An experimental study measured the effective secondary electron emission in argon gas breakdown using copper, aluminum, and stainless steel electrodes. Paschen curves were obtained for gaps of 2mm, 10mm, and 20mm. The effective secondary electron yield (γ) was determined from the curves. Including the effects of electron diffusion and an equilibration distance allowed γ to be consistently modeled versus E/p for different gaps. Copper generally had the lowest breakdown voltage and highest γ. The γ values were compared to previous studies.

1. Study of Effective Secondary Electron
Emission in DC Breakdown of Argon
with Various Metal Electrodes
Steven Adams, XuHaiHuang,
K.C. Howe, Vladimir Demidov
Air Force Research Laboratory
Wright Patterson AFB, OH
Boyd Tolson, Amber Hensley
UES Inc.
Dayton, OH

2. Abstract
An attractive aspect of Townsend’s expression for the ionization
coefficient, α = A exp[-B/(E/p)], is that the exponential form allows a
derivation of a neat analytical expression for the Paschen curve.
Notwithstanding the elegance and fame of this expression, the theoretical
Paschen curve does not always provide an accurate prediction for all E/p
ranges and all gases. Deviations can be attributed to a variety of factors,
including non-exponential behavior of α at higher E/p, variations of γ with
E/p and geometric effects. An experimental study of the effective
secondary electron emission in Townsend breakdown has been
conducted in Ar using a variety of electrodes. The threshold breakdown
voltage was measured when the current became self-sustained, which
corresponded to a specific effective secondary emission coefficient. This
allowed a fundamental relationship to be derived between γ and E/p from
an experimental Paschen curve. In this work, argon gas was studied with
copper, aluminum and stainless electrodes. The trends of the effective
secondary electron emission are analyzed in different E/p ranges for
various modes of secondary electron emission, including Ar ion impact,
photon absorption, Ar metastable collisions and heavy-particle-ionization.

3. Energy Sciences Facility
AFRL Aerospace Systems Directorate , Wright Patterson AFB, OH
Bldg 23, WPAFB, OH

4. Paschen’s Law
𝜶/𝒑 = 𝑨 𝒆𝒙𝒑
−𝑩
𝑬/𝒑
Townsend determined that
the ionization for gases often
followed the expression
where A and B were constants
Using this expression for 𝜶 in
with self-sustaining current
leads to a theoretical threshold
breakdown voltage of
𝑽 𝑩 =
𝑩 𝒑𝒅
𝒍𝒏 𝑨 𝒑𝒅 − 𝒍𝒏 𝒍𝒏 𝟏 + 𝜸−𝟏
which is Paschen’s Law

5. Secondary Electron Yield, 𝜸
Effective secondary electron yield may include
contributions from other than Ar+ ions at cathode
e-
Ar+
e-
e- e-
Ar*
Ar
i
a
ph
i = electron yield per Ar+ ion incident on
cathode. Primary contribution in model
Secondary electrons possible from Ar*
metastables incident on cathode
Secondary electrons possible from Ar atoms
incident on cathode
Secondary electrons possible from
photons incident on cathode: Previous
work says 𝜸 𝒑𝒉 is significant at lower E/p
m

6. Paschen’s Law Inaccuracies
𝜶/𝒑 ≅ 𝑨 𝒆𝒙𝒑
−𝑩
𝑬/𝒑
One problem is that Townsend’s
expression for 𝜶 is only APPROXIMATELY
accurate for some gases, like Argon
A more accurate empirical formula for Argon is
𝜶/𝒑 ≅ 𝑪 𝒆𝒙𝒑
−𝑫
𝑬/𝒑 𝟏/𝟐
with A = 12 cm-1 Torr-1 and B = 180 V/(cm Torr)
with C = 29.2 cm-1 Torr-1 and B = 26.6 V/(cm Torr)
Swarm experiments also show that the
ionization coefficient deviates from
either formula at higher E/p

7. Paschen’s Law Inaccuracies
𝑽 𝑩 =
𝑩 𝒑𝒅
𝒍𝒏 𝑨 𝒑𝒅 − 𝒍𝒏 𝒍𝒏 𝟏 + 𝜸−𝟏
Argon with copper electrodes (1 cm gap) modeled using 𝜸 = 𝟎. 𝟎𝟎𝟓
𝜶/𝒑 = 𝑨 𝒆𝒙𝒑
−𝑩
𝑬/𝒑
Paschen’s analytical expression for Vb is
accordingly inaccurate for Argon
But, assuming

8. Modeling Paschen Curves using
Empirical Ionization Coefficients
Experimentally measured 𝜶 values can be used along with
a constant 𝜸 to improve the predicted breakdown voltage
Dutton, J. Phys. Chem. Ref. Data, Vol. 4, No. 3, 1975
For Argon with copper electrodes (1 cm gap) and 𝜸 = 𝟎. 𝟎𝟎𝟔, the fit to
experiment was better, especially for pd values 1-3 Torr-cm.
𝜸 𝒆𝒙𝒑 𝜶𝒅 − 𝟏 = 𝟏
Predicted Vb occurs at

9. Argon with copper
electrodes (1 cm gap) and
variable 𝜸 shown
Modeling of Paschen Curves Using
Variable Secondary Electron Yields
If  is allowed to vary as a
function of E/p, then
different ’s can be
assigned to each pd value
and a perfect fit results
𝜸 𝒆𝒙𝒑 𝜶𝒅 − 𝟏 = 𝟏
Again, predicted Vb occurs at
Assignment of  vs E/p
that provides best fit of
experimental data

10. Paschen Curve Experiment
Experimental setup: inter-changeable
electrodes, variable gap and pressure.
Voltage slowly increased until
threshold breakdown voltage is found
Automated system produces
reliable Paschen curves over
extended range of pd.

11. 2 mm gap 10 mm gap 20 mm gap
Various Electrode Gaps in
Wineglass Container
All data taken with parallel disc shaped electrodes (various metals)
5 cm in diameter

12. Electron Diffusion Effect
with Wider Gaps
e-
e-
e-
e-
e- e-
e-
e-
e-
e- e-
Diffusion DiffusionDrift
Axial diffusion of electrons within the gap will
effectively reduce the ionization coefficient, a,
especially at wider gaps. The effective Townsend
coefficient, 𝜶, is expressed as
𝜶 = 𝜶 − 𝝀 𝑻
𝟐. 𝟒
𝑹
𝟐
where R is the electrode radius (2.5 cm in our case) and
𝝀 𝑻 is the electron diffusion length which is a complex
function of the electron temperature and electric field
As a first order approximate model of this diffusion
effect, we approximated 𝜶 as a simple percentage of
a, where the percentage, 𝑲, was a variable with the
gap size
𝜶 = 𝑲𝜶
𝜶𝜸 𝒆𝒙𝒑 𝜶𝒅 − 𝟏 = 𝜶
This alters our condition of the breakdown
threshold, where Vb now occurs when
Kolobov and Fiala, Phys Rev E, Vol50, p3018 (1994)

13. Electron Equilibration Distance and the
Effect on Breakdown Modeling
It has been theorized that electrons leaving the cathode require a
certain equilibration distance (d0) before they reach equilibrium
with the gas and ionization begins as predicted by a.
𝜶𝜸 𝒆𝒙𝒑 𝜶(𝒅 − 𝒅 𝟎) − 𝟏 = 𝜶
d
d0
(d - d0)
This again alters the avalanche condition and the prediction
that breakdown threshold now occurs when
In this work, we assign d0 based on an empirical equation
for the effective value of the electrode potential difference
(V0) before exponential electron current growth occurs
Phelps and Petrovic, Plasma Sources Sci. Technol., R21 (1999)
𝑽 𝟎 = 𝟏𝟔 𝟏 +
𝑬/𝒑
𝟑𝟐𝟎
𝟐
𝒅 𝟎 =
𝒅
𝑽 𝒃𝒅
𝟏𝟔 𝟏 +
𝑽 𝒃𝒅
𝟑𝟐𝟎(𝒑𝒅)
𝟐
Assuming a uniform E field when the breakdown voltage (Vbd) is
applied across the gap distance (d), the d0 is assigned as

14. Raw Paschen Curves for
Various Metal Electrodes
Copper Electrodes
Aluminum Electrodes
Stainless Steel Electrodes
pd was varied by holding gap (d)
constant while adjusting pressure.
Applied voltage was increased
slowly and automatically until
breakdown detected electronically

15. Paschen Curves for 3 Metals Compared
with 1 cm gap
Of the 3 metal electrodes studied, Copper had the lowest
minimum threshold breakdown voltage at each gap distance
and the lowest pd value at the minimum breakdown voltage
Aluminum
Vbd-min = 272 V
pdmin = 1.33 Torr-cm
Stainless Steel
Vbd-min = 263 V
pdmin = 1.7 Torr-cm
Copper
Vbd-min = 228 V
pdmin = 1.05 Torr-cm
All data in this plot used a gap spacing of 1 cm

16. Aluminum Effective
Secondary Electron Yield
𝜸 𝒆𝒙𝒑 𝜶𝒅 − 𝟏 = 𝟏
𝜶𝜸 𝒆𝒙𝒑 𝜶(𝒅 − 𝒅 𝟎) − 𝟏 = 𝜶
𝜸 values determined with basic
Townsend model showed
significant variation as the gap
varied from 2mm to 20 mm.
When including diffusion and
equilibration distance effects,
the 𝜸 values where much more
consistent for the various gaps
Ionization reduction constants K
due to diffusion for various gaps:
𝜶 = 𝑲𝜶
for d = 2mm, 𝑲 = 𝟏. 𝟎𝟎
for d = 10mm, 𝑲 = 𝟎. 𝟗𝟓
for d = 20mm, 𝑲 = 𝟎. 𝟖𝟖

17. Copper Effective
Secondary Electron Yield
𝜸 𝒆𝒙𝒑 𝜶𝒅 − 𝟏 = 𝟏
𝜶𝜸 𝒆𝒙𝒑 𝜶(𝒅 − 𝒅 𝟎) − 𝟏 = 𝜶
𝜸 values determined with basic
Townsend model again showed
significant variation as the gap
varied from 2mm to 20 mm.
Copper 𝜸 values were generally
higher than Aluminum or
Stainless Steel
When including diffusion and
equilibration distance effects,
the 𝜸 values where much more
consistent for the various gaps
Ionization reduction constants K
due to diffusion for various gaps:
𝜶 = 𝑲𝜶
for d = 2mm, 𝑲 = 𝟏. 𝟎𝟎
for d = 10mm, 𝑲 = 𝟎. 𝟗𝟓
for d = 20mm, 𝑲 = 𝟎. 𝟖𝟖

18. Stainless Steel Effective
Secondary Electron Yield
𝜸 𝒆𝒙𝒑 𝜶𝒅 − 𝟏 = 𝟏
𝜶𝜸 𝒆𝒙𝒑 𝜶(𝒅 − 𝒅 𝟎) − 𝟏 = 𝜶
𝜸 values determined with basic
Townsend model showed
significant variation as the gap
varied from 2mm to 20 mm.
When including diffusion and
equilibration distance effects,
the 𝜸 values where much more
consistent for the various gaps
Ionization reduction constants K
due to diffusion for various gaps:
𝜶 = 𝑲𝜶
for d = 2mm, 𝑲 = 𝟏. 𝟎𝟎
for d = 10mm, 𝑲 = 𝟎. 𝟗𝟓
for d = 20mm, 𝑲 = 𝟎. 𝟖𝟖

19. Analysis of Effective
Secondary Electron Yields
Comparison of Effective
Secondary Electron Yields
for 3 Metals Studied
Copper Shows Greatest
Secondary Electron Yield
with Values Exceeding .01
For E/p < 100 V/(cm-Torr), the
uncertainty in 𝜸 is increased
due to possible rise in
effective yield due to electron
production by photons
𝜶𝜸 𝒆𝒙𝒑 𝜶(𝒅 − 𝒅 𝟎) − 𝟏 = 𝜶
Our Copper results can be
compared with measurements
by Auday et al. (1998) and
Maric et al. (2014).

20. Summary of Study of Effective Secondary
Electron Emission in DC Breakdown of Argon
• Experimental study of the effective secondary electron yield in
Townsend breakdown conducted in Argon gas.
• Copper, aluminum and stainless steel electrodes studied.
• Parallel electrodes with 25 mm radius and 2mm, 10mm and 20mm gap
• Effective secondary electron yields determined from Paschen curves
• Diffusion effect and equilibration distance considered in modeling
Paschen curve
• Allowed model of 𝜸 vs E/p to be consistent at various electrode gaps
Energy Sciences Research Team 2015,
Wright Patterson AFB, OH
• Model of 𝜸 at low E/p varied somewhat
with gap size, likely due to increased
influence of photoelectric effect
• Copper generally had lowest breakdown
threshold and highest secondary
electron yield of the metals studied.
• Future plans to apply model to Paschen
curves in microdischarge devices