Coupling of high frequency oscillations in a non-transferred dc
plasma torch
Jinwen Cao, Heji Huang, Wenxia Pan
State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics,
Chinese Academy of Sciences, Beijing, China, 100190
Email: [email protected]
Abstract
The coupling among high-frequency oscillations of arc voltage, arc current and cathode
cavity pressure in a non-transferred dc plasma torch were observed experimentally. These
oscillations co-occur with the same frequency of 4 kHz in an argon plasma. The oscillation of
cathode cavity pressure is inspired by the input electric power when the electric power increases to
a threshold value. And the relationship between the amplitudes of arc voltage oscillation and arc
current oscillation is also obtained.
Keywords: Helmholtz mode, high frequency oscillation, coupling
1. Introduction
Non-transferred direct current plasma torch with long inter-electrode channel and abruptly
expanded anode has its advantages in thermal plasma coating process. Compared to conventional
torch with self-setting arc, the arc length is fixed in such kind of torches, which helps to restrict
large amplitude movement of arc root and hence large fluctuations of arc voltage. Moreover, the
longer arc is also beneficial for obtaining relatively high enthalpy which allows effective
convection of heat and momentum to injected particles [1,2]. However, even with such kind of
torch configuration, there are still small amplitude and high frequency oscillations in arc voltage,
arc current and consequently in input electric power. Previous results show that the time scale of
the high frequency oscillation is close to the order of characteristic residence time of nano-sized
particles as feedstock in plasma spraying. Therefore, the fluctuation may lead to different thermal
history for different particles which remain as one of the main issues hampering the application of
dc plasma in advanced coating deposition [1].
The high frequency coupling phenomena also occur in self-setting arc length torch and have
been studied in large amount of work. Cheron firstly suggested that the high frequency fluctuation
in arc voltage might be caused by Helmholtz oscillation in cathode cavity [3]. This inspiring idea
was developed by J. F. Coudert, V. Rat, etc. in their studies on the coupling between arc voltage
and cathode cavity pressure in non-transferred dc plasma torch [4-6]. In the torch the nozzle acts
as a Helmholtz resonator and the rear cold gas chamber and the plasma are similar to a
spring-mass system. The pressure fluctuation is generated by the oscillation of the plasma in the
nozzle channel which plays the role of a plug. The oscillation in the nozzle which superimposed in
mean flow causes the oscillation movement of arc root and the voltage variation, and the voltage
variation influence cathode cavity pressure [4].
In this paper, the coupling phenomena among arc voltage, arc current and cathode cavity
pressure in non-transferred dc plasma torch with inter-electrode channel and abruptly expanded
anode were studied.
2. Experimental details
The torch and power supply are the same
as those shown in ref. [1], the schematic
diagram of the torch is shown in Figure 1 [2].
The plasma-formed gas was pure Argon with
the total flow-rate fixed in 6 standard liters per
minute (slm). The chamber pressure was kept
below 500Pa in all experiments. The cathode
cavity pressure was measured by a
piezoelectric pressure sensor connected to the
Fig.1 schematic diagram of the experimental system.
rear part behind the injection ring with an
accuracy of 0.5% and a working range of
0~100 kHz.
The distance from pressure sensor to cathode cavity was varied with different length copper
tubes to study the phase-shift phenomena between pressure and arc voltage. The distance varied
among l0 +4.14cm, l0 +10.87cm, l0 +13.77cm and l0 +17.80cm. l0 related to other parts of the
pressure sensor and was constant. The arc current was measured by a hall-effect sensor with
working range of 0~100 kHz. Temporal data on arc voltage, arc current and cathode cavity
pressure were recorded synchronically by an oscilloscope (Textronic TBS 2024).
3. Results and discussion
Figure 2 is a typical result of the arc voltage, arc current, cathode cavity pressure fluctuations
together with their FFT analysis results. The black curve is the arc voltage, the red one is the
pressure and the blue one is the arc current. It shows that the oscillations of the three signals have
the same high frequency of 4 kHz. The voltage ratio of high frequency fluctuation to mean value
is almost 2.2%, much larger than the arc current and the pressure which are less than 1%.
U (V)
P (kPa)
I (A)
77
Amplitude (V)
Amplitude (kPa)
Amplitude (A)
20.0
19.8
76
19.6
96
95
1.6
1.4
19.4 94
1.0
74
19.2 93
0.8
73
19.0 92
0.6
72
18.8 91
18.6 90
0.004
0.005
0.006
T (s)
0.007
0.008
0.08 0.4
1.2
75
71
0.10 0.5
0.06 0.3
0.04 0.2
0.4
0.02 0.1
0.2
0.0
0
5000
10000
15000
Frequency (Hz)
0.00 0.0
20000
Fig.2 Arc voltage, arc current, cathode cavity pressure fluctuations in time (a) and frequency (b) domains
The phase difference between the pressure and arc voltage corresponds to the propagating
time of the pressure variation from downstream to cathode cavity [4]. This coupling might be
caused by Helmholtz oscillation [4-6].
The phase difference changes while the tube length changes as shown in figure 3. The data is
filtered by low-pass filter with the cutoff frequency of 4.5 kHz. Figure 3(d) is the linear fitting
between the four kinds of distance and corresponding time delay. The ordinate is the distance
minus l0 , and the abscissa is the time delay. The slope of the fitting line is 332m/s with a standard
error of 34.9m/s which corresponds the acoustic velocity in the tube.
(a)
Voltage (V)
Pressure (kPa)
19.4
76
19.3
74
(c)
U (V)
P (kPa)
20.0
80
19.8
78
19.6
76
19.2
72
19.1
70
19.4
74
19.2
72
0
0.0000
0.0002
0.0004
0.0006
Time (s)
0.0008
0
0.0010
19.0
0
0.0000
0.0002
0.0004
0.0006
T (s)
0.0008
0.0
0.0010
(d)
(b)
U (V)
P (kPa)
0.18
20.0
0.16
80
0.14
78
19.6
76
19.4
74
19.2
72
Length (m)
19.8
0.12
0.10
0.08
0.06
0.04
0.02
0
0.0000
0.0002
0.0004
0.0006
T (s)
0.0008
19.0
0.0
0.0010
0.00
Equation y = a + b*x
Value
Intercept
Slope
0.07135
332.29578
Standard Error
0.00866
34.88696
0.00000 0.00005 0.00010 0.00015 0.00020 0.00025 0.00030 0.00035 0.00040
Time delay (s)
Fig.3 Different phase-shift with different tube length (a-c), and the fitting line between distance and time
delay (d). (a):L= l0 +10.87cm; (b): L= l0 +13.77cm; (c): L= l0 +17.80cm.
Linear relationship between mean electric power and the cavity pressure is shown in figure
4(a), which can be explained by equation deduced from [4] as below:

 1 m
P0  Pa 
(1   L)  (U * I  Pth )
2 pa s 2
(3)
Figure 4(b) shows an almost linear relationship between mean electric power and the
pressure fluctuation. When the mean electric power is lower than 6.2kW in this experimental
condition, both the vibrations of cathode pressure and arc voltage are hard to be observed. This is
because the amplitude of Helmholtz oscillation is proportional to the square root of the inspiring
energy.
(a)
20.5
(b)
0.14
0.12
19.5
0.10
19.0
0.08
δp (kPa)
p (kPa)
20.0
18.5
0.06
0.04
18.0
0.02
17.5
0
0.00
0
0
5500 6000 6500 7000 7500 8000 8500 9000
U*I (W)
5500 6000 6500 7000 7500 8000 8500 9000
U*I (W)
Fig.4 Dependence of the pressure and pressure vibration on electric power fluctuation.
As shown in Figure 2 the high frequency vibration of arc current has almost inverse phase
with the vibration of arc voltage. Figure 5(b) shows a non-linear relationship between δI and δU,
which indicates that the arc has inductive or capacitive impedance.
(a)
2.5
2.5
2.0
2.0
1.5
1.5
1.0
0.5
(b)
3.0
δU(V)
δU (V)
3.0
1.0
0.5
0.0
0.0
0
5500 6000 6500 7000 7500 8000 8500 9000
U*I (W)
0.0
0.1
0.2
δI(A)
0.3
0.4
0.5
Fig 5. dependence of arc voltage vibration on electric power and arc current vibration.
Acknowledgement
This work is supported by the National Natural Science Foundation of China. (No. 11175226)
References
[1] Heiji Huang, Wenxia Pan, Chengkang Wu 2011 Plasma Chem Plasma Process 32:65-74
[2] Heiji Huang, Wenxia Pan, Zhiying Guo, Chengkang Wu 2010 J.Phys. D: Appl. Phys. 43
085202
[3] L. Delair, X. Tu, A. Bultel, B. G. Cheron, High Temperature Material Processes, 9(4):
p.583-597
[4] J F Coudert, V Rat, D Rigot 2007 J.Phys. D: Appl. Phys. 40 7357-7366
[5] V. Rat and J. F. Coudert 2010 Journal of Applied Physics 108, 043304
[6] V. Rat and J. F. Coudert, Improvement of Plasma Spraying Torch Stability by Controlling
Pressure and Voltage Dynamic Coupling. 2011 Journal of Thermal Spraying Technology 20:28-38