st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
Time resolved ion density and electrical field determination by electrical current
measurements in a self-pulsing plasma at atmospheric pressure air
T Gerling, R Bussiahn, C. Wilke, and K-D Weltmann
Leibniz Institute for Plasma Science and Technology (INP Greifswald), Greifswald, Germany
Abstract: High resolution current signals of a self-pulsing discharge revealed characteristic
oscillations in the pulse decay phase. These oscillations appear with decreasing frequency
between 250 MHz and 75 MHz. It is expected, that these oscillations are the result of ion
acoustic waves. From frequency and current amplitude measurements, the ion density and
electric field strength is calculated over time.
Keywords: Electrical characterization, ion acoustic wave, ion density, electrical field strength
1. Introduction
Atmospheric pressure plasmas are a field of great potential in the industrial and medical sector [1]. A challenging part for the characterization of plasma sources
remains the determination of plasma parameters like species densities. The variety of techniques to determine these parameters is still very limited and mostly involves
costly equipment.
Current and voltage measurements are a simple method
to gain first information about a plasma discharge. In previous experiments, we observed weak oscillations in the
current and voltage signals [2]. The oscillations were interpreted to be a result from ion acoustic waves, with densities well in the range of estimated electron densities.
The experimental setup and new results on the oscillations will be presented here. Possible sources of errors
will be discussed along with the setup to underline the
sensitivity of highly resolved electrical measurements.
Afterwards, the origin of the oscillations is evaluated.
Finally, the resulting ion density and electrical field calculations are presented.
2. Experimental Setup
For this investigation, a self-pulsing, discharge as in
[2,3] is used (see figure 1). A negative DC voltage (-5 …
-10 kV) is applied by a high resistive power supply to a
hollow needle electrode (0.8 mm outer diameter). The
grounded counter electrode is a 4x4 mm² copper plate in a
distance of 8 mm. A quartz capillary surrounds the needle
electrode (3 mm outer diameter) and is placed 5 mm from
the needle tip [2]. An argon gas flow between 0.2 and 0.5
slm is supplied through the needle electrode. The created
discharge filament (transient spark [2,4]) has a diameter
of 60 μm (measured by photography). Current amplitudes
between 0.2 A and 3.8 A are possible. The applied voltage
charges the device capacity until the breakdown voltage is
reached. Since the discharge operates in flowing argon,
the breakdown conditions are not stable and the repetition
frequency varies between 0.5 and 3 kHz.
The electrical measurements were done with two dif-
Fig.1: ground loop free experimental setup
ferent setups. In accordance with the arrangement in [2],
the first setup consisted of a high voltage probe (Tektronix P6015A) mounted in open air as an antenna and a
second voltage probe (Tektronix P5100) was connected
before a 100 Ω resistor at the grounded electrode. The
discharge was grounded in the same spot as the oscilloscope (both probes connected, Tektronix DPO7104) and
the power supply. For the second setup, the voltage
probes were removed and only a current probe (Tektronix
CT1) placed after the resistor (see figure 1). For some
measurements the signal of the probe was split on two
channels of the oscilloscope to have high resolution for
small changes on the one and low resolution but therefore
absolute peak values on the other channel.
3. Results of electrical Measurements
Typical current and voltage slopes for the measurement
with voltage probes are shown in figure 2. The voltage
slope of the antenna probe (red curve) shows the voltage
breakdown after a discharge event. The voltage jumps
from its negative value (around -5 kV [2]) to 0 kV (figure
2 has only relative values) within 30 ns. After the breakdown, some oscillations are observed on the voltage signal. The current signal for the discharge is overexposed to
record the oscillations with higher resolution. While the
scale in figure 2 is limited to a current amplitude of 50
mA, the discharge current peak in this case is about -400
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
mA. At the beginning of the current signal, the breakdown
is visible by a steep drop. Afterwards, the current decays
towards zero in damped oscillations with obviously different, overlapping frequencies.
Fig.4: current signal of the discharge with measurement
of the peak value (160 mA) and overexposed signal with
weak current spikes (some mA amplitude). QAr = 500
sccm, UA = -10 kV
Fig.2: current and relative voltage signal (antenna) for the
breakdown. The current signal is overexposed to enhance the
visibility of the oscillations (QAr = 500 sccm, UA = -10 kV)
In figure 3, the fast Fourier transformation (FFT) of the
signals from figure 2 is shown. Several characteristic frequencies are observed, whereas the peak at 73 MHz was
seen on both signals. By changing cable lengths and
grounding conditions, differences in the frequencies could
be observed. But even with a single voltage probe, the
oscillation with its sensitivity towards cable length and
grounding remained.
Fig.3: FFT analysis of current and voltage
signal from figure 2.
When all voltage probes were removed and only the
current probe inserted (see figure 1), the signal was almost free of oscillations. This indicates, that the reason
for the oscillations were ground loops with lengths in the
order of some 10 m.
Nevertheless, this new setup revealed some even
smaller signals on the decaying current peak. Examples
are shown in figure 4. The main current peak is about 160
mA and decays within 150 ns. The same signal is given
onto a second channel of the oscilloscope and the sensitivity increased many times, shown in figure 4 as well. A
very weak oscillation is detected with amplitudes up to 3
mA. In general, the cycle duration increases (repetition
frequency decreases) while the amplitude is slightly reduced. To be precise, the signal presented in figure 4 is
not the regular signal of the setup. It is more like a rare
exception, only occurring every ten or twenty discharges.
The trigger for this type of discharge seems to be very
sensible. With this setup, the observed signal is invariant
to the variation of the cable length or grounding.
The conditions for its appearance were found to be
strongly dependent on the gas flow. While for small argon
flow rates from 200 sccm up to 450 sccm, the signal was
not visible, above 450 sccm argon it could be observed
with a higher rate. For the measurements presented here,
the trigger of the oscilloscope was set to glitch mode for
peaks faster then 10 ns.
The interpretation of these peaks is quite sensitive. To
extinguish electrical reasons like low resolution of the
applied equipment, a 4 GHz oscilloscope (Tektronix
DPO70404B) together with a 2 GHz current probe (Tektronix CT6) were used. The observed current peaks stayed
the same. Therefore, we believe the peaks to result from
plasma activity under very sensitive, external conditions.
4. Discussion
Figure 4 shows electrical current oscillations with a
repetition frequency from 250 down to 75 MHz. This
range of repetition frequency was measured for several
series. Meanwhile the peak amplitudes range from 4
down to 0.5 mA, decreasing with time.
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
One possible explanation for a plasma caused oscillation in this frequency range is the presence of ion acoustic
waves. Within some discharges, the system seems to generate resonance conditions for an ion acoustic wave.
While their observation in low temperature plasma discharges was done under quasi static conditions with nearly no damping, atmospheric pressure with great damping
constants has to be considered here. Until now, the observation is rarely reported and the aspect of save electrical
setups not discussed [5]. For our experiment, we assume
the observed pulse repetition frequency to be the ion
plasma frequency
f 
pi
1 e² n
2  m
(1)
i
0
i
where e is the elementary charge, ni the ion density, ε0 the
dielectric permittivity and mi the ion mass. Argon is assumed to be the dominant ion in these calculations.
By measuring the times between the oscillation maxima
in figure 4, it is thus possible to analyze the time dependence of the plasma ion frequency and therefore the ion
density.
In the moment of maximal discharge current, the discharge gap is bridged by a glow discharge like structure
[2]. Therefore the plasma is considered to be a conducting
channel with a diameter of 60 μm. The current density is
proportional to the electron density with (e – elementary
charge and c – speed of light):
I A  e  n  c (2)
e
An electron density of 1.18 * 1012 cm-3 is calculated.
To evaluate the current peaks in the decay slope, the
velocity in equation (2) is exchanged by the drift velocity
of the electrons:
I A  en v  en   E
1
I (t )
E (t ) 

(3)
e  A   n (t )
e
d ,e
e
e
e
e
The electron mobility in argon is taken from [6]
(Nair=2.44*1019 cm-³ at 300°K): μe=613 cm²/Vs. For the
current peaks, the underground created by the main discharge current is subtracted from the current peaks. Based
on the assumption of quasi neutrality, the electron density
in equation (3) is equal to the ion density from equation
(1).
Observed current oscillation amplitudes as well as the
results from equation 1 and 3 are shown in figure 5. The
current signal shows an increase at the beginning before it
decays from 3 mA to 0.6 mA. The increase of the peak
values at the beginning indicates the build up of the ion
acoustic wave. After the maximum value, the current
value decreases, especially through collisions and diffusion. The argon ion density decreases with the oscillation
frequency (equation (1)) exponentially from 5*1013 cm-3
Fig.5: current value of the peaks in the decay phase
(rectangular), calculated argon ion densities and electrical field strength according to equation (1) and (3)
down to 2*1012 cm-3. The values for the ion density are
one order of magnitude higher then the calculated electron
density from equation (2). This great difference is explained by the uncertainty of the filament cross section.
The used diameter value is evaluated from pictures of the
whole discharge (some μs accumulation), while the peaks
in the decay phase occur directly after the transient spark
breakdown and the created species could not diffuse that
far in that short time. Therefore, the diameter of the filament will grow in time by diffusion, as will be discussed
later on. From the value of current peaks and densities in
figure 5, the electrical field strength is calculated according to equation (3). It shows an increase from 5*103 V/cm
up to 15*104 V/cm. Such high values as well as the rising
tendency are illogical. A voltage of -6.1 kV was applied
over the gap width of 8 mm, hence an electrical field in
the order of 8*103 V/cm and a decreasing slope were expected. Again the diameter of the filament was set to a fix
value, creating a possible source of error.
To account for the radial diffusion in the time scale observed in this investigation, the equation of motion for the
ions is solved. The equation of continuity, mass flux and
charge balance were involved. For our experiment the
filament is assumed to be cylindrical. The radial electrical
field is neglected as well. We get:
n
 (n  v)  0
t
j   ( n  b  E  D  n )   D  n
V  e /   (n  n )  0
e
e
0
i
e
e
The solution of this set of equations is:
n(t , r )  n exp( t / t )  B  1 /(t  D )  r  (4)
0
0
0
0
e
where B is the Bessel function of the first kind with the
root at
1 /(t  D )  r  2.405 (5)
0
e
0
st
21 International Symposium on Plasma Chemistry (ISPC 21)
Sunday 4 August – Friday 9 August 2013
Cairns Convention Centre, Queensland, Australia
The value of the diffusion constant De is accessible from
the Einstein relation De=Ue*μe. The electron energy Ue is
set to 2 eV. For each time step t, t0 was set to the time,
when the exponential decay reaches 1/100 of its start
value, with:
ln( n / n )  ln(1 / 100)  4.6  t / t
t  t / 4.6 (6)
0
0
0
Therefore it is possible to get the time dependend increase
of the filament radius based on diffusion alone. A second
aspect will add up from the radial electrical field
component, which is neglected for now. Equation (6)
inserted in equation (5) gives
r (t ) t  D / 4.6  2.405 (7)
0
e
For t = 100 ns, an increase of the filament radius about
112μm is calculated.
Considering the radial expansion for each instant of a
current peak allows the recalculation of electrical field
strength according to equation (3). The result is shown in
figure 6. Electrical field values around 6.3 kV/cm are
calculated. This range is within the expectations.
Furthermore, the electrical field strength stays almost
constant over the whole range (if the first two values of
the data-set are omitted).
5. Conclusions
Investigations concerning high frequency oscillations of
the discharge current are presented. One source of oscillation are voltage probes. It was found, that ground loops
create high frequency oscillations. Therefore special care
has to be taken for high sensitive current measurements.
An improved setup with only a current probe proved to
be sensitive and free of ground loops. This setup revealed
weak current oscillations of 3 mA amplitude in the decay
phase of a transient spark discharge, where current peaks
of typically 200 mA had been observed. The oscillation
repetition frequency decreases from 250 down to 75 MHz.
This is within the range of the plasma ion frequency. The
propagation of an ion acoustic wave within the remaining
discharge channel is proposed.
From the observed oscillation frequency and the current
amplitudes, the electrical field strength and the argon ion
density is calculated. Diffusion processes are considered
to describe the growth of the discharge channel during the
decay of the main discharge peak and to improve the
electrical field strength calculations.
The presence of ion acoustic waves, despite high collisions at atmospheric pressure, leads us to reasonable results for the argon ion density and hence electrical field
strength.
6. Acknowledgements
The authors are grateful to P. Holtz for providing practical assistance. This work was realized within the
framework of the multi-disciplinary research cooperation,
``Campus PlasmaMed'', supported by German Ministry of
Education and Research (BMBF, grant no, 13N11188)
which is gratefully acknowledged.
Fig.6: calculated electrical field strength according to equation (3) under consideration of radial diffusion (equation 7)
This finally shows, that an evaluation based on the ion
acoustic wave interpretion gives plausible results. The
electrical field strength as well as the argon ion density
calculations are within reasonable scales. Furthermore we
would like to point out, that smaller peaks with a second
frequency were observed, but the evaluation of these
signals was not possible until now.
7. References
[1] Th. v Woedtke et al, Phys. Rep, (2013) DOI:
10.1016/j.physrep.2013.05.005.
[2] T. Gerling et al, J. Phys. D: Appl. Phys., 46, 145205
(2013) DOI: 10.1088/0022-3727/46/14/145205
[3] R. Bussiahn et al, Appl. Phys. Lett., 96, 143701
(2010) DOI: 10.1063/1.3380811
[4] M. Janda et al, Plasma Sources Sci. Technol., 20,
035015
(2011)
DOI:
10.1088/0963-0252/20/3/035015
[5] B. Qi et al, Phys. Plasma, 18, 083302 (2011) DOI:
10.1063/1.3622632
[6] S. Pfau and A. Rutscher, Annalen d. Physik, 22, 166
(1969)