- Email: [email protected]
Plasma length on characteristics of DC argon plasma torch arc
Vacuum 65 (2002) 299–304
Plasma length on characteristics of DC argon plasma torch arc T. Iwaoa,*, T. Inabab a
JSPS Research Fellow and Chuo University, The Graduate School of Science and Engineering, 1-13-27 Kasuga, Bunkyo, Tokyo, 112-8551, Japan b The Institute of Science and Engineering, Chuo University, 1-13-27 Kasuga, Tokyo, 112-8551, Japan
Abstract The effect of the plasma length on the characteristics of a DC argon plasma torch arc generated by a transfer-type plasma torch (ISET-PSA, Atlanta I (1995) 13) has been investigated for treatment of waste. The voltage gradient of the plasma torch arc was measured to be about 3–4 V/cm. It remains almost constant with the plasma length. The central temperature increases with the current and decreases with the plasma length. The radial temperature distribution becomes flatter when the current increases and the sectional position moves away from the torch surface. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Plasma torch arc; Plasma length; Argon; Temperature distribution; Plasma torch
1. Introduction The plasma torch arc has many useful characteristics such as high current, high temperature, and highly intense radiation power. These properties can be used for plasma treatment of waste [1]. We focus on the DC argon plasma torch arc, that is, a kind of stabilized plasma arc that is easily controlled [2]. The characteristics of the plasma torch arc have been examined considering the influence of various parameters such as the current, the plasma gas flowrate and especially the plasma length in this report. 2. Experimental equipment to generate plasma torch arc Major specifications of the experimental equipment, the plasma torch, to generate the plasma *Corresponding author. Fax: +81-3-3817-1641. E-mail address: [email protected] (T. Iwao).
torch arc employed in this study are as follows: The maximum rating of the actual electric power source is DC 150 V, 400 A in current, with a noload voltage of 300 V. The plasma torch arc is produced between a negatively charged Th–W tip electrode and a positively charged water-cooled stainless-steel thick disk through a water-cooled nozzle. The size of the plasma chamber is 50 cm in diameter and 60 cm in length. The working gas of the plasma torch arc is argon, and the gas flowrate F is mainly 12 l/min (normal) as shown in Fig. 1 [1].
3. Influence of plasma length on terminal voltage and voltage gradient 3.1. Terminal voltage As the appearance plasma length increases, the terminal voltage Va ðV Þ of the plasma torch arc
0042-207X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 4 3 4 - 1
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
300
Torch Surface Xa: Appearance Plasma Position L a: Appearance Plasma Length
Anode
Cathode(W) Plasma
Xa axis
0
Li
La
Fig. 1. Profile of plasma torch arc.
Fig. 2. Terminal voltage vs. appearance plasma length.
increases linearly with the increment of the appearance plasma length, which is the plasma length outside the torch, excluding the inner plasma inside the torch. The longer the appearance plasma length La ; the higher is the terminal voltage. Fig. 2 shows the characteristics of the terminal voltage vs. appearance plasma length at 150 A in current I: This tendency is held in a wide range of the current from 50 to 200 A. The terminal voltage is expressed as follows: Va ¼ Vf þ EL;
L ¼ Li þ La ;
ð1Þ
where Vf ðV Þ is the voltage drop of both electrodes, E (V/cm) is the voltage gradient, Li (cm) is the inner plasma length within the torch, La (cm) is the appearance plasma length, and L (cm) is the total plasma length. The terminal voltage increases the appearance plasma length and gas flow-rate because the convection heat loss increases in proportion to the appearance plasma length and gas flow-rate.
Fig. 3. Voltage gradient vs. arc current.
voltage gradient will remain mostly unchanged at more than 200 A of current. It also remains constant with the appearance plasma length up to 8 cm.
3.2. Voltage gradient In Fig. 3, the voltage gradients of the plasma torch arc at F ¼ 12 l/min (normal) are plotted as a function of the current I: The voltage gradient E is decided as dVa =dLa along the plasma torch arc column. As the current increases, the voltage gradient decreases. This effect, however, becomes less as the current increases. It is expected that the
4. Estimate of radial and axial temperature distribution within plasma by using photo radius 4.1. Relation of photo-radius vs. current and gas flow-rate Fig. 4 shows the characteristics of the photoradius Rp (cm) vs. appearance plasma position Xa
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
301
Voltage gradient × Photo radius ERp
10
I =150A, F =12 l/min(Normal) L a =8cm
ER p = 3.40 I/R p
-0.14
1 100
1000
Current / Photo radius I /R p
Fig. 4. Characteristics of photo-radius.
Fig. 5. Voltage gradient vs. current curve normalized by radius.
at I ¼ 150 A and F ¼ 12 l/min (normal). The photos of the plasma were taken in a specified condition with TMAX-400 film, ND-8 filter, f ¼ 11 exposure scale, and 1/8000 s exposure time in order to define distinctly the radius of the plasma torch arc. The photo-radius along appearance plasma was measured as shown in Fig. 4. As the Rp for each La is slightly different along appearance plasma, Rp could be expressed by the straight line except the extent near anode as follows:
radius Rp instead of Rs [4]. The value of Ex decreases gradually along the axis and disruptively near the opposite electrode at Xa ¼ La : The electrode fall voltage as a function of gas flow-rate is shown in Fig. 6. As the gas flow-rate increases, the electrode fall voltage also increases. It is considered that the electrode fall voltage depends on gas flow-rate.
Rp ðcmÞ ¼ 0:39 þ 0:018Xa ðcmÞ:
4.3. Estimate of average temperature
ð2Þ
The actual average current density, however, is not constant with the current, but increases slightly with the arc current. Therefore, the photo-radius increase is lesser than the square root of the arc current.
Assuming that the plasma torch arc has a constant temperature distribution over the cross section, the average arc current pffiffiffidensity can be pffiffiffiffiffiffiffiffiffiffi calculated from Rp ¼ I=pJ%p I as
4.2. Relation between voltage gradient vs. La
J% ¼ I=fpR2p g:
According to the so-called normalized theory [3], the product value of ERs remains constant at any thermal radius of Rs in all the wall-stabilized arcs in this current range. In this experiment, the ERp is in proportion to the 0.14th power of the I=Rp as shown in Fig. 5. Therefore, this theory would be applied to the plasma torch arc. If this theory can be applied to the plasma torch arc, then the partial voltage gradient Ex at the position Xa is inversely proportional to the arc
ð3Þ
Using the voltage gradient E (V/cm) at each current and gas flow-rate in Fig. 4, the average electrical conductivity (S/cm) can be evaluated as % s% ¼ J=E:
ð4Þ
From the relationship of s and T of Ar reported by Devoto [5], we can obtain the average temperature T% as a function of s% as follows: T1 TðsÞ: %
ð5Þ
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
Electrode fall voltage Vf (V)
302
tribution, the averaged temperature (K) in the arc column can be shown as Z Rp 1 T2 2prTðrÞ dr: ð8Þ pR2p 0
50 45 40 35 30 25 20 15 10 5 0
Therefore, in this article, the estimation was carried out under the following assumptions [7]:
I =150A, F =12 l/min(Normal) L a =8cm
0
10
20
30
(1) The convection loss inside Rp can be negligible. (2) No electrically conductive region exists outside the Rp : (3) The plasma torch arc is uniform along the axis.
Gas flow-rate F (l/min(Normal)) Fig. 6. Electrode fall voltage as a function of gas flow-rate.
4.4. Estimate of radial temperature distribution Elenbaas–Heller’s equation that represents the energy balance in the arc column is [6] 1q qT rk ð6Þ Q þ sE 2 Pc ¼ 0; r qr qr where r (cm) is the radial distance from the column center, E (V/cm) is the axial voltage gradient measured in this time, Q (W/cm3) is the radiant power density, TðKÞ is the temperature, k (W/cm K) is the thermal conductivity, s (S/cm) is the electrical conductivity and Pc (W/cm3) is the convection loss. On this experimental condition, Q cannot be ignored because of the relatively higher temperature more than 12,000 K. Pc is negligible in the surface of the photo-radius, but on the outside it is significant due to the high speed of the gas flow. Pc is proportional to the temperature difference between that within and outside the boundary, to the peripheral length of the boundary and to the gas flow-rate. Employing the boundary condition at the center of r ¼ 0; T ¼ T0 ;
qT ¼0 qr
at r ¼ 0;
4.5. Estimate of radial temperature distribution influenced by Xa The influence of the appearance plasma position on the radial temperature distribution is shown in Fig. 7. T0 decreases with appearance plasma position and decreases with radius Rp : Then TðrÞ; radial temperature, becomes flatter and the radius of arc becomes larger with the current. The appearance plasma position and TðrÞ decrease with radius r; departing from a model of radially constant temperature, because the radial temperature gradient is owing to the thermal conduction power or thermal conductivity. The central temperature in the plasma torch arc depends on the current I and the photo-radius Rp : It increases in
ð7Þ
where T0 is the central temperature, the radial temperature distribution from r ¼ 0 to Rp in the arc column can be estimated. By calculating the circumferential integral of the temperature dis-
Fig. 7. Radial temperature distribution in column (influence of appearance plasma position).
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
proportion to the current and is in inverse proportion to the photo-radius. This is the same as the wall-stabilized arcs, such as air and SF6 gases. The surface temperature of appearance plasma at the photo-radius is many thousands of degrees. Because the gas flow runs rapidly around the appearance plasma, the peripheral thermal conductive part surrounding the axial electric conductive area is revealed by the gas flow. Therefore, the boundary of the plasma torch arc can be easily recognized. 4.6. Estimate of axial temperature distribution It is estimated that the central temperature with radiation, Tor ; is about 15,000 K at I ¼ 150 A, F ¼ 12 l/min (normal), La ¼ 5 cm and Xa ¼ 0 as shown in Fig. 8. Tor decreases with the appearance plasma position and then rapidly decreases near the opposite positive electrode due to the larger radius.
5. Conclusion The terminal voltage and the photo-radius of argon plasma torch arc have been examined as functions of current, gas flow-rate and mainly of the appearance plasma length. Then, the radial and axial temperature distribution in the plasma
303
torch arc was estimated by using the measured voltage gradient and the photo-radius. The main results are as follows: (1) The terminal voltage of the plasma torch arc is 30–60 V at 50–150 A of current and 4B8 cm of appearance plasma length. It increases linearly with the increment of the gas flow-rate and the appearance plasma length. This shows that the convection heat loss increases in proportion to the gas flow-rate and the appearance plasma length. (2) The voltage gradient of the plasma torch arc is 3–4 V/cm, which decreases with the current. However, it will remain 3 V/cm at more than 200 A, and at 12 l/min (normal) of gas flowrate. On the other hand, the voltage gradient remains almost constant irrespective of the appearance plasma length. (3) The photo-radius of the plasma torch arc seems to increase almost linearly with the appearance plasma position or the distance from the torch surface. (4) The radial temperature distribution in the plasma torch arc becomes flatter and reaches a radially constant temperature model with the increment of the appearance plasma position. The temperature of the surrounding surface of the plasma torch arc is thousands of degrees and it forms a distinct boundary of the temperature. (5) The central temperature in the plasma torch arc increases nearly in proportion to the current I and the photo-radius Rp ; but is almost regardless of the gas flow-rate. This is the same as the wall-stabilized arcs, such as air and SF6 gases. Moreover, the central temperature in the plasma torch arc decreases slightly with the appearance plasma length and decreases almost linearly with the plasma position.
Acknowledgements
Fig. 8. Axial distribution of central temperature in column (influence of appearance plasma position).
The authors thank Prof. I. Miyachi of Aichi Institute of Technology for his fruitful suggestions and the students belonging to the Power Energy Laboratory of Chuo University for
304
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
their experimental efforts. This research was supported by High-Tec Project on High Temperature Plasma by The Institute of Science and Engineering of CHUO University, and Japan Society for Promotion of Science.
References [1] Inaba T, Nagano M, Endo M. Trans. IEE of Japan 1997;117-D(7):831–8; Inaba T, Nagano M, Endo M. Electr Eng Jpn 1999;126-3:73–82.
[2] Inaba T, Endo M, Watanabe Y, Shibuya M. ISPC-12 1995;III:1725–30. [3] Inaba T. Trans IEE of Japan 1974;94-A(3):83–90. [4] Iwao T. ISPC-14, I, Prague, 1999:373–8. [5] Devoto RS. Phys Fluids 1973;16:616. [6] Inaba T, Kito Y, Miyachi I. Z Physik 1971;247:227–37. [7] Inaba T, Watanabe Y, Nagano M, Ishida T, Endo M. Thin Solid Films 1998;316:111–6.
Plasma length on characteristics of DC argon plasma torch arc T. Iwaoa,*, T. Inabab a
JSPS Research Fellow and Chuo University, The Graduate School of Science and Engineering, 1-13-27 Kasuga, Bunkyo, Tokyo, 112-8551, Japan b The Institute of Science and Engineering, Chuo University, 1-13-27 Kasuga, Tokyo, 112-8551, Japan
Abstract The effect of the plasma length on the characteristics of a DC argon plasma torch arc generated by a transfer-type plasma torch (ISET-PSA, Atlanta I (1995) 13) has been investigated for treatment of waste. The voltage gradient of the plasma torch arc was measured to be about 3–4 V/cm. It remains almost constant with the plasma length. The central temperature increases with the current and decreases with the plasma length. The radial temperature distribution becomes flatter when the current increases and the sectional position moves away from the torch surface. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Plasma torch arc; Plasma length; Argon; Temperature distribution; Plasma torch
1. Introduction The plasma torch arc has many useful characteristics such as high current, high temperature, and highly intense radiation power. These properties can be used for plasma treatment of waste [1]. We focus on the DC argon plasma torch arc, that is, a kind of stabilized plasma arc that is easily controlled [2]. The characteristics of the plasma torch arc have been examined considering the influence of various parameters such as the current, the plasma gas flowrate and especially the plasma length in this report. 2. Experimental equipment to generate plasma torch arc Major specifications of the experimental equipment, the plasma torch, to generate the plasma *Corresponding author. Fax: +81-3-3817-1641. E-mail address: [email protected] (T. Iwao).
torch arc employed in this study are as follows: The maximum rating of the actual electric power source is DC 150 V, 400 A in current, with a noload voltage of 300 V. The plasma torch arc is produced between a negatively charged Th–W tip electrode and a positively charged water-cooled stainless-steel thick disk through a water-cooled nozzle. The size of the plasma chamber is 50 cm in diameter and 60 cm in length. The working gas of the plasma torch arc is argon, and the gas flowrate F is mainly 12 l/min (normal) as shown in Fig. 1 [1].
3. Influence of plasma length on terminal voltage and voltage gradient 3.1. Terminal voltage As the appearance plasma length increases, the terminal voltage Va ðV Þ of the plasma torch arc
0042-207X/02/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 4 3 4 - 1
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
300
Torch Surface Xa: Appearance Plasma Position L a: Appearance Plasma Length
Anode
Cathode(W) Plasma
Xa axis
0
Li
La
Fig. 1. Profile of plasma torch arc.
Fig. 2. Terminal voltage vs. appearance plasma length.
increases linearly with the increment of the appearance plasma length, which is the plasma length outside the torch, excluding the inner plasma inside the torch. The longer the appearance plasma length La ; the higher is the terminal voltage. Fig. 2 shows the characteristics of the terminal voltage vs. appearance plasma length at 150 A in current I: This tendency is held in a wide range of the current from 50 to 200 A. The terminal voltage is expressed as follows: Va ¼ Vf þ EL;
L ¼ Li þ La ;
ð1Þ
where Vf ðV Þ is the voltage drop of both electrodes, E (V/cm) is the voltage gradient, Li (cm) is the inner plasma length within the torch, La (cm) is the appearance plasma length, and L (cm) is the total plasma length. The terminal voltage increases the appearance plasma length and gas flow-rate because the convection heat loss increases in proportion to the appearance plasma length and gas flow-rate.
Fig. 3. Voltage gradient vs. arc current.
voltage gradient will remain mostly unchanged at more than 200 A of current. It also remains constant with the appearance plasma length up to 8 cm.
3.2. Voltage gradient In Fig. 3, the voltage gradients of the plasma torch arc at F ¼ 12 l/min (normal) are plotted as a function of the current I: The voltage gradient E is decided as dVa =dLa along the plasma torch arc column. As the current increases, the voltage gradient decreases. This effect, however, becomes less as the current increases. It is expected that the
4. Estimate of radial and axial temperature distribution within plasma by using photo radius 4.1. Relation of photo-radius vs. current and gas flow-rate Fig. 4 shows the characteristics of the photoradius Rp (cm) vs. appearance plasma position Xa
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
301
Voltage gradient × Photo radius ERp
10
I =150A, F =12 l/min(Normal) L a =8cm
ER p = 3.40 I/R p
-0.14
1 100
1000
Current / Photo radius I /R p
Fig. 4. Characteristics of photo-radius.
Fig. 5. Voltage gradient vs. current curve normalized by radius.
at I ¼ 150 A and F ¼ 12 l/min (normal). The photos of the plasma were taken in a specified condition with TMAX-400 film, ND-8 filter, f ¼ 11 exposure scale, and 1/8000 s exposure time in order to define distinctly the radius of the plasma torch arc. The photo-radius along appearance plasma was measured as shown in Fig. 4. As the Rp for each La is slightly different along appearance plasma, Rp could be expressed by the straight line except the extent near anode as follows:
radius Rp instead of Rs [4]. The value of Ex decreases gradually along the axis and disruptively near the opposite electrode at Xa ¼ La : The electrode fall voltage as a function of gas flow-rate is shown in Fig. 6. As the gas flow-rate increases, the electrode fall voltage also increases. It is considered that the electrode fall voltage depends on gas flow-rate.
Rp ðcmÞ ¼ 0:39 þ 0:018Xa ðcmÞ:
4.3. Estimate of average temperature
ð2Þ
The actual average current density, however, is not constant with the current, but increases slightly with the arc current. Therefore, the photo-radius increase is lesser than the square root of the arc current.
Assuming that the plasma torch arc has a constant temperature distribution over the cross section, the average arc current pffiffiffidensity can be pffiffiffiffiffiffiffiffiffiffi calculated from Rp ¼ I=pJ%p I as
4.2. Relation between voltage gradient vs. La
J% ¼ I=fpR2p g:
According to the so-called normalized theory [3], the product value of ERs remains constant at any thermal radius of Rs in all the wall-stabilized arcs in this current range. In this experiment, the ERp is in proportion to the 0.14th power of the I=Rp as shown in Fig. 5. Therefore, this theory would be applied to the plasma torch arc. If this theory can be applied to the plasma torch arc, then the partial voltage gradient Ex at the position Xa is inversely proportional to the arc
ð3Þ
Using the voltage gradient E (V/cm) at each current and gas flow-rate in Fig. 4, the average electrical conductivity (S/cm) can be evaluated as % s% ¼ J=E:
ð4Þ
From the relationship of s and T of Ar reported by Devoto [5], we can obtain the average temperature T% as a function of s% as follows: T1 TðsÞ: %
ð5Þ
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
Electrode fall voltage Vf (V)
302
tribution, the averaged temperature (K) in the arc column can be shown as Z Rp 1 T2 2prTðrÞ dr: ð8Þ pR2p 0
50 45 40 35 30 25 20 15 10 5 0
Therefore, in this article, the estimation was carried out under the following assumptions [7]:
I =150A, F =12 l/min(Normal) L a =8cm
0
10
20
30
(1) The convection loss inside Rp can be negligible. (2) No electrically conductive region exists outside the Rp : (3) The plasma torch arc is uniform along the axis.
Gas flow-rate F (l/min(Normal)) Fig. 6. Electrode fall voltage as a function of gas flow-rate.
4.4. Estimate of radial temperature distribution Elenbaas–Heller’s equation that represents the energy balance in the arc column is [6] 1q qT rk ð6Þ Q þ sE 2 Pc ¼ 0; r qr qr where r (cm) is the radial distance from the column center, E (V/cm) is the axial voltage gradient measured in this time, Q (W/cm3) is the radiant power density, TðKÞ is the temperature, k (W/cm K) is the thermal conductivity, s (S/cm) is the electrical conductivity and Pc (W/cm3) is the convection loss. On this experimental condition, Q cannot be ignored because of the relatively higher temperature more than 12,000 K. Pc is negligible in the surface of the photo-radius, but on the outside it is significant due to the high speed of the gas flow. Pc is proportional to the temperature difference between that within and outside the boundary, to the peripheral length of the boundary and to the gas flow-rate. Employing the boundary condition at the center of r ¼ 0; T ¼ T0 ;
qT ¼0 qr
at r ¼ 0;
4.5. Estimate of radial temperature distribution influenced by Xa The influence of the appearance plasma position on the radial temperature distribution is shown in Fig. 7. T0 decreases with appearance plasma position and decreases with radius Rp : Then TðrÞ; radial temperature, becomes flatter and the radius of arc becomes larger with the current. The appearance plasma position and TðrÞ decrease with radius r; departing from a model of radially constant temperature, because the radial temperature gradient is owing to the thermal conduction power or thermal conductivity. The central temperature in the plasma torch arc depends on the current I and the photo-radius Rp : It increases in
ð7Þ
where T0 is the central temperature, the radial temperature distribution from r ¼ 0 to Rp in the arc column can be estimated. By calculating the circumferential integral of the temperature dis-
Fig. 7. Radial temperature distribution in column (influence of appearance plasma position).
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
proportion to the current and is in inverse proportion to the photo-radius. This is the same as the wall-stabilized arcs, such as air and SF6 gases. The surface temperature of appearance plasma at the photo-radius is many thousands of degrees. Because the gas flow runs rapidly around the appearance plasma, the peripheral thermal conductive part surrounding the axial electric conductive area is revealed by the gas flow. Therefore, the boundary of the plasma torch arc can be easily recognized. 4.6. Estimate of axial temperature distribution It is estimated that the central temperature with radiation, Tor ; is about 15,000 K at I ¼ 150 A, F ¼ 12 l/min (normal), La ¼ 5 cm and Xa ¼ 0 as shown in Fig. 8. Tor decreases with the appearance plasma position and then rapidly decreases near the opposite positive electrode due to the larger radius.
5. Conclusion The terminal voltage and the photo-radius of argon plasma torch arc have been examined as functions of current, gas flow-rate and mainly of the appearance plasma length. Then, the radial and axial temperature distribution in the plasma
303
torch arc was estimated by using the measured voltage gradient and the photo-radius. The main results are as follows: (1) The terminal voltage of the plasma torch arc is 30–60 V at 50–150 A of current and 4B8 cm of appearance plasma length. It increases linearly with the increment of the gas flow-rate and the appearance plasma length. This shows that the convection heat loss increases in proportion to the gas flow-rate and the appearance plasma length. (2) The voltage gradient of the plasma torch arc is 3–4 V/cm, which decreases with the current. However, it will remain 3 V/cm at more than 200 A, and at 12 l/min (normal) of gas flowrate. On the other hand, the voltage gradient remains almost constant irrespective of the appearance plasma length. (3) The photo-radius of the plasma torch arc seems to increase almost linearly with the appearance plasma position or the distance from the torch surface. (4) The radial temperature distribution in the plasma torch arc becomes flatter and reaches a radially constant temperature model with the increment of the appearance plasma position. The temperature of the surrounding surface of the plasma torch arc is thousands of degrees and it forms a distinct boundary of the temperature. (5) The central temperature in the plasma torch arc increases nearly in proportion to the current I and the photo-radius Rp ; but is almost regardless of the gas flow-rate. This is the same as the wall-stabilized arcs, such as air and SF6 gases. Moreover, the central temperature in the plasma torch arc decreases slightly with the appearance plasma length and decreases almost linearly with the plasma position.
Acknowledgements
Fig. 8. Axial distribution of central temperature in column (influence of appearance plasma position).
The authors thank Prof. I. Miyachi of Aichi Institute of Technology for his fruitful suggestions and the students belonging to the Power Energy Laboratory of Chuo University for
304
T. Iwao, T. Inaba / Vacuum 65 (2002) 299–304
their experimental efforts. This research was supported by High-Tec Project on High Temperature Plasma by The Institute of Science and Engineering of CHUO University, and Japan Society for Promotion of Science.
References [1] Inaba T, Nagano M, Endo M. Trans. IEE of Japan 1997;117-D(7):831–8; Inaba T, Nagano M, Endo M. Electr Eng Jpn 1999;126-3:73–82.
[2] Inaba T, Endo M, Watanabe Y, Shibuya M. ISPC-12 1995;III:1725–30. [3] Inaba T. Trans IEE of Japan 1974;94-A(3):83–90. [4] Iwao T. ISPC-14, I, Prague, 1999:373–8. [5] Devoto RS. Phys Fluids 1973;16:616. [6] Inaba T, Kito Y, Miyachi I. Z Physik 1971;247:227–37. [7] Inaba T, Watanabe Y, Nagano M, Ishida T, Endo M. Thin Solid Films 1998;316:111–6.