Stokes' scalar potential for the velocity

Stokes' vector potential for the velocity

Ω

0

ion's collision cross section

ω

equipotential line parameter

Laplace operator

Chapter 1Fundamentals of Electrical Discharges

1.1 Introduction

Natural phenomena, such as gamma rays produced by radioactive decay processes in the soil and cosmic radiation originating from solar flares and other galactic objects, can ionize the air molecules and give rise to free electrons and positive and negative ions. Under normal conditions of temperature and pressure, the conduction in air at low field ranges from 10−16 to 10−17 A/cm2 in proximity to the Earth's surface, so normally air could be considered an excellent insulating material. When in an air-filled volume the electron concentration increases, an electrical breakdown process takes place and this gas becomes conductive.

1.2 Ionization Processes in Gases

As defined in IEEE Std. 539 (2005), the term “ionization” indicates “the process by which an atom or molecule receives enough energy (by collision with electrons, photons, etc.) to split it into one or more free electrons and a positive ion.” This kind of collision is called inelastic