Excited Atoms and Molecules in High Pressure Gas Discharges
L. Vušković and S. Popović
Old Dominion University, Department of Physics
4600 Elkhorn Avenue, Norfolk, VA 23529
Abstract. Various types of high-pressure non-thermal discharges are increasingly drawing attention in view
of many interesting applications. These, partially ionized media in non-equilibrium state, tend to generate
complex effects that are difficult to interpret without a detailed knowledge of elementary processes involved.
Electronically excited molecules and atoms may play an important role as intermediate states in a wide range
of atomic and molecular processes, many of which are important in high-pressure discharges. They can serve
also as reservoirs of energy or as sources of high energy electrons either through the energy pooling or
through superelastic collisions. By presenting the analysis of current situation on the processes involving
excited atoms and molecules of interest for high-pressure gas discharges, we will attempt to draw attention on
the insufficiency of available data. In the same time we will show how to circumvent this situation and still
be able to develop accurate models and interpretations of the observed phenomena.
particles by optical lattices that were proposed
recently [3].
The reason for our present interest in
the ionization of excited atoms per se, is twofold.
First, a detailed study of hydrodynamic
properties of non-thermal discharges requires an
accurate
ionization-recombination
model.
Thermodynamic equilibrium conditions are not
fulfilled and implementing available data into an
ionization-recombination model in a consistent
manner has proved to be a difficult task. Second,
the availability and quality of data is far from
satisfactory. This situation has not been a serious
problem in modeling low-pressure discharges,
where processes involving excited atoms were
less important [4-6]. However, at pressures
above 10 Torr, this is not the case. Relative
contribution of particular elementary processes
in high-pressure discharges may differ
substantially with respect to the low-pressure
discharges, since the pressure and temperature
dependence of rate coefficients of involved
species have nonlinear dependence on pressure
and temperature.
In a gas discharge, excited atoms
interact with photons, electrons, ions, and other
ground state or excited atoms. In these
interactions they may gain or lose energy, or may
be transformed into ions. We are focused here on
the processes leading to ionization of excited
atoms. In gas discharges at elevated pressures
ionization
involves
several
competitive
processes. These are electron-impact ionization
from excited states, ionization in collision
between two excited states, associative
ionization in three body processes involving a
highly excited atom and two ground state atoms,
Introduction
High-pressure non-thermal discharges
are always partially ionized and their
thermodynamic state is quite different from
equilibrium. Kinetic energy of free electrons is
higher than the temperature of heavy particles.
Electron energy distribution is far from
Maxwellian. It usually, but not always,
parameterized by the reduced electric field.
Population distribution of the excited states
reflects
the
nonequilibrium
conditions.
Moreover, the physical conditions of these
discharges are influenced by the action of the
discharge-generating fields, by time and space
constraints that all affect the relaxation
processes.
Extensive research has been conducted
on the radiative properties of high pressure
discharges and the development of new types of
lasers and non-coherent light sources. Present
work is inspired by the emerging interest to other
physical properties of these discharges, which
are less understood. These are the interaction of
high-pressure
discharges
with
external
electromagnetic fields, generation of internal
electromagnetic effects closely related to the
interaction of the discharges with acoustic
waves, general aerodynamic properties, and the
effects of chemical reactions on discharge
parameters and kinetics. Applications of highpressure non-thermal discharges include, for
instance, polymer surface modification by pulsed
two-dimensional microwave discharges [1] and
generation of fast adaptive microwave optics
using sub-nanosecond discharges [2] and new
schemes for acceleration of polarizable neutral
CP680, Application of Accelerators in Research and Industry: 17th Int'l. Conference, edited by J. L. Duggan and I. L. Morgan
© 2003 American Institute of Physics 0-7354-0149-7/03/$20.00
172
compilation for excited atoms and ions still does
not exist.
Our measurements of electron impact
ionization of laser-excited sodium 3P state [20],
and the experiment of Trajmar et al. [21] on
barium, still remain the only ionization
measurements on short-lived excited states. We
measured the absolute cross sections in the
incident electron energy range from threshold to
30 eV for both excited and ground state sodium.
Excited-state results are given in Fig. 1(a)
together with calculations [16-18,22]. It can be
seen that the CCC calculation tend to agree with
experiment near threshold, but remain below
experimental data at higher energies. On the
other hand, the calculations employing
generalized oscillator strength (GOS) based on
the Born approximation [22] tend to
underestimate cross sections near the threshold,
but agree better with experimental data at higher
energies. Position of the maximum is close to the
one predicted by the GOS calculation, while the
CCC treatment underestimates the energy at the
maximum by 3 eV. However, the semi-empirical
Eq. (2) agrees surprisingly well with the
experiment, much better than the two, more
elaborate calculations. Fig. 1(b) presents a
comparison of experimental data for metastable
helium (He 21S) and the ionization cross section
calculated using the Eq. (2). The formula
overestimates the cross section around threshold
and maximum, and agrees rather well with the
experimental results at higher energies.
and an atomic or molecular ion and two ground
state atoms. This work mainly covers the
electron-impact and energy pooling ionization
processes.
Trajmar and Nickel [7] gave a
comprehensive review on electron impact by
excited atom species. Lin and Anderson [8] have
presented a review of the work on the electron
excitation processes of rare-gas atoms. Siska [9]
gave an extensive review of Penning ionization
and energy-pooling processes. However, data on
collisions involving excited atoms of the same
species are still quite sparse. A review of the
work on the subject before 1990 was given by
Kolokolov and Blagoev [10]. Associative
ionization was studied by Weiner et al. [11].
Smirnov [12,13] reviewed ion conversion, ion
cluster growth, as well as homonuclear
associative ionization processes. A review of
collisional ionization of excited atoms, including
the analysis of the homonuclear associative
ionization process is given by Wuilleumier et al.
[14].
Ionization by Electron Impact
In high pressure discharges, ionization
by electron impact is rarely achieved directly
from the ground state,
e − + A → A + + 2e − .
(1a)
Step-wise ionization
e − + A → A* + e −
e − + A* → A + + 2e −
(1b)
is by far more effective even at relatively low
pressures (around 1 Torr).
It has required considerable work to
achieve convergence between experimental and
theoretical results on ionization of excited atoms
by electron impact. Most experimental data refer
to an integral ionization cross section involving
metastable targets [15]. The calculations of cross
sections have still not achieved the desired level
of accuracy. The Convergent Close-Coupling
(CCC) calculations of ionization cross section
[16] describe correctly the threshold behavior.
However, CCC method tends to underestimate
absolute values of ionization cross section at
higher energies. In modeling, the most frequently
used data are based on simplified empirical or
semi-empirical analytical fitting formulae [1719]. Wide range of analytical fitting formulas has
been proposed for impact ionization of ground
state atoms and ions [19]. An analogue
FIGURE 1. Electron impact ionization cross section
as a function of electron energy.
Fig. 1(a). Na(3P): circle, Tan at al. [20]; full line,
Vriens [17]; cross, McGuire [22]; square, Bray [16].
Fig. 1(b). He(21S): circle, Dixon et al. [15]; full line,
Vriens [17].
Energy - Pooling Processes
Ionization in a collision involving two
excited states has two types of ion products:
173
EP
A* + A* k→
A + + A + e − (∆E )
k AI
A* + A* →
A2+ + e − (∆E )
Available data on the collision of two
lowest-energy metastable helium atoms He(3S)
allow comparison of all three types of data. The
orbiting model reduces the problem of the
collision cross section calculation to the
attractive van der Waals potential between two
excited atoms.
In Fig. 2 we show the ionization rate for
the energy pooling process between two He(3S)
metastable atoms, based on the cross section data
and on the Maxwell-Boltzmann velocity
distribution of excited atoms. The cross section
data were obtained using the exact theory of
autoionization of the intermediary state and the
approximate orbiting model as outlined in Refs.
[23, 25]. Also, several experimental results given
in terms of cross section [7, 26-29] were
compared and found that the results from Refs.
[26] and [29] agree rather well with calculations.
Comparison includes ionization rates calculated
from the cross sections evaluated in Ref. [23]
which we will label “exact theory”, ionization
rates calculated by Bates et al. [24] with the
orbiting model, ionization rates calculated by
Kolokolov and Blagoev [10], present calculation,
as well as the ionization rate evaluated on the
basis of the frequently used simplification of
constant cross section. The ionization rate has a
relatively weak dependence on temperature,
since the decreasing energy dependence of the
cross section compensates the temperature
dependence of the velocity distribution.
Most estimates of energy pooling
ionization rates in the gas discharge models
assume a constant cross section over the relevant
energy range. As shown on Fig. 2, this
assumption can produce an error of more than a
factor of two. Moreover, the ionization rate has
usually been taken as 2×10-9 cm3s-1 over the
whole gas temperature range. This assumption
can produce an error between 25% and 75%.
Therefore, in the cases where a relatively wide
gas temperature range is expected, as in high
pressure discharges, these crude approximations
may produce substantial error. As seen in the
Fig. 2, the orbiting model formula derived by
Bates et al. [24] overestimates, while Kolokolov
and Blagoev [10] data underestimate the
ionization rate in comparison to the present
calculation. Experimental values for ionization
rates differ substantially, and we tend to believe
that the measured quantity is an average over all
excited states. Therefore, most of the
experimental values are larger than the ionization
rates for the lowest lying states. On the other
hand, the method used by Kolokolov et al. [10]
(2a)
(2b)
where kEP and kAI are the rate coefficient for
energy pooling (atomic ion production) and for
associative
ionization
(molecular
ion
production), respectively. In both ionization
channels, the ejected electrons carry out most of
the excess kinetic energy. These features of the
process contribute to the recovering of the
excited state population and affect the electron
energy distribution in the discharge. However,
this aspect of the energy pooling process has
usually been neglected in most models of gas
discharges. Since the process depends
predominantly on the long range van der Waals
attraction forces, the polarized excited states
have a much higher collision probability than the
unpolarized states.
Experimental data on
energy-pooling processes are sparse, but there is
no justification for using arbitrary values for rate
coefficients in the models of gas discharge. With
the aim to overcome this situation we will
present here three kinds of data: experimental,
analytical based on exact theories involving ab
initio calculation of the potential and
autoionization shift curves [23], and approximate
analytical data, based on a simplified orbiting
collision model [24]. With the knowledge of ion
potential curves, one can also determine the
cross section for the associative ionization.
However, it was shown for helium that the
orbiting method grossly overestimates the
contribution of associative ionization in the total
ionization cross section [23].
FIGURE 2. Energy pooling ionization rate as a
function of temperature: full line, present data; xxx,
Garrison et al. [23]; dash line marked by cross,
Kolokolov and Blagoev [10]; dash line marked by
circle, Bates et al. [24]; dash line marked by triangle,
frequently used simplification k=<v>σ(300 K).
174
has the capability of discriminating between the
higher excited states. Their experimental values,
however, tend to be lower than the calculated
values. On the calculation side, it is known that
the Slater-Kirkwood relation tends to
underestimate the van der Waals constant, which
leads to lower values of cross sections and
ionization rates. Clearly, further work on
clarifying these discrepancies is needed.
Based on the results shown in Fig. 2 for
excited helium, we proceed applying the above
approximation to calculate the ionization
collision rates of other excited noble gas atoms.
There are almost no experimental data for cross
sections and ionization rates of gases other than
helium. Although one should not expect a
surprise, the experimental verification of the
theory is always favorable, especially in cases
when the only two available data points differ by
a factor of three or more.
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FIGURE 3. Ionization rates for energy-pooling
involving the lowest metastable state of noble atoms:
full line, the suggested values for indicated noble
atom; dash-dot line, most frequently used value for all
noble atoms.
Having in mind large uncertainties and
an insufficient amount of reliable experimental
data, the suggested values of the energy-pooling
ionization rates involving the lowest metastable
state are given in Fig. 3. They are based on the
simplified calculations using the orbiting model
and the Slater-Kirkwood relation. Therefore they
tend to underestimate the ionization rates.
However, except partially for Kr and Xe, they
are substantially larger than the constant value
usually used in modeling the discharges at low
pressures (see, for instance Refs. [4-6]).
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