Experiments and Simulations of stripes in pulsed DC-discharge
Xiaofei Zhao, Feng He, and Jiting Ouyang*
School of science, Beijing Institute of Technology, Beijing 100081, P. R. China
Abstract: The striation phenomenon in pulsed DC-discharge was investigated by
an intensified charge coupled device (ICCD) camera and Particle-In-Cell/Monte
Carlo simulation. We obtained time-resolved images to reveal the development
of the striation in the positive column. The spatio-temporal distribution of
electron density, electron energy are also obtained by simulation. The discharge
current and the evolution of particle distribution in the simulation are in
consistent with the experimental results. The results of experiment and
simulation show that the striation of pulsed DC-discharge is formed one by one.
The average energy of electron change remarkably as the striation forms.
Keywords: striation, time-resolved image, simulation
*Corresponding author. Email: [email protected]
1. Introduction
Positive column in direct current discharge is one of
the excellent longitudinal instable systems. Striation
in positive column of DC discharge is an important
instable phenomenon[1], which are considered as the
results of ion-acoustic and ionization waves[2].
Stratification phenomenon is also observed in other
gas discharge system (DBD, RF discharge) and
semiconductor device. The study on striation
characteristics and mechanism is helpful to
understand the longitudinal instability of plasma
system, and helpful to prevent striation in many
applications of gas discharge, such as laser device,
fluorescence lamp, semiconductor manufacturing.
In the past years, many experiment and theoretical
studies have been done on striation formation of
different discharge conditions. However the
mechanism of striation forming and the instability
phenomenon in gas discharge system is still not
obtained a “full micro-physical explanation”[2]. In
this paper, we investigate the evolution of the
striation in DC discharge tube drived by a pulsed
square-waveform source. The images of straition
forming process are obtained by ICCD. And this
process is also simulated by PIC/MCC method. The
results of experiment and dynamic simulation are
compared, and the formation of striation is analyzed.
2. Experiment and Simulation Setup of
the discharge
2.1. Experiment setup
The schematic diagram of the expereimental
apparatus and the discharge tube used in our study is
shown in Figure 1. The discharge device is a
classical DC discharge tube. It consists of a pair of
plane aluminium electrodes (A and C) and a
cylindrical glass tube. The two electrodes is sealed
in the tube, and 80%Ar+20%Ne of 40 Pa(0.3 Torr)
is filled in the discharge space. The distance between
the two electrodes is d=0.15m. The inner diameter of
the glass tube (also the diameter of the electrodes) is
D=0.01m. The thickness of the glass tube is 1mm.
Figure 1.The schematic diagram of the experimential apparatus
and the discharge tube
In our experiment, the cathode is ground through a
resistor, and a square-wave with positive high
voltage is applied to the anode. The frequency of the
square wave is f = 1 kHz, and the duty ratio is 50%.
So the width of the voltage pulse is 0.5ms, which is
much larger than the time span from the gas
breakdown to the stable discharge( the time span in
this discharge tube is on the order of tens of
microsecond). So we consider that the discharge in
our experiment is a pulsed DC discharge, and the
whole process of DC discharge will be repeated in
each voltage pulse.
than that in the experiment. The simulation is
correspond to one discharge pulse, so constant
voltages 1200V (VA) and 0V (VC) are applied on
electrodes A and C respectively. At boundary no
electrode placed, Neumann condition is used. The
relative permittivity of glass is 6.
The waveform of the voltage source is obtained by a
oscilloscope through a high voltage probe P6015A.
A resistor used to measuere the discharge current is
24 kΩ(Figure 1).
3.1. images of striation in pulsed dc discharge
The light emission was measured by using an
intensified charge coupled device (ICCD) camera
(PI MAX-2) from side view of the discharge tube.
The ICCD camera is synchronized with the squarewave voltage source by a trigger signal exported
from the oscilloscope. The time-resolved ICCD
images were recorded by integrating the light
emitted from the discharge over several cycles
during a time interval (gate), which was moved over
the entire duration of the voltage pulse. In our
experiment, the gate of ICCD is set to be 100ns,
which is much shorter than the duration of the
voltage pulse (0.5ms).
The initial density of electron and Ar+ are both
1012cm–3. The maximum total number of macroparticles is 106. The time step of Poisson solver is
10–11s.
3. Results and Discussion
Figure 2 is the light emission of standing striation
during one discharge pulse at applied voltage
V=900V. This image is obtained by integrating the
light emission from the rising edge to the falling
edge of a voltage pulse( the gate of ICCD is set to be
0.5ms). From this Figure, one can see that the
striations are formed clearly. If the light emission
was integrated in several discharge pulses, the image
of the light emission is similar with that of Figure 2.
It means that the standing striations can be obtaiend
in our dc discharge experiment, and each discharge
process of the pulsed voltage is repetitive. So the
forming process of striations can be obtained by
integrating the light emission at the different
moment in several discharge pulse.
2.2. Simulation model
The evolution of the pulsed DC gas discharge was
also simulated by PIC-MCC method[3] in a
cylindrical coordinate system. The structure used in
simulation is the same as that in Figure 1. The
discharge gas is argon, and the gas pressure is 40Pa.
Two species are considered in the simlulation:
electron and Ar+. The ionization and elastic collision
process between electron and Ar atoms, also the
excitation collision of Ar are considered. The cross
sections of those collision process are taken from
Ref.4. The coefficients of secondary electron
emission by Ar+ impacting on electrode is 0.2 (γAr).
Dirichlet boundary condition is adopted at where the
electrodes located. The voltage applied on the
electrodes A and C in the simulation is a little higher
Figure 2. Light emission during one discharge pulse, V=900V,
f=1kHz
Figure 3(a) shows the waveforms of the current and
the voltage from the rising edge of the voltage to the
stable discharge when a pulsed voltage 900V is
applied. Figure 3(b) is the images of light emission
at different moments after the rising edge of voltage
pulse. Each image is obtained by integrating the
light emission with ICCD in 10 pulses.
From the waveform in Figure 3, one can see that a
small current about 0.5mA is measured during 0μs
~0.2μs. In this period, the voltage oscillates with
wide-range, and the peak is over 1100V. High
voltage cause intense ionization/ excitation
processes, and a bright region is detected near anode
(Figure 3(b) at 0.1μs). This bright region expands
toward the cathode, and lasts in a short time. At
t=1.1μs, a light emission region is formed near the
cathode, which means that the cathode region and
the negative glow region formed. The intensity of
light emission is much lower than that of 0.1μs. In
this phase, no striation is detected between negative
glow and the anode. At t=4.1μs, a luminous region
appear near the negative glow, and the first striation
is formed at the left side of the negative glow. The
dark region between them corresponds to the
Faraday dark space. At t=9.1μs a long positive
column is formed and several striations appear.
6
1.0
5
0.8
4
0.6
3
0.4
2
0.2
1
0.0
-2
0
2
4
t / μs
6
8
Figure 4 shows the evolution of the current on anode
and the spatial distribution of electrons obtained by
simulation. From Figure 4(a), one can see that it
takes about 1.5μs for the discharge current to rise to
a stable value of 0.7mA. The evolution of the current
can be divided into 3 stages. In the first stage, after
the voltages are applied on the electrodes, the
electrons shift toward the anode and ionize the argon
atoms. The density of the charged particles increases
and a group of electrons appears near the anode
(Figure 4(b) t=0.3 μs). This correspond to the image
of Figure 3(b) at 0.1μs. As the density of electrons
increasing, the cathode sheath begins to form and the
positive column appears (Figure 4(b) t=0.8μs).
(a)
1.2
1.0
0
10
I / mA
1.2
current / mA
7
voltage / kV
(a) 1.4
3.2. Evolution of electron density and energy
0.8
0.6
0.4
0.2
0.0
(b)
0.1μs
1.1μs
4.1μs
9.1μs
Figure 3. (a)The waveform of applied voltage and discharge
current with 900 V plused voltage at 1kHz. (b)The time-resolved
image of light emission in the pulsed discharge at 0.1 μs, 1.1 μs,
4.1 μs and 9.1 μs.
Figure 3(b) show that before the first striation is
formed, the positve column is not luminuous and no
intensive excitation processes take palce in the
positve column during 0.2~1.1μs. This also indicates
that only few high energy electrons will pass
through the positive column in this phase. After the
negative region formed, the striations of pulsed dc
discharge appear one by one in the positve column
(4.1μs ~9.1μs) .
(b)
0.0
0.5
1.0
1.5
t / μs
2.0
2.5
0.1μs
0.3μs
0.8μs
1.0μs
1.4μs
2.6μs
Figure 4. The evolution of the discharge current(a) and the
spatial distribution of electrons(b)
In the second stage, the current grows from 0.1mA
at t=0.8μs to 0.7mA at t=1.4μs. The cathode sheath
contracts, from about 2cm to less than 1cm,
respectively. The first striation of electrons appears
in the positive column (Figure 4(b) t=1.0μs).
As the cathode sheath contracting, the current
reaches a stable value of 0.7mA. The striation moves
toward the cathode (Figure 4(b) t=1.4s). At the same
time, several striations are formed in the positive
column. After that, the current maintains about
0.7mA. The results show that the striations appear
in the positive column one by one, and the evolution
of striations is accord with the experiment results.
in positive column is uniform approximately.
However, the mean electron energy increases in
region R2 (as shown in Figure 5(a)). But the mean
electron energy is much lower than the excitation
energy 12eV and the ionization energy 15.76 eV of
Ar. As the negative glow moving towards the
cathode, a strong-field area forms in R1 which cause
the mean electron energy increasd over 12eV at z =
9cm. The electrons move toward the anode and
ionize neutral particles in area R2. A striation with
high density of electrons appears. High electron
density also causes a potential well. Thus electrons
can hardly gain energy from the electric field in the
striation area. Because the energy is dissipated on
ionizing atoms, the mean electron energy is reduced
to about 5eV at the tail of the striation. The
simulation results show that the striation appears
accompanying high energy electron pass through the
striation region.
4. Conclusion
R2 R1
(a) t=800ns
In this paper, the standing striation of pulsed DCdischarge was investigated by experiment and
numerical simulation. The time-resolved images of
striation evolution are obtained by ICCD camera.
The result shows that the striations of pulsed dc
discharge appear one by one. The simulation result
is accord with that of the experiment. The spatiotemporal distribution of the mean energy of electron
changes markedly, and the striation appears as high
energy electron moving through the positive column.
Acknowledgments
R2 R1
This work was supported in part by the National
Science Foundation of China under Grant No.
11005009.
References
1
(b) t=1000ns
2
Figure 5. The spatial distribution of the mean energy of electron,
electron density and potential at 800ns and 1000ns
3
Figure 5 shows the distribution of mean electron
energy ε e and the potential before and after the
4
striation forming. One can see that at 800ns (before
the first striation appearacne), the density of electron
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