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4th International Conference on Applied Electrical and Mechanical Engineering 2017 (ICAEME 2017),
Nongkhai, Thailand, August 31 - September 2, 2017
-9-
Behavior Analysis of Arc Current Using Copper
Cathode and Cathode Spot Theory for Instability
Phenomenon in Vacuum Arc
Noritsugu Kamata1,*, Narong Mungkung1, Somchai Arunrungrusmi1, Pakpoom Chansri1,
Toshifumi Yuji2 and Hiroyuki Kinoshita3
1Department of Electrical Technology Education, King Mongkut's University of Technology Thonburi Bangkok 10140,
Thailand.
2Faculty of Education University of Miyazaki, 889-2192 Miyazaki Japan.
3Department of mechanical design systems engineering University of Miyazaki, 889-2192 Miyazaki Japan.
*Corresponding author e-mail: narong_kmutt@hotmail.com
Abstract - In vacuum breakers, the instability phenomenon
occurs in the arc current at a current value before current
cutting is generated. This arc phenomenon sometimes
causes a current cutting due to this arc phenomenon.
Therefore, it is the purpose of this report to capture the
instability phenomenon due to vacuum arc discharge in
the small-current arc region when cupper electrodes are
used. A cathode spot model where a collision less sheath
and collision plasma was connected to each other was
constructed. A unique solution to the arc current
(independent variable of discharge phenomenon) was
obtained by simulation of dichotomy. As a result, it was
supposed that the current that gives a real solution has a
lower limit, the electrons that back-diffused from the
collision plasma in cathode ion sheath exceed the ion under
19 A and the cathode spot that requires the existence of the
ion sheath as a necessary antecedent or precondition does
not exist anymore. It was concluded the non- existence of
the cathode spot is connected the current instability
phenomenon.
I INTRODUCTION
In this paper, the current-chopping phenomenon is
simulated in the vacuum circuit breaker using the
copper electrodes without providing the transition
region but making the region quite close to the
transition region in the collision less sheath and
collisional plasma regions, and 8 equations of the
cathode spot model are developed (voltage applied to
sheath section, cathode spot radius, current density,
percentage of electron current on the cathode surface,
cathode spot surface temperature, strength of electric
field on the cathode surface, plasma density at the end
of sheath, and plasma temperature). In these 8 equations,
there are two unknown parameters that cannot be
theoretically calculated (percentage of ion current
moving toward the anode in plasma, and cathode input
Veff (I) which changes as the arc current changes). For
this reason, we used the experimental data and bisection
method, and found out that the arc became unstable
when the solution for two unknown parameters of the
arc current threshold was in the region of imaginary
numbers [1-2].
II ARC CATHODE SPOT MODEL
Input voltage (electrode)
G. Ecker presented a view that the rapid increase of
the electron current in low current region led to
increased loss and that might be the source of unstable
arc phenomenon. They attached plasma approximate to
the electromagnetic fluid to the collision less sheath
mentioned previously to analyze the cathode spot. In
this analysis, the cathode input Veff that changes as the
arc current I changes is expressed as Equation (1)
the percentage of the ion current flowing back to the
anode side in the plasma as Equation (2) and used them
as experimental parameters for analysis. Electrodes
(both anode and cathode) have symmetrical structure
and a thermocouple is embedded in each of the Cu
electrodes. After supplying DC arc current I, the rise of
Tc Ta is measured on the
cathode and anode respectively. Using the arc voltage
Va at this point, the cathode input Vef f and anode input
Veff a were verified. The cathode and anode inputs can
be obtained using the following two methods. The arc
voltage in low-current vacuum is constant regardless of
the distance between electrodes, and when there is no
potential gradient in the arc collisional plasma region,
the voltage drop in the arc positive column is ignored.
Therefore, the input by the arc voltage Va is
considered to be the cathode and anode inputs as shown
4th International Conference on Applied Electrical and Mechanical Engineering 2017 (ICAEME 2017),
Nongkhai, Thailand, August 31 - September 2, 2017
-10-
in the Equation (1). The Equation (1) and Equation (2)
are shown below.
Fig. 1 illustrates the cathode spot model. The figure
shows the region connecting the collisionless sheath and
collisional plasma, and no transition region is provided
between two regions. When we try to attach plasma
approximate to fluid to the sheath, there is no rationale
to determine Vp, the voltage applied to the sheath.
...................................... (1)
.................................... (2)
Fig. 1. Cathode spot model.
B. Arc current equation
Fig. 2 illustrates the cathode spot radius a. With the
relational expression between the average cathode
surface temperature and thermal flow rate toward the
cathode, JVeff= (3 Ko/8a) U where U= (0.45 T+348)
for copper cathode. The relation of Equation (1) is true
among current I, current density J, and cathode radius a.
I (3)
Using the relation of JVeff= (3 Ko/8a) U, the basic
analysis equation is transformed to eliminate the
cathode spot radius a and thus, a= (3 KoU/8JVeff).
Using I= a2J, I= (3 KoU/8JVeff)2J. Therefore,
the variable J will be J = (9 3Ko2U2/64IV2
eff). Ion
current density (1-S) J the ion current density in the
sheath, is assumed to be equal to the ion saturation
current density from the plasma. Which means that the
Equation (3) will be true;
(4)
Fig. 2. Cathode spot radius a.
EXPERIMENT DATA
A. Monovalent fully ionized
Let's assume that the entire plasma will be singly
ionized. The Equation (2) shown below represents the
mass flow of the atom evaporated from the cathode, and
the second term represents the ion mass flow moving
from the plasma side to the anode and is determined by
the ion saturation current density. The right side of the
equation means that only ( ) M in the cathode
material represent the ion mass flow moving toward the
anode.
(6)
Fig. 3 shows the flow of atoms evaporated from the
cathode and the mass of the ion moving toward the
anode, under the assumption that the plasma is fully and
singly ionized.
C. Electron emission
The electron emission obtained with T-F theory and
the one obtained from the thermionic emission
considering Schottky effect show nearly no difference.
Here we use the Equation (4), the equation for
thermionic emission that gives simplified calculation
formula. It shows the positive charge of the ion current
(1-S) J flowing from the plasma side into the cathode
and the negative charge of the electron current SJ
emitted from the cathode.
4th International Conference on Applied Electrical and Mechanical Engineering 2017 (ICAEME 2017),
Nongkhai, Thailand, August 31 - September 2, 2017
-11-
Fig. 3. Collision less sheath and collision less plasma.
(5)
Fig. 4. Collisionless sheath and electron current
D. Electrode surface electric field
Considering the positive charge of the ion current (1-S)
J flowing from the plasma side into the cathode, the
negative charge of the electron current SJ emitted from
the cathode, and electron that diffuses reversely into the
sheath after getting over the potential barrier Vp from
the plasma side, the poisson equation inside the sheath
is developed. When the electric field on the plasma side
of the sheath is 0 and the potential is Vp, the Equation
(5), known as Mackeown equation, is obtained for the
electric field F0 on the cathode surface. The equation for
the electric field on the cathode surface is shown below.
(6)
You have to provide the positive charge J of the ion
current (1-S), negative charge of the electron current SJ,
and negative charge plasma side parameters No and Te
caused by the back-diffusion electron. You need to
know the plasma side parameters No and Te to obtain F.
In the simplified sheath theory, No and Te are not
provided and the numerical evaluation is not conducted.
The back diffusion term is ignored since its contribution
is small. When the back-diffusion term is not considered,
it will be Fo
2 > 0 because of the magnitude of (M/rm)1/2,
and normally the ion sheath is stable. Affected by the
back-diffusion electron from the plasma side, the
number of ions in the sheath may get smaller than the
number of electrons, and the presence of the ion sheath
may be lost. The Equation (6) shows the average
temperature of the energy balance on the cathode
surface.
(7)
The Equation (7) expresses the heat flux toward the
cathode. The first term on the right represents the input
through the ion collision. The second term is the loss
caused by electronic emission, and the third term is the
loss caused by metal vaporization.
78)
The Equation (8) shows the energy conservation
equation for plasma. Integrating the energy conservation
equation for plasma gives this expression. Solving the
equation of motion will be as follows [3,4].
(8)
SIMULATION RESULTS
Now that eight relational expressions are obtained,
we should be able to obtain the solution if the arc
current I, an independent variable, is given. Solutions
obtained by using bisection method on the eight systems
of equations shown so far are eight (Vpa J S T
FoNo Te).
These values are shown using the arc current as a
parameter for both of the silver cathode spot and copper
cathode spot. Here we used thermally measured data. In
order to eliminate the voltage Vp applied to the sheath,
we thermally measured the effective thermal input.
Measurement conditions are: Arc current of 16.16 to
83.4 A, electrode opening of 1 to 2 mm, and arc time of
several seconds. The parameters Fo and S, Vp, T
dropped suddenly when the arc current I reached around
18 to 19 A. To have no solution at 18 A or lower, the
plasma density No must be high in discharge state with
current density J being high as the arc current decreases.
In the Equation (5), the number of ions is excessive
4th International Conference on Applied Electrical and Mechanical Engineering 2017 (ICAEME 2017),
Nongkhai, Thailand, August 31 - September 2, 2017
-12-
compared to electrons in the sheath due to the
back-diffusion electrons into the ion sheath. With this,
the steady arc that assumes the presence of the ion
sheath will be no more present. This means Fo
20, and
an imaginary root will appear.
Therefore, the mechanism to maintain the cathode
spot changes and it is believed that this contributed to
the appearance of unstable arc phenomenon.
Electrode input measurement circuit
Fig. 5. Measurement of electrode input
A. Relationship between electron current fraction and
arc current
Fig.6 shows the relation between the electron current
fraction and arc current. Here, the electron current
fraction bears an inverse relation to the arc current. With
the arc current of 15 A, 18 A, and 20 A.
Fig. 6. Relationship between electron current fraction and arc
current
It is believed that the electron current fraction increases
because the cathode surface temperature and cathode
electric field increase as the arc current decreases.
B. Examination of degree of ionization
In this study, we assumed full univalent ionization
and also studied the divalent ionization. We also studied
the copper cathode with 25 A current supplied as an
analysis condition. The Equation (9) is formed using
(kTe/q)= 2.3 eV and Pp= 1×106 N/m2. With the
ionization voltage Vi= 7.68 eV for univalent ionization,
the degree of ionization was X= 1. Similarly, with the
ionization voltage Vi 20.2 eV for divalent ionization,
the degree of ionization was X= 0.7.
(9)
(10)
(11)
(12)
CONCLUSIONS
The analysis of this study allowed us to obtain the
solution for unknown parameters VpJ S T Fo
NoTe and a for the arc current I. So far, a report on the
proper assumption of full univalent ionization has been
made. Developing Saha ionization formula, we
confirmed the degree of ionization X for divalent
ionization. Aggregating the values obtained from the
result of executing the program, we evaluated the
electron current fraction and cathode temperature when
the cur = 0.1.
The result showed that the solution for unknown
parameter was an imaginary number when the arc
current reached 19 A or lower using the copper cathode,
which contributed this region to be unstable.
In the future, we are going to perform similar
simulation evaluation using bisection method on the
composite material used as new electrode material to
study resistance heating within the cathode spot solid,
and analyze the degree of ionization in the collision less
sheath with new conditions.
REFERENCES
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Comparison with probe measurement of the analysis
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No. 5 pp.436-442 (2003).
[2] G. Ecker in
4th International Conference on Applied Electrical and Mechanical Engineering 2017 (ICAEME 2017),
Nongkhai, Thailand, August 31 - September 2, 2017
-13-
Vacuum arcs J.M.Lafferty(Editor) John Wiley & Sons
pp.242-251 (1980).
[3] O. Morimiya and N. Ikeno: An Analysis of a Stationary
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[4] O. Morimiya S. Suzuki and K. Watanabe: An Analysis of
the Instability Phenomena of a Low current Vacuum Arc T.
IEE Japan Vol.119 No.2 pp.190-196 (1999).in Japanese
[5] T. H. Lee and A. Greenwood: Theory for the cathode
mechanism in metal vapor arcs J. Appl. Phys.32 5
pp.916-923 (1961).
[6] Y. Niwa and E. Kaneko: of High Interruption
Capability Vacuum Circuit Breaker: Technology of Vacuum
Arc Control J. Plasma Fusion Res Vol.81, No.1, pp.5-11
(2005).in Japanese
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