Optics and Photonics Journal, 2013, 3, 313-317
doi:10.4236/opj.2013.32B073 Published Online June 2013 (http://www.scirp.org/journal/opj)
Simulation of Gas Discharge in Tube and Paschen’s Law
Jing Wang
Department of Physics and chemistry, Air Force Engineering University, Xi’an, China
Received 2013
ABSTRACT
According to the related theory about gas discharge, the numerical model of a gas discharge tube is established. With
the help of particle simulation method, the curve of relationship between gas ignition voltage, gas pressure and elec-
trode distance product is studied through computer simulation on physical process of producing plasma by DC neon
discharge, and a complete consistence between the simulation result and the experimental curve is realized.
Keywords: Gas Discharge; Ignition Voltage; Density; Ionization
1. Introduction
Plasma is one of the four material forms which also in-
clude the other three states: solid, liquid, and gas. Plasma
is a kind of matter with high-energy state of aggregation
in the ionization status. It can reflect different character-
istics from that of general conductor or medium when the
electromagnetic waves interact with the plasma. It can
realize the purpose of stealth if it is applied into the mili-
tary affairs [1]. At present, there are two primary ways in
producing stealth plasma, one is to use the plasma gen-
erator, the other is to coat a layer of radioactive isotope
in the specific parts of the weapon (such as strong scat-
tering area). Compared with the former methods, the
latter is more expensive and more difficult in mainte-
nance [2].
The author believes that it has many unfavorable fac-
tors to use the air near the surface of air vehicle to pro-
duce plasma sheath. The first one is that the density and
temperature of the atmosphere changes with the flying
height, and it is difficult to control and regulate the plasma
parameter technically. In addition, electrode scale and
high-energy power unit will be a difficult technical prob-
lem, because the breakdown voltage of atmosphere is
very high. The second one is that the motion of the air
vehicle will affect the surface airflow and formation of
the plasma, which will be an extremely disadvantageous
factor to ensure the stability and reliability of the stealth
system. In contrast, the mentioned difficulties can be
overcomed by using the mechanism of surface discharge
tube to a certain extent. The ignition voltage can be
greatly reduced and the plasma state be controlled con-
veniently through the study of nature and ratio of the gas
in the discharge tube.
2. The Theory of Gas Discharge
The phenomenon that all current goes through the gas is
called gas electric or gas discharge. The charged particles
which form the current must interact with gas atom.
Generally, part or all of the charged particles are supplied
by gas atom (namely ionization process), or the charged
particles must at least collide with the gas atom (such as
motivated conduction). Here the gas conductivity is not
constant, and it depends on the gas ionization effect by
the outside world and the size of the current, and even
the leader process in unstable condition.
2.1. The Volt-Ampere Characteristic of Gas Dis-
charge
The simplest circuit model of gas discharge consists of
three parts: the dc power, discharge tube and load resis-
tance. And discharge tube includes cathode (K), anode
(A) and glass tube or metal tube filling with gas.
When the gas discharges, a large number of electrons
and positive ions will be produced in the discharge space;
and they will migrate and form current under the role of
the inter-electrode electric field. Positive space electric
charge will be formed in the discharge space due to the
large quality and slow motion of the positive ions, and it
is helpful for the electronic to run to the anode, which
makes the discharge tube to gain large current in low
voltage. The relationship between the voltage drop and
the discharge current is called the volt-ampere character-
istic of gas discharge. Figure 1 describes the volt-ampere
characteristic curve about discharge tube filled with 133
pa neon, it can be divided into seven areas.
I (OC section) is the non-self-sustaining discharge area.
The so-called non-self-sustaining discharge means that

J. WANG
314
the initial charged particles are caused by outside ioniza-
tion source, and discharge stopped immediately when the
outside ionization source is removed.
II (CD section) is the self-sustaining dark discharge area.
This kind of discharge means that the medium conduc-
tivity remains and continuous discharge is resulted in by
the ways that the regeneration of ionization offsets the
composites and its loss mechanism. The corresponding
voltage of C point is the ignition voltage, and tube volt-
age drop is close to the power voltage. But the discharge
current is still very low and light is faint, so, it is called
dark discharge.
III (DE section) is the transition area and remains ex-
tremely unstable. It will quickly transfer to E point as
soon as the circuit current increases slightly.
IV (EF section) is the normal glow discharge area. In
this area, the tube voltage drop keeps almost unchanged
if current increases. Gas discharge will produce glow in
this area, therefore it is named.
V (FG section) is the abnormal glow discharge area. In
this area, the tube voltage drop will grow along with the
increasing of the current.
VI (GH section) is the transition to arc discharge area.
VII (after H) is the arc discharge area. Bright arc will
occur in the tube while discharging, meanwhile tube
voltage drop is lower and current is larger.
From the volt-ampere characteristic we can obtain that
the gas discharge has two stable discharge areas: normal
glow discharge area and arc discharge area [3].
2.2. Townsend’s Discharge Theory
British physicist Townsend holds the opinion that when
the electrons move in a homogeneous electric field, on
the one hand, they will continue to get energy from the
field, on the other hand, the energy will lose because
ionization caused by electrons impact gas atoms. As a
result, the two parts of energy should be equal while the
two kinds of effect achieve balance. When the charged
particles generated by impact ionization are accelerated
by electric field, new impact ionization can be caused.
Ua (V)
600
800
1010
-5
10
-15
10
-12
10
-4
10
-1
1
I (A)
Ⅰ Ⅱ Ⅳ Ⅲ Ⅴ Ⅵ Ⅶ
O
C D
EF
G
H
400
0
Figure 1. Volt-ampere characteristic curve.
When thode,
im
2.3. Gas Breakdown and Paschen’s Law
gree,
igni-
tio
arge Tube
in
an initial electron runs to anode from ca
pact ionization will occur in order 1, 2, 3, and 4 and so
on. And new generated electrons will also run to anode
and cause new impact ionization, the electron number
which move to anode will increase correspondingly to 2,
4, 8, and 16 and so on. It is called electron avalanche
because electrons become more and more like avalanche
growth. The avalanche theory can apply to the discharge
area in which directed movement of the electrons is
dominant and random thermal motion of the electrons is
secondary.
When the external voltage is raised to a certain de
discharge mode turns into glow discharge or spark dis-
charge and the conversion process is breakdown. The
inter-electrode voltage needed for the transition from
non-self-sustaining discharge to self-sustaining discharge
is called ignition voltage or breakdown voltage, and this
is an important parameter of gas discharge device.
Through measuring the relationship between the
n voltage and breakdown distance and gas pressure
Paschen discovered a law that: the homogeneous field
will be formed between the inter-electrodes after apply-
ing DC voltage to the two parallel plate electrodes. The
inter-electrode distance is made as d(mm) and pressure is
p(Pa), if gas components and electrode stuff are assured,
and the gas is homoiothermal, then ignition voltage Ub is
a function of pd instead of the two variables: p and d ,
under the cold electrode condition, and Ub have a mini-
mum Ubmin when the numerical value of pd is changed.
Later, the law is called Paschen’s Law [4].
3. Simulation of Gas Discharge
3.1. The Numerical Model of Disch
The numerical model of gas discharge tube established
this paper is shown in Fig ure 2.
A
K
x
zi)
（
y
(j)
Figure 2. Numerical model.

J. WANG 315
The upper and the lower boundaries are plane parallel
electrodes (secoentndary electron emission coeffici 0.40


),
in
= 13
133Pa·cm), and adjust the
. Then the variable curves
the middle is the discharge gap, and discharge gas Ne
(anode-to-kathode distance d = 20 cm, pressure p 3
Pa) is sealed. The gas in the discharge gap will discharge
and produce plasma when some certain voltage is added
on the electrodes.
3.2. Results of Simulation
First, given pd value is 10 (×
voltage Ua between electrodes
as shown in Figure 3 to Figure 8 about charged particle
density at discharge gap will be obtained while Ua gradu-
ally increases.
0.0 0.4
t(μs)
0 1.874(×10
4
)
n(/m3)
Figure 3. Electron density curve (Ua = 150 V).
×10
6
)
n(/m
3
)
t(μs)
0.0 0.4
0 1.017(
Figure 4. Ion density curve (a = 150 V).
0.4
t
(μs)
0.226 1.
n(×10
4
/m
3
)
874
0.0
n(/m
3
)
1.700(×10
3
)
0.0 0.
2.682(×10
6
)
4
t(μs)
Figure 6. Ion density curve(Ua = 300 V).
0.0 0.4
1.788(×104) 2.08 8( ×10 9)
n(/m
3
)
t(μs)
Figure 7. Electron density curve (Ua = 400 V).
1.700(×10
3
) 7.762(×10
9
)
n(/m
3
)
t(μs)
0.0 0.4
Figure 8. Electron density curve (Ua = 400 V).
Figures 3 and 4 show the changing rule of charged
particles density when applied voltage is lower than igni-
tion voltage. At this point, the electron density can quickly
reduce to zero, and the ion density will increase first and
then decrease gradually to zero, the gas discharge cannot
last. Figures 5 and 6 indicate that the density of charged
particles will increase in accordance with the index law
when the applied voltage just reaches the ignition voltage,
and it is the result of electron avalanche. Figures 7 and 8
show that the increasing of electron density and ion
sity ter
an ignition voltage. According to the above phenomena,
w
den-
are more apparent when applied voltage is grea
th
e can get a critical value of inter-electrode voltage at dif-
ferent
Figure 5. Electron density curv(Ua = 300 V).

J. WANG
316
cor
5
Table 1. pd and responding UB.
pd (×133Pa·cm) 1 2 3 10 20 30 50 100 200
Ub(V) 360 270 230 260 300 350 480 600 750 〉1000
0 1 2 3 5 10203050100
900
200
300
400
500
600
700
800
U
b
(V)
pd(×133P a·cm)
Figure 9. Simulation curve.
values of pd by changing the external condition such as
gas pressure p and inter-electrode distance d, here the
voltage is the ignition voltage. Record each ignition
voltage measured as is shown in Table 1.
We draw the corresponding curve as shown in Figure
9 according to the data in Table 1.
The curve has the following features: U has a bearing
le the pd value
in
e increasing intensity
of
mulation curve in the same direction.
In
pletely, which can eliminate the error between MCC
method and experiment and can correct the program.
The changing rule that ignition voltage varies with the
value of gas pd is shown in Figure 9. And the phenome-
non can be interpreted as whepd is very low, the colli-
ncy or ratio will increase if value of pd in-
creases, but the probability of ionization changes little,
the
to
n
sion freque
b
on pd product; the curve goes down first and then rises
with a minimum value; the curve in the left of the mini-
mum value is very steep, but that in the right is relatively
smooth. Two conflicting factors work whi
creases. On the one hand, the colliding numbers of
electrons and atoms grow due to th
pressure, and it is favorable for discharge. On the
other hand, average free path decreases and the energy
that the electrons obtain from the electric field also re-
duces in each free path, and it is unfavorable for dis-
charge. The ignition voltage depends on the contrast of
these two factors.
It’s worth mentioning that the simulation results of the
voltage value and experimental value at each point have
the certain error in the same direction because only some
influential collision effects have been considered in the
MCC model of program. This phenomenon represents a
certain numerical value deviation between the experi-
mental curve and si
order to make the simulation results to agree with ex-
perimental results, we have prescribed the adjustment
coefficients icxfactor and ecxfactor of the relative colli-
sion cross section, and adjust their values to make theo-
retical data to be consistent with experimental data com-
and the result makes ionization frequency has a trend of
growth. At this point, only low applied voltage is needed
if we want to maintain gas discharge, therefore, Ub will
decrease along with the increase of pd. However, when
pd is very high, the electrons get smaller energy from
electric field in each average free path, so the electronic
energy decreases with the increase of pd value, and the
probability of ionization reduces proportionally which
leads to the rise of ignition voltage. Simultaneously,
tal number of collision will increase in proportion
along with the increase of pd, and the ignition voltage
will have a downward trend. The roles of these two fac-
tors neutralize each other and the ignition voltage in-
crease little, so the characteristic curve goes up compara-
tively smoothly.
Thus it can be seen that the ignition voltage will rise
no matter the value of pd is too high or too low, so there
is a proper pd value which can make the ignition voltage
at the minimum.
Through simulation of the gas discharge process, we
can see that using the gas discharge tube technology can
produce plasma with certain density under hundreds of
voltage. And it can substantially reduce the discharge
voltage compared with the solution that uses the ioniza-

J. WANG 317
tion of air near the surface of air vehicle to produce
plasma. This is an outstanding advantage of the mecha-
nism of gas discharge tube.
REFERENCES
[1] R. J. Vidmar “Electromagnetic Wave Propagation in
Unmagnetized Plasmas,” AD-A250710, 1992.
[2] A. B. Petrin, “Nonlinear Interaction of Microwave and
Vol.26, No.4, pp.150-158.
doi:10.1109 /27.669617
Plane Magnetoactive Plasma Layer,” IEEE Transactions
on Plasma Science, 1998,
[3] J. L. Qiu, “Gazhong University
of Science an Wuhan, 1999, pp.
s, 1960,
aseous Electronics,” Hu
d Technology publisher,
81-90.
[4] J. M. Dawson, Physics Review Letter
pp.118-391.