Table Of ContentSwarms of
Ions and Electrons
in Gases
Edited by
W. Lindinger, T. D. Miirk,
and F. H oworka
Springer-Verlag Wien New York
Prof. Dr. Werner Lindinger
Prof. Dr. Tilmann D. Mark
Prof. Dr. Franz Howorka
Institut fUr Experimentalphysik,
Universitiit Innsbruck, Austria
This work is subject to copyright.
All rights are reserved, whether the whole or part of the material is concerned,
specifically those of translation, reprinting, re-use of illustrations, broadcasting,
reproduction by photocopying machine or similar means, and storage in data banks.
© 1984 by Springer-VerJag/Wien
Softcover reprint of the hardcover 1st edition 1984
With 82 Figures
Library of Congress Cataloging in Publication Data. Main entry under title: Swarms of ions and electrons in gases. Includes index.
I. lon.-Congresses. 2. Electrons-Congresses. 3. Gases-Congresses. 4. Collisions (Nuclear physics)-Congresses.l. Lindinger, W.
(Werner), 1944-. II. Mark, T. D. (Tilmann D.), 1944-. III. Howorka, F. (Franz), 1937-. QC702.S93. 1984.530.4'4.84·10485.
ISBN-13:978-3-7091-8775-3 e-ISBN-13:978-3-7091-8773-9
DOl: 10.1007/978-3-7091-8773-9
Preface
Our understanding of elementary processes in plasmas has been increasing
dramatically over the last few years. The development of various swarm
techniques, such as the temperature variable selected ion flow tube or the
selected ion flow drift tube, has provided the prerequisite for detailed
investigations into ion molecule reactions both in binary and three body
collisions, and the mechanisms of many reactions are now understood quite
satisfactorily.
This information could not have been obtained without a detailed knowledge
of the transport phenomena involved. Some of these, such as the
internal-energy distribution of drifting ions, have only very recently been
tackled both theoretically and experimentally; a consistent model is now being
developed.
As the interactions between the various branches of swarm research have
become more and more intense, the most obvious thing to do was putting
together a review on the present state of this subject, which is the aim of this
book.
Since about ten years we have been involved in swarm research ourselves. This
was made possible through the generous funding of the Innsbruck
Forschungsschwerpunkt Plasmaphysik by the Austrian Science Foundation
(Fonds zur Forderung der wissenschaftlichen Forschung), for which we would
like to express our gratitude. In this context a cooperation has developed with
outstanding scientists in the field, many of whom have contributed to this
book. We also would like to thank our colleagues throughout the world for
their continuous encouragement and support, which has been providing
constant nourishment for swarm research at the Leopold Franzens Universitat,
Innsbruck.
Innsbruck, April 1984 W. Lindinger, T. D. Mark, and F. Howorka
Contents
1. Introduction
McDaniel, E. W.: Historical Development and Present State of Swarm
Research ................................................... 1
2. Ion-Transport
SkuUerud, H. R., Kuhn, S.: Velocity Distribution Functions of Atomic
Ions in Drift Tubes ........................................... 13
Viehiand, L. A.: Internal-Energy Distribution of Molecular Ions in
Drift Tubes ................................................. 27
Gatland, I. R.: Determination of Ion-Atom Potentials from Mobility
Experiments ................................................ 44
Mark, E., Mark, T. D.: Transverse Ion Diffusion in Gases ........... 60
Howorka, F.: Runaway Mobilities of Ions in Helium ................ 87
3. Ion-Reactions
Flannery, M. R.: Theory of Ion-Molecule Collisions at
(1 eV-5 keV)/AMU ......................................... 103
Ferguson, E. E.: Vibrational Excitation and De-Excitation and
Charge-Transfer of Molecular Ions in Drift Tubes ................ 126
Lindinger, W.: Kinetic and Internal Energy Effects on Ion-Neutral-
Reactions ................................................... 146
Castleman, Jr., A. W., Keesee, R. G.: Cluster Ion Association
Reactions: Thermochemistry and Relationship to Kinetics ........ 167
Adams, N. G., Smith, D.: Temperature Dependences of Positive-Ion
Molecule Reactions .......................................... 194
Viggiano, A. A., Paulson, J. F.: Reactions of Negative Ions .......... 218
4. Electron Interactions
Christophorou, L. G., Hunter, S. R.: Electrons in Dense Gases ...... 241
Ogawa, I.: Electrons in Inert Gases ............................... 265
Smith, D., Adams, N. G.: Studies of Plasma Reaction Processes Using
a Flowing-AfterglowlLangmuir Probe Apparatus ................ 284
Subject Index ................................................... 307
Historical Development and Present State
of Swarm Research
E. W. McDaniel
Georgia Institute of Technology, Atlanta, GA 30332, U.S.A.
This book addresses several areas of research in the field of
atomic physics that may be investigated by swarm techniques.
Most of the chapters assume that the reader is conversant with
the topic, and the emphasis is on the latest results. However,
in order to establish a broader perspective and a suitable
background, this introduction provides some definitions,
sketches some of the historical developments, and gives some
general references that may be of interest to the reader.
Basic Considerations
We shall define an electron or ion swarm to be a large number
of the particles in question moving about with a random velo
city component in a gas of neutral molecules. The number den
sity N of the charged particles may be large enough that space
charge effects are important; in most of the situations co
vered in this book that is not the case. In the absence of an
externally applied electric field, there is no net motion of
the charged particles, and their velocity distribution is
Maxwellian. If an external field E is present, the distribu
tion is non-Maxwellian, and the swarm moves along the field
lines. The average velocity of the charge carriers is called
the drift velocity ~d; it is constant if the gas is uniform,
the field is constant and uniform, and steady-state condi
tions have been achieved. These conditions should be assumed
to be fulfilled here unless there is an indication to the
contrary.
2
Diffusion of the ions or electrons DCCur if there is a
grad1ent in the relative concentration of the charge carriers.
This diffusion is characterized by a scalar diffusion coef
ficient D in the limit E/N + o. When a field is present, dif
E
fusion occurs at different rates in directions parallel to
E
(longitudinal diffusion) and perpendicular to (transverse
diffusion). In this case, the diffusion coefficient is a
tensor quantity
..
o o
De 0 o (1)
o
where DL and DT are the longitudinal and transverse diffusion
coefficients, respectively. Measurements of steady-state drift
velocities and diffusion coefficients are performed, for the
most part, under conditions where space charge effects are
negligible. An important exception occurs in certain after
glow experiments, where the diffusion is ambipolar. Another
useful quantitity is the mobility of the charged particles,
K = Vd/E. We should note that K, vd' D, DL, and DT are
examples of "transport coefficients" because they are measures
of the rate of transport of physical quantities through the
gas.
Most measurements of ionic and electronic transport coeffi
cients have been made with "drift tubes", and recently with
"flow tubes" in the case of ions, by techniques described
herein. These instruments can also be used to obtain reaction
rate coefficients and sometimes cross sections for various
kinds of atomic collision processes that have a direct bearing
on drift and diffusion and that are of great relevance to all
kinds of swarm phenomena. These processes include momentum
transfer, ion-molecule interchange and association reactions,
charge transfer, excitation and de-excitation of molecules,
electron attachment and collisional detachment, photo- de
tachment of electrons from negative ions, and photodissocia
tion of molecular ions~ The energy dependence of these pro
cesses is obtained by varying the energy parameter E/N, which,
along with the gas temperature T, determines the average ener-
3
gy of the charged particles in the steady state. The trans
port properties depend only on E/N, T, and the charge carrier
gas combination.
Great interest centers on these aspects of electron and ion
swarm research. Additional interest is provided by applica
tions of swarm data to the modeling of laboratory discharges,
gas lasers, radiation detectors, lightning and other kinds of
natural discharges, radio communications, flames, ionospheric
phenomena, and planetary atmospheres. These applications will
not be treated here, nor will the connection of swarm to plasma
physics and plasma chemistry be systematically explored.
Some Historical Comments and General References
Recently a friend who is a Professor of English at the Univer
sity of Strathocmulgee told me that he had come across the
name of James Clerk Maxwell, read a biography of him, and been
duly impressed. He then asked me if I though that Maxwell would
be interested in the current research in my field were he to
be brought back here to observe what is going on. My initial
reaction was one of shock, during which I had the disturbing
vision of the shade of Maxwell circulating around the various
laboratories, kicking the tires, and demanding to know what all
of us are up to. After recovering, I answered my friend in the
affirmative, and I believe that my answer can be justified in
two ways.
First, between about 1859 and 1866, Maxwell laid the foundations
of much of the kinetic theory of gases, which is the main theo
retical basis of all transport phenomena in gases. He also
pointed out the unique significance of the l/r4 potential in
his collision integrals, thus foreshadowing the role to be
played by the "polarization potential" decades later. Finally,
he personally made measurements of the viscosity of gases,
demonstrating his administrative ability by inducing his wife
to serve as stoker during the runs at high temperature. At
this time (30 or more years before the discovery of X-rays,
radioactivity, the electron, and the nature of gaseous ions)
experiments on ion and electron swarms were far in the future.
However, it is hard to resist the temptation to believe that
Maxwell would have been one of the first researchers in our
field had the requisite tools become available at the appro
priate time.
The second reason for Maxwell's putative interest is provided
by the contents of this book, which convey a sense of the
breadth, vitality, and sophistication of the research now being
performed. A description of the book and its place in the
literature will be given in the next section. First, we shall
enumerate a few general references in chronological order and
gain some historical perspective while discussing them.
We shall confine ourselves to books published after World War
II and start with the encyclopedic book by Loeb (1), which
gives an exhaustive account of ion and electron swarm research
from its beginnings immediately after the discovery of X-rays
in 1895 up until the mid- 1950's. Among the earliest workers
were Rutherford, Thomson, Townsend, Tizard, and of course
Langevin, whose 1905 landmark paper contained a calculation
of the zero-field diffusion coefficient and mobility of gase
ous ions. (Were it not for the fear of being accused of gerry
mandering, we would include Einstein in this hagiology. After
all, we constantly use the "Einstein relation" between the
mobility and diffusion coefficient of charge carriers in the
limit E/N + 0 that Einstein derived in 1905. It had been ob
tained earlier by Nernst (1888) and Townsend (1899) in dif
ferent contexts). This calculation was based on Maxwell's
momentum transfer method and the assumption of a polarization
attraction potential to describe the ion-neutral interaction.
Results were obtained with and without an additional hard
core repulsion. Langevin's contribution was truly remarkable-
it had no rival until the introduction of the Chapman-Enskog
method described below, and Langevin's polarization limit of
the mobility still plays an important role today. The next
"generation" of swarm researchers discussed by Loeb included
Chapman, Enskog, Tyndall, Powell, Druyvesteyn, Penning, Huxley,
Brandbury, Nielsen, Allis, and Morse. Their work extended
from about the middle of World War I on past World War II. The
Chapman-Enskog method (circa 1917) in the kinetic theory of
gases has been of great general interest and utility. In our
field, it was especially important in permitting an extension
5
of Langevin's results for the l/r4 potential to an arbitrary
(but still spherically symmetric) potential. Unfortunately the
Chapman-Enskog method is not well suited for extension of the
transport calculations upward out of the region of very low
E/N. The first major improvement along these lines came in the
early 1950's when Wannier used the Boltzmann transport equa
tion (published in 1872) to investigate the motion of gaseous
ions at high E/N. Wannier (whose work Loeb discusses at length)
was able to obtain detailed solutions in the high-field re
gion only for two simple limiting models-- constant mean free
time and constant mean free path. These models, which corre
spond to the polarization potential and the hard sphere poten
tial, respectively, provided much needed insight into the high
field regime. Wannier's paper also contains results that are
quite useful at low E/N. We are now at the end of our discus
sion of Loeb's book except to say that he not only treats ion
and electron transport, but also electron velocity distribu
tions, the theory and use of probes, the formation of negative
ions, ionic recombination, electron avalanches, and the Towns
end ionization coefficients. I find the book to be of consider
able historical interest.
By the mid- 1950's, swarm research had grown to such propor
tions that it is impossible to outline the subsequent history
of the entire field in this short introduction and even to
give credit specifically to the many important contributors.
The remaining reference (2-8) are useful in this connection,
but they should be supplemented by books on electrical dis
charges and plasma physics.
Thus far we have emphasized the swarm transport phenomena
themselves, making only peripheral mention of atomic colli
sion phenomena. It is now appropriate to take a closer look
at the latter, because so many of them enter into the forma
tion of swarms, their detailed properties, and their ultimate
destruction in the gas phase or on surfaces. First some defini
tions: By "atomic collisions" we mean collisions between
electrons, photons, heavy particles and surfaces in the energy
range where the phenomena are electronic and atomic,not nuclear.
The maximum energy considered in each case is below that at
which nuclear interactions become significant. By "heavy par-
