1. An understanding of electric discharge in gases is of fundamental importance in
fields ranging from consumer product manufacturing to global weather
modeling. Unfortunately, there is wide disagreement in the literature about the
specific values of certain physical quantities, so-called Townsend coefficients,
which are necessary for predictive modeling of electric discharge in gases. I
discuss here my research towards theoretical modeling and experimental
verification of the effects of geometrical shape factors on the Townsend
coefficients in cylindrical containment vessels over pressures 10-4 Torr < p < 101
Torr.
A special thank you to Tom Fleming, Department of Physics, and to Dr.Robin Datta,
Department of Political Science, Edmonds Community College, for all their conversations and
the support they have provided during this research, as well as to the Community College
Undergraduate Research Initiative (CCURI) for making this presentation of my work
possible.
Alexandra Serdyuk: aleeraalexia@gmail.com
In 1889 Friedrich Paschen discovered an empirical relationship between the
discharge breakdown voltage in a gas as a function of the product of pressure and
separation distance between electrodes.
Where and were poorly-understood empirical constants “specific to the
particular gas.”
Townsend later modeled dielectric breakdown in gases in terms of statistical
models of ionization including the probability per unit mean free path of a free
electron causing a neutral gas atom to ionize, the so-called first Townsend
coefficient
in the process
and a second Townsend coefficient, giving the probability per-ion cathode
collision of producing a secondary electron.
The Townsend criterion that a self-sustaining discharge in a gas will occur reflects
that for each electron-induced ionization of a neutral gas, there must be at least
one replacement electron emitted from the cathode due to secondary emission,
This condition can be expressed as
The minimum breakdown voltage can then be determined as
The Paschen coefficients and can also be determined from the electron-
neutral cross sections as
where is the scattering cross-section for electron-neutral ionization, for a
given neutral atom with first ionization energy .
Object Oriented Particle in Cell (OOPIC) simulations showing critical discharge transition
(Number Density for argon gas vs. axial and radial coordinates)
Fig.1 : z =1cm Fig.2: z=2cm
The Townsend results rely on an assumption of infinite planar geometry (cylindrical plates with finite separation distance but infinite radius.)
Realistic finite systems with boundaries, such as those actually used in laboratories and product engineering, have finite ratios of L/R. Because of
this, radial diffusion of the electrons plays a substantial role in modifying the first Townsend coefficient since it couples to electron mobility and
the temperature dependence of the ionizing electron-neutral scattering cross section. The radial dependence can be seen to appear in the Engel-
Steenbeck relation
and the familiar drift/mobility Einstein relation
Recent work by Lisovskiy, et. al., has furthered an understanding of the dependence of the minimum breakdown voltage in terms of the geometric
shape parameter
This work, however, does not include any explicit measurement of actual electron temperatures, and it can be shown that deviations in electron
temperature could be misinterpreted to correspond to effects of deviations in the geometric parameter
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In an attempt to separate effects due to electron temperature deviations from
geometric deviations, my current work involves extensive computational simulations
of Townsend discharge in cylinders containing neutral argon using Object Oriented
Particle in cell (OOPIC) PIC-MCC methods as developed by Verbancouver, et. al. In
this way, I will be able to understand and optimize the engineering design of the
discharge apparatus prior to construction and ensure design suitability.
Findings include that in order to make meaningful comparisons with Lisovskiy data
over the domain with , a basic physical design
with fixed and will allow for study of Townsend discharge
across the critical transition from non-sustaining “flash” discharge to self-sustaining
Townsend discharge.
The addition of a Langmuir probe will allow for direct measurement of electron
temperatures in order to separate temperature from geometric effects.
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 Fine-resolution modeling of plasma sheath boundary formation during discharge over
operating inter-plate separations
Design and construction of Langmuir probe based on plasma sheath simulations
Final engineering and construction of discharge apparatus
Comparison of Lisovskiy model for given control information for actual measured
electron temperature
Publication of results
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Langmuir probes are used for plasma diagnostics to measure local plasma parameters such as
plasma density, plasma frequency and electron temperature. Probes collect electrons that
have high enough kinetic energy to overcome the field barrier created by current through the
probes. Placing probes into plasma will cause bombarding of its surface by electrons, ions and
neutral particles. If the electron distribution is in local thermal equilibrium, then the particle
impact rate is
where is the mass of the particles, is the temperature, and is the number density.
Since , , and the probe located in the plasma will collect more electrons
than ions and eventually will reach negative charge. Net current will equal zero, resulting in a
floating potential .
The thickness of the plasma electron sheath is described by the Debye length
For , the probe saturation current is saturated at . For , electrons
are partially repelled by the probe, and for , all electrons are repelled and the
electron current is zero,
The electron saturation current is related to the probe geometry and electron impact rate as
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