Plasma Formulary for Physics, Astronomy, and Technology E-Book

Declan Diver

• Herausgeber: Wiley-VCH
• Kategorie: Lebensstil
• Sprache: Englisch
• Veröffentlichungsjahr: 2013

Seitenzahl: 211

Beschreibung

Plasmaphysik hat sich in den letzen Jahren rapide entwickelt und Einfluss auf verschiedene andere Forschungsgebiete in Physik, Chemie und Astrophysik, aber auch in der industriellen Praxis gewonnen. An all jene, die sich mit Plasmen oder ionisierten Gasen beschäftigen, wendet sich diese Nachschlagewerk: Es bietet eine kompakte, übersichtliche Zusammenstellung grundlegender Formeln und Definitionen, illustriert durch Tabellen und Abbildungen. Auf langwierige Ableitungen wird verzichtet; ein mathematischer Anhang vermittelt die wichtigsten verwendeten Methoden. Ein Literaturverzeichnis auf dem neuesten Stand gibt Anregungen zum tieferen Eindringen in die Materie. Alle Aspekte der Plasmaphysik werden erfasst, inklusive Fusionsplasma - ein unverzichtbares Nachschlagewerk für Physiker, Astrophysiker und Ingenieure.

Leseprobe

Contents

Preface to the Second Edition

Preface to the First Edition

1 Basic Physical Data

1.1 Basic Physical Units

1.2 Maxwell’s Electromagnetic Equations

1.3 Special Relativity

1.4 Physical Constants

1.5 Dimensional Analysis

1.6 Ionization Energies of Gas-Phase Atoms and Molecules

1.7 Electron Affinities of Selected Atoms and Molecules

1.8 Atomic and Molecular Notation

1.9 Characteristic Parameters for Typical Plasmas

2 Basic Plasma Parameters

2.1 Notation

2.2 Natural Timescales

2.3 Natural Scale Lengths

2.4 Natural Speeds

2.5 Miscellaneous Parameters

2.6 Nondimensional Parameters

2.7 Parameter Relationships

3 Discharge Plasmas and Elementary Processes

3.1 Notation

3.2 Plasma Sheath

3.3 Double Layer

3.4 Diffusion Parameters

3.5 Ionization

3.6 Ionization Equilibrium

4 Radiation

4.1 Notation

4.2 Radiation from a Moving Point Charge

4.3 Cyclotron and Synchrotron Radiation

4.4 Bremsstrahlung

4.5 Radiation Scattering

5 Kinetic Theory

5.1 Notation

5.2 Fundamentals

5.3 Boltzmann Equation

5.4 Maxwellian Distribution

5.5 Relativistic Maxwellian

5.6 Vlasov Description

5.7 Collisional Modeling

5.8 Driven Systems

6 Plasma Transport

6.1 Notation

6.2 Basic Definitions

6.3 Binary Collisions

6.4 Particle Dynamics

6.5 Transport Coefficients

7 Plasma Waves

7.1 Notation

7.2 Waves in Cold Plasmas

7.3 Fluid Plasmas

7.4 Waves in Hot Plasmas

8 Flows

8.1 Notation

8.2 Fundamental Results

8.3 Hydromagnetic Flows

8.4 Solar Wind

8.5 Neutral Gas/Magnetized Plasma Flows

8.6 Beams

8.7 Hydromagnetic Shocks

8.8 Ion-Acoustic Shock

9 Equilibria and Instabilities

9.1 Notation

9.2 General Considerations

9.3 Fluid Equilibria

9.4 Fluid Instabilities

9.5 Kinetic Instabilities

10 Mathematics

10.1 Vector Algebra

10.2 Vector Calculus

10.3 Integral Theorems

10.4 Matrices

10.5 Eigenfunctions of the Curl Operator

10.6 Wave Scattering

10.7 Plasma Dispersion Function

Appendix: Guide to Notation

List of Figures

List of Tables

References

Index

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The Author

Dr. Declan A. Diver Dept. of Physics & Astronomy University of Glasgow Glasgow, United Kingdom

[email protected]

Cover PictureGrafik-Design Schulz, Fuβgönnheim, Germany

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Preface to the Second Edition

This revised edition contains hopefully additional useful data, including atomic and molecular information. Once again I am very grateful for the tireless efforts of the team at Wiley-VCH, particularly Ulrike Werner and Vera Palmer, whose patience with my missed deadlines is very much appreciated.

Glasgow, November 2012

Declan Andrew Diver

Preface to the First Edition

Plasma physics has rapidly matured as a scientific and technological discipline with a vast span of relevant applications in many different fields. As a consequence, no single textbook is able to address all aspects of plasma physics that are relevant to such a burgeoning community.

With this reference text, I have attempted to bridge the gap between the excellent variety of traditional, broadly-based plasma books, and more specialist, device-oriented reference texts. David L. Book’s NRL Plasma Formulary was an inspiration, as too was André Anders’ Formulary for Plasma Physics; however, I believe that this book offers a different perspective which makes it complementary to existing handbooks. I have tried to give the reader an overview of the key aspects of plasma physics without being too much of a specialist in any particular area. Since this book is not a textbook, there is more room for not only contemporary findings, but also many traditionally established results from the 1950s and 60s that are not often found in modern texts, and which are once more becoming important as imperfectly ionized and bounded plasmas enjoy a resurgence in relevance.

The diverse nature of the plasma science community is matched by a confusing miscellany of physical units. Throughout this handbook, all formulae are quoted in both SI and cgs-Gaussian units where it is relevant. I hope this will maximize the book’s practicality and utility, and perhaps even assist the whole community in the smooth transition to using SI units only…

It has been a guiding principle to reference the source (or sources) of any formula quoted in this book, together with whatever caveats or restrictions that apply to its use. Where practical, I have referenced the original articles, subject to the important constraint that verifiable sources are accessible to the general reader. Please accept my apologies in advance for any misquotes or omissions, and please do let me know about them. As for the formulae themselves, I am indebted to Professor E.W. Laing for his patient and exacting examination of the manuscript, which led to the elimination of a very large number of errors. Thanks are also due to my colleagues Brendan Dowds, Hugh Potts, Richard Barrett, Graham Woan, Norman Gray and Graeme Stewart, for answering endless questions on formatting and graphics, and pointing out still more howlers in the ith iterate of the book. Despite all this invaluable and talented assistance, I have no doubt that there remain, lurking in dark corners of the text or even brazenly displayed in large, open areas, errors in physics and formatting. I have no excuse; please let me know, and I shall correct these mistakes.

I am also grateful to Professor Ken Ledingham for letting me use his wonderful image of a laser-produced plasma plume; likewise, to Professor Bill Graham for the beautiful high-pressure discharge picture.

It is appropriate to acknowledge the kind support offered by David Hughes in guiding me initially on this project, and additionally, Vera Dederichs for patiently enduring one delay after another in its prosecution. Thanks are also due to Professor A.E. Roy for much wise advice at the outset. Finally, I am grateful to my institute for granting me the sabbatical leave which was instrumental in allowing me to complete the book.

Glasgow, July 2001

Declan Andrew Diver

1

Basic Physical Data

1.1 Basic Physical Units

1.1.1 SI Units

Table 1.1 Fundamental and supplementary SI units.

Quantity

Unit

Abbreviation

Fundamental Units

Amount of substance

mole

mol

Electrical current

ampere

A

Length

meter

m

Luminous intensity

candela

cd

Mass

kilogram

kg

Plane angle

radian

rad

Solid angle

steradian

sr

Temperature

Kelvin

K

Time

second

s

Selected derived units

Capacitance

farad

F

Current density

ampere per square meter

A/m

2

Electrical charge

coulomb

C

Electric potential

volt

V

Electrical resistance

ohm

Ω

Energy

joule

J

Frequency

hertz

Hz

Force

newton

N

Inductance

henry

H

Magnetic flux

weber

Wb

Magnetic flux density

tesla

T

Power

watt

W

Table 1.2 Standard prefixes for SI units.

1.1.2 cgs-Gaussian Units

For a useful overview of non-SI units, see [1].

Table 1.3 Comparison of SI and cgs units.

1.2 Maxwell’s Electromagnetic Equations

Table 1.4 Maxwell’s equations.

Boundary conditions The boundary conditions at an interface for Maxwell’s electromagnetic equations are that the tangential component of E, and the normal component of B, must each be continuous, where normal means parallel to the local normal vector to the interface, and tangential means in the plane perpendicular to the local normal.

1.3 Special Relativity

Table 1.5 Lorentz transformations.

1.4 Physical Constants

The values of the constants quoted here are the 2006 CODATA recommended values [3].

Table 1.6 Values of physical constants.

1.5 Dimensional Analysis

Table 1.7 Dimensions of common variables.

1.6 Ionization Energies of Gas-Phase Atoms and Molecules

The energies of first ionization Ei for certain gas-phase molecules are given here, selected from [4]

Table 1.8 Ionization energies of gas-phase atoms and molecules

Substance

Formula

E

i

/eV

Acetylene

C

2

H

2

11.400

Ammonia

NH

3

10.070

Argon

Ar

15.759 62

Boron

B

8.298 03

Calcium

Ca

6.113 16

Carbon dioxide

CO

2

13.773

Carbon monoxide

CO

14.014

Chlorine

Cl

12.967 64

Chlorine

Cl

2

11.480

Chlorosilane

ClH

3

Si

11.4

Cyanide

CN

13.598 4

Disodium

Na

2

4.894

Ethylene

C

2

H

4

10.513 8

Fluorine (atomic)

Fl

17.422

Fluorine

Fl

2

15.697

Formaldehyde

CH

2

O

10.88

Formic acid

CH

2

O

2

11.33

Helium

He

24.587 41

Hydrogen (atomic)

H

13.598 44

Hydrogen

H

2

15.425 93

Hydrogen chloride

HCl

12.749

Hydrogen sulfide

H

2

S

10.457

Hydroxyl

HO

13.017 0

Krypton

Kr

13.999 961

Mercury

Hg

10.437 50

Methane

CH

4

12.61

Methanol

CH

3

OH

10.85

Methyl

CH

3

9.843

Methylene

CH

2

10.396

Neon

Ne

21.564 54

Nitrogen

N

14.534 14

Nitrogen

N

2

15.580 8

Oxygen

O

13.618 06

Oxygen

O

2

12.069 7

Silane

SiH

4

11.00

Silicon

Si

8.151 69

Sodium

Na

5.139 08

Tetrachloromethane

CCl

4

11.47

Tetrachlorosilane

SiCl

4

11.79

Water

H

2

O

12.620 6

Xenon

Xe

12.129 87

1.7 Electron Affinities of Selected Atoms and Molecules

The electron affinity EA is defined to be the energy difference between the ground state of the neutral, and the lowest energy state of the corresponding negative ion. If EA > 0, then the negative ion is stable; if EA < 0, the negative ion is unstable. Selected data is presented below, drawn from [4, 5]

Table 1.9 Electron affinities of selected atoms and molecules.

Substance

Formula

E

i

/eV

Aluminum

Al

0.432 8

Argon

Ar

–

Beryllium

Be

–

Boron

B

0.279 7

Calcium

Ca

0.024 55

Carbon

C

1.262

Chlorine (atomic)

Cl

3.613

Chromium

Cr

0.675 84

Cobalt

Co

0.663 3

Copper

Cu

1.235

Deuterium

D

0.745 6

Fluorine (atomic)

F

3.401

Helium

He

–

Hydrogen

H

0.7541

Iron

Fe

0.151

Krypton

Kr

–

Lithium

Li

0.618 0

Magnesium

Mg

–

Manganese

Mn

–

Nickel

Ni

1.157 16

Nitrogen (atomic)

N

–

Neon

Ne

–

Oxygen (atomic)

O

1.461

Phosphorus

P

0.746 5

Potassium

K

0.501 459

Scandium

Sc

0.188

Silicon

Si

1.390

Sodium

Na

0.547 9

Sulfur

S

2.077

Titanium

Ti

0.084

Tritium

T

0.754 8

Vanadium

V

0.525

Xenon

Xe

–

Diatomic molecules

Carbon

C

2

3.27

Chlorine

Cl

2

2.28

Cyanide

CN

3.862

Fluorine

F

2

3.01

Methylidine radical

CH

1.238

Oxygen

O

2

0.450

Disilicon

Si

2

2.201

SiH

1.277

TiO

1.30

Triatomic molecules

C

3

1.981

CCl

2

1.593

CF

2

0.180

CH

2

0.652

C

2

O

2.311

Ozone

O

3

2.103

SiF

2

0.10

Si

2

F

1.99

SiH

2

1.124

Si

2

H

2.31

Si

3

2.29

Titanium dioxide

TiO

2

1.59

Water

H

2

O

1.078

1.8 Atomic and Molecular Notation

1.8.1 Atomic Electron Configurations

The electronic configuration in atoms is characterized by four quantum numbers (n, l, ml, ms) that define the distribution of electrons across the available atomic levels and orbitals, with no two electrons allowed to share the same four quantum numbers (the Pauli Principle). The classification is arranged in descending significance in terms of energy contribution.

1.8.1.1 Principal Quantum Number, n

1.8.1.2 Azimuthal Quantum Number, l

Figure 1.1 The angular dependence of the s, p and d orbitals, showing symmetry about the principal (horizontal) axis.

1.8.1.3 Magnetic Quantum Number, ml

Given that an electron is in subshell l, its angular momentum component along the principal axis (the main symmetry axis for the wavefunctions) is further quantized by the magnetic quantum number ml, which can take integer values in the range (–l, –l + 1,…, 0,…, l – 1, l), yielding 2l + 1 states in total.

1.8.1.4 Spin Quantum Number, ms

Finally, there are two spin states for each electron in any n, l, ml state: spin-up and spin-down, corresponding to .

As a consequence of the distribution of electrons across the possible angular momentum, magnetic and spin quantum states, the total number of electrons in each of the principal quantum levels is 2n2, as can be seen from Table 1.10. In the standard notation for the configuration of electrons in an atom, each shell and subshell is given as a character string, with the number of electrons in each subshell stated as a superscript on the l value: for example, the configuration of electrons in He can be stated as 1s2; for Carbon atoms, 1s22s22p2, and so on. The ground-state configuration of selected atoms is given in Table 1.11.

Table 1.10 Atomic notation: under each principal quantum number, the subshells are denoted, along with the number of electrons per subshell.

Table 1.11 Electronic configuration of ground states for selected atoms.

Atom

Ground state

Comment

H

1s

He

1s

2

filled

K

shell

Li

1s

2

s

filled

K

shell

Be

1s

2

2s

2

filled

K

shell

B

1s

2

2s

2

2p

filled

K

shell

C

1s

2

2s

2

2p

2

filled

K

shell

N

1s

2

2s

2

2p

3

filled

K

shell

O

1s

2

2s

2

2p

4

filled

K

shell

F

1s

2

2s

2

2p

5

filled

K

shell

Ne

1s

2

2s

2

2p

6

filled

K

,

L

shells

Na

[Ne]3s

filled

K

,

L

shells

Si

[Ne]3s

2

3p

2

filled

K

,

L

shells

Ar

[Ne]3s

2

3p

6

filled

K

,

L

,

M

shells

Table 1.12 Selected significant spectral lines of atomic and singly ionized elements, as observed in air, and chosen for the greatest relative intensity; * denotes Fraunhofer lines.

Atomic spectra arise when electrons make the transition from one set of (n, l, ml, ms) to another, losing energy by emission of photons (or gaining energy by absorption). Examples of important spectra are given in Table 1.12.

1.8.1.5 Multielectron Atoms

For atoms with several electrons [6], there is strong electrostatic coupling between the orbital angular momentum and the spins across the populated states, leading to additional energy structure in the electronic configuration.

The total resultant orbital angular momentum vector arising from the li of the electrons in the atom is a quantum vector denoted as L. The underlying quantization comes from the interaction of electrons with different values of n and l, and is expressed in the quantum-mechanical vector addition of the associated vector angular momenta li to produce a resultant total orbital angular momentum L, the possible quantized values of which are given by ml. In a similar way, the resultant of the quantum spins over the ms,i is designated by S. These resultants, L and S, can be added to produce a total resultant angular momentum J of the electrons in the atom, which is also quantized. The magnitude of the quantized resultant of L and S can only take the values L + S, L + S – 1,…, |L – S|, denoted by J (this is a general rule for all quantum vectors).

1.8.1.6 Selection Rules for Transitions

For electric dipole transitions, the following rules apply:

1.8.1.7 Emission and Absorption

The spectral emission coefficient ε(ν) due to a spontaneous electronic transition from an upper state u to a lower state l in an atom resulting in the emission of a photon of frequency nu0 is given by

(1.1)

In the case of electric dipole transitions, Aul is defined to be

(1.2)

where μul is the transition dipole moment.

1.8.2 Molecular Electron Configurations

The configurations of electrons in molecules is more complicated than the single atom case because the nuclear motion of the constituent species influences the electron energy levels, along with the persistent internuclear electric field that bonds the molecule together [7, 8].

The ground electronic state of a molecule is designated by X, with excited states of the same multiplicity (i.e., spin quantum number in Section 1.8.2.3) as the ground state denoted by A, B, C,… in ascending order of energy; if excited states have a different multiplicity from the ground state, then these states are labeled with lower-case letters a, b, c,… The details of the electronic configurations in such states is given in the following paragraphs, which apply mainly to diatomic molecules.

1.8.2.1 Born–Oppenheimer Approximation

The Born–Oppenheimer approximation separates out the nuclear motion (vibration and rotation) from the electron behavior, under the assumption that the electrons will move much faster than the heavier nuclei. This assumption means that the electronic transition energies Eel (a few eV) are taken to be much larger than the vibrational energies Evib (around 0.1 eV), which in turn are much larger than the rotational energies Erot (a few meV):

(1.3)

1.8.2.2 Λ Quantum Number

1.8.2.3 Spin Quantum Number

1.8.2.4 Molecular Term Notation

Table 1.13 Molecular electronic state notation, showing the associated quantum numbers and electron degeneracy g.

1.8.2.5 Symmetry

The symmetry of the electron orbitals is a further complication: for a homonuclear molecule, the electron density must be symmetric with respect to the midpoint between the nuclei (that is, the center of mass), but the wavefunction of the electron can be even or odd parity, denoted g or u, respectively (from the German gerade and ungerade). For Σ states, symmetry of the wavefunction with respect to a mirror reflection through a plane containing the internuclear axis is denoted by a right superscript + if symmetric; – if not.

1.8.2.6 Selection Rules for Transitions

Electric dipole transitions between electronic levels in diatomic molecules obey the following selection rules:

The spectra of molecules is considerably more complex than that of atoms because of the more extensive range of possible transitions. Molecular spectra consist of bands, which are very tightly grouped series of emission (or absorption) lines within an amplitude envelope that may extend only for a few nanometers. The spacing of the lines within the band head is controlled by electron transitions between the molecule’s rotational states. The envelopes are not symmetric: the conspicuous sharp edge is termed the band head, with the envelope fading smoothly in amplitude towards increasing wavelength (termed ‘degraded to red’) or decreasing wavelength (‘degraded to violet’).

Certain molecules exhibit very extensive band systems that span wide spectral ranges with little variation in band intensity or structure, such as H2 (more than 100 strong bands between 406 and 835 nm), Cl2 (mixture of continuum and band emission in 480–600 nm, strong continuous absorption in 250–400 nm), CO (198–860 nm, including third positive, Asundi, triplet, Cameron, 3A, Knauss & Kaplan bands, in addition to those in Table 1.14).

Table 1.14 Selected significant molecular spectral bands, as observed in air, and chosen for greatest relative intensity; § denotes extensive number of bands of similar intensity in the indicated wavelength range, with more prominent heads identified in final column; r, v denotes degraded to red, violet; * denotes forbidden line. Data taken from [9], with additional information on ozone from [10].

1.9 Characteristic Parameters for Typical Plasmas

1.9.1 Laboratory Plasma Reactors

There is a wide variety of vessel and electrode geometry in laboratory devices; the following list is indicative, but not exhaustive. Table 1.16 gives typical operating parameters for various plasma devices.

1.9.1.1 Corona Discharge

Also known as ‘point-to-plane’ discharge [11, 12], the ionizing electric field is produced by a marked asymmetry in the electrodes. The standard configuration, shown in Figure 1.2, is a sharply pointed electrode paired with a planar electrode, with the former producing a localized high electric field sufficient to ionize the neutral gas, and strike a plasma; a similar effect can be produced by electrodes in the form a wire inside a hollow cylinder. The ionization region is generally confined to a small area close to the high-field electrode, producing a drift region (between the ionization region and the flat electrode) in which charged particles (mainly electrons) react with neutrals and induce electron-moderated chemical reactions, including radical production. If the electric field is very high, plasma streamers can extend the ionizing region to encompass the second electrode. It is suitable for use over a wide range of pressures (including atmospheric), with applications that include ozone production, surface modification and combustion promotion.

1.9.1.2 Dielectric Barrier Discharge

Also known as silent discharges, dielectric barrier discharges (DBD) [13] generally consist of a pair of AC-powered plane electrodes with at least one covered in a dielectric layer (Figure 1.3). The neutral gas breaks down in the usual manner, forming streamers. However, when the streamers bridge the gap between the electrodes, the dielectric layer allows free charge to accumulate which significantly affects the ongoing development of the discharge, including self-quenching. In particular, charge accumulated from one half-cycle of AC power is available to enhance the field in the subsequent half-cycle.

Figure 1.2 Typical configuration of a point-to-plane corona discharge, showing a plasma ionization region close to the high field at the point electrode, and the region of ion drift impinging on the flat electrode plate.

Figure 1.3