Experimental Study on the Instability Arc of a Low - Current Vacuum Arc for Copper Based Cathode Material. Narong Mungkung Department of Electrical Technology Education, Faculty of Industrial Education and Technology King Mongkut s University of Technology Thonburi, Bangmod, Thungkru, Thailand Tel:+66-2-47-854, Fax:+66-2-478541 E-mail: narong_kmutt@hotmail.com The purpose of this research was to analyze instability phenomena in low-current metal vacuum arc using the experimental data comparison with the calculation data. The instability phenomena are characterized by noise on the current trace prior to the actual current chopping. The instability current were investigated for various electrode material. However, the thermal conductivity effect on the instability phenomena of low-current metal vacuum arc are important for low surge switching electrode material development. Therefore, the experimental of major commercial switching electrode such as Cu-W are performed in this study. The arc during time and the maximum arc current were fixed to 8 ms and 1 A, respectively. The vacuum electrodes were set in the vacuum chamber. The cathode and anode diameters were 2.4*1-2 m and 4.*1-2 m, respectively. The vacuum was maintained to about 5*1-6 Pa. The observed waveforms, instability current, chopping current are measured by the oscilloscope. As the results, the critical current of the stable current is inversely dependent on the thermal conductivity of the cathode material. This is very important result for the development of cathode materials for low-surge vacuum interrupters. 1. Introduction The phenomena of cathode spot of low-current vacuum arc discharge continues to cause confusion in spite of progress in understanding the processes of instability phenomena. The qualitative discussion of physical mechanism of the stability phenomena of a low-current metal vacuum arc as shown in Figure 1 remains unclear[1]-[3]. These investigations are very important for the development of cathode materials for low-surge switching vacuum circuit breakers. It is believed that the parameters of the instabilities directly reflect the interruption characteristics of the cathode material. However, in order to clarify the instability phenomena characterized by noise on the current trace prior to the actual current chopping, the chopping and instability current for the major commercial switching cathode material such pure copper and compound copper with tungsten were performed in this study [3-6]. A single cathode spot of low-current vacuum arc as shown in Figure 2. is performed. In order to confirm the validity of the study, the experimental results are compared with analytical results. Figure 1. Typical Instability Arc Current
Cathode Cathode Spot Anode 2. Experimental Arrangement Figure 2. A Single Cathode Spot An experimental circuit is shown in Figure. 3. The current amplitude was adjusted using amount of charging voltage of capacitor. The arc during time and the maximum arc current were fixed to 8 ms and 1 A, respectively. The arc time was controlled by the thyrister. L R CT Cathode 11 µf + Trigger Power Supply Osc Figure. 3. Experimental Arrangement 3. Experimental equipment The comercial vacuum electrodes were set in the vacuum chamber. The cathode and anode diameters were 2.4*1-2 m and 4.*1-2 m, respectively. The vacuum was maintained to about 4.5*1-6 Pa. The vacuum electrodes were made of Cu-W (W: %), Cu-W (W: 1. %), Cu-W (W: 2%), Cu-W(W: 3%). They were prepared by the vacuum melting process. The gap lengths of pure copper and compound copper were 8 mm and 4 mm, respectively. When the vacuum arc was ignited, the opening velocity of the cylinder were.3 m/s.
4 Experimental method Typical measured arc current and voltage waveforms on oscilloscope are shown in Figure 2. The arc voltage (Varc), chopping current (Ic) and initial instability current (Ii) were measured in near the region of current zero. As shown in Figure 2, the current reached zero before natural line current zero. The initial noise on current trace occurs irregular oscillation is defined the minimum stable arc current or instability start arc current. The transient recovery voltage is generated after chopping current. The transient recovery voltage peak value (V P ) is expressed as the following. V L (1) C P I C 5. Calculation of Thermal Conductivity Pure copper Cu and Cu-W alloys were made using a vacuum melting process. The thermal conductivity for Cu-W alloys have been calculated from Wienemamn-Franz s law [7]. The relations between the compositions and thermal conductivities of Cu-W is shown in Figure 4. 45 Thermal Conductivity Ko [W/m K] 4 35 3 25 2 15 1 5 1 2 3 4 Percentage of Tungsten, W [At, %] Fig.4 Thermal Conductivity for Cu - W Minimum Stable Current [A] 2 15 1 25 3 35 4 45 Thermal Conductivity Ko, [W.m/K] Figure. 5. Minimum Stable Arc Current Ii vs Thermal Conductivity, Ko
Nn 6. Experimental Results Figure 5 shows plots of the average values from forty trials for each data points of Ii. The values of Ii is inversely proportional to thermal conductivity. Decreasing thermal conductivity of cathode, the heat flow cathode spot is obstructed from cathode spot to main cathode area. As the result, it may be interpreted that the cathode spot is difficult to cool and that its temperature remains higher as thermal conductivity becomes smaller. Due to this reason, the cathode spot keeps stable at a smaller arc current for supplying metal vapor to the vacuum discharge gap. Potential Vp a + Cu N o X e Cu e Reverse Diffusion r Electrode Collisionless Sheath Collisiona l Plasma Diffused Plasma Fig.6. Cathode spot model 7. Analytical Model[3][8] In order to confirm the effect of low thermal conductivity, the cathode spot model is used with various thermal conductivity as Figure 9.The cathode spot model assumes that the collisionless sheath and collisional plasma are directly connected by neglecting the transition region, as show in Fig.6. All of the dependent variables have been treated as averaged values over the spot area r a. Eight equations arc required to determine the eight dependent variables. For the lack of a simple exact formula to determine the sheath voltage Vp, some other means is required. The experimental data of cathode input Veff (I) and ion current fraction δ(i) flowing toward the anode were applied to obtain the solution of an equation in eight dependent variables. The minimum stable arc current is 7.1 Nomenclature 1. Independent Variable 2. Experimental Data I Arc current (A) V eff ( I ) Effective cathode heating voltage (V) δ (I ) Ion current fraction flowing toward the anode 3. Dependent Variables V p Sheath voltage (V) a Cathode spot radius (m) J Current density (A/m 2 ) S Electron current fraction
T Temperature of cathode spot (K) F o Cathode electric field (V/m) N o Plasma density (1/m 3 ) T e Electron temperature (K) 4. Physical Properties and Constant Γ ev Evaporation rate (kg/m 2 s) m Electronic mass (kg) P ev Evaporation energy (W/m 2 s) Electronic charge(c) K Thermal conductivity (W/mK) k Boltzmann s constant (J/K) Φ o Work function of Copper 4.5 (ev) V i Ionization voltage of Copper 7.73 (ev) A Richardson s constant 1.2 1 6 (A/m 2 K 2 ) Φ( F o, T ) Cooling effect of electron emission (ev) M Mass of atom and ion of Copper (kg) H o (T ) Heat of evaporation per atom (J/atom) Two region equations are sheath region equation and equation of the plasma region. 7.2 Equation of sheath region 7.2.1 Equation of current 2 I = πa J (2) 7.2.2 Equation of mass flow 1 kt J T N M e 2 δ Γev ( ) = M (3) 2πM q The first term of the left-hand side of equation (3) is atom flux due to evaporation from the cathode, and the second term is the return flux of ions from the plasma to the cathode. The right hand-side of the equation (3) is mass flow to the anode provided by the ion current. 7.2.3 Equation of ion current The ion current density (1-S)J in the pace charge sheath is assumed to be equal to the ion saturation current density of collisional plasma. Thus, equation (4) is concluded as 1 kt 1 o 2πM 2 ( S ) J = qn e (4) 7.2.4 Equation of electron emission current The electron emission current from the cathode is determined primarily via thermionic mechanism, together with the Shottky effect. qfo q o o Φ 4πε 2 SJ = AT exp (5) kt 7.2.5 Equation of electric field The equation of the electric field of the cathode surface is given by the Mackeown equation, including the effect of the space charge of the electrons returning from the collisional plasma to
the sheath. 2 4 F M = ( 1 S ) J ε 2q m SJ 2q 2 kteno qvp Vp 1 exp εo kt e (6) 7.2.6 Equation of energy balance The equation (7) is the solution of heat of conduction ( K T ) = T K = JVeff, r a. X 8a Ko. 45T + 348) = JV eff 3π ( (7) The temperature dependence on thermal conductivity of copper is considered [5]. The heat loss due to thermal conduction into the cathode is as follows: ( ) ) ( 1 S) J V + V Φ + H ( T ) SJΦ( F, T ) P ( T (8) JVeff = p i o o The first term of the right-hand side of the equation (8) is the input due to the ion bombardment, the second term is power dissipated by the electron emission, and the third term is the power dissipated by vaporization. 7.3 Equation of the plasma region 7.3.1 Particle conservation The equation of particle conservation is as same the equation (3). 7.3.2 Energy conservation of the collisional plasma. kte Γev J ( 2 + 2δ S) + qv.851a J 2 i = η (9) q M The first term of the left hand side of the equation (9) is the energy flow into the cathode and the anode, and the second term is the power required by ionization. The right-hand side is the input power to the plasma by joule heating, where η is the plasma resistance expressed by the Spitzer formula. 8. Analytical Results ev The simultaneous algebraic equation (2) (9) are solved numerically using a bisection method. At the arc current of 19 A, the cathode electric field, Fo, and the electron current fraction, s, change rapidly. When the arc current decreases below 19 A, no real solution exists. As the arc current decreases, with increasing the current density in high value. For this condition, the plasma
2 density also becomes very high. As a result, F o becomes negative due to the effect of the space charge of the electrons returning from the collisional plasma to the sheath. The current of 19 A may correspond to the instability onset current, as previously proposed. S (1-2 ), Fo (1 8 ) [V/m], Te (1-1 ) [ev] 45 4 35 3 25 2 15 1 5 Fo S Te Vp a 25 2 15 1 5 Vp [v], a (1-5 )[m] 1 2 3 4 5 6 7 8 Arc Current I [A] Figure.7. Electron Current fraction S, Cathode Electric Field Fo, Plasma Temperature Te, Sheath Voltage Vp and Cathode Spot Radius a 14 6 12 J No T 5 J (1 9 ) [A/m 2 ], No (1 25 ) [1/m 3 ] 1 8 6 4 2 4 3 2 1 T [K] 1 2 3 4 5 6 7 8 Arc Current I [A] 9. Conclusion Figure 8. Current Density J, Plasma Density No and Cathode Temperature T This study investigated the effect of thermal conductivity to instability of low current arc. As the results, the critical current of the stable arc current is highly dependent on the thermal conductivity of the cathode material. The increasing of stable arc current is performed by material composition for reducing thermal conductivity by increasing the percentage of Tungsten. It may be interpreted that the cathode spot is difficult to cool and that its temperature remains higher as thermal conductivity becomes smaller. For this reason, the cathode spot keeps stable at a smaller low arc current for supplying metal vapor to the vacuum discharge gap. As Figure 9, it was found that the experimental results of the instability-initiative current were similar to Analytical model
results. This is very important result for the development of cathode materials for low-surge vacuum interrupters [8]. 25 Analytical Results Minimum Stable Current Ii [A] 2 15 Experimental Results 1 25 3 35 4 45 Thermal Conductivity Ko [W/ m K] Figure 9. Comparison between Analytical results and Experimental results vs Thermal Conductivity 1. References [1] R.P.P. Smeets, Stability of low-current vacuum arcs, J. Phys. D: Appl. Phys., vol. 19, pp. 575-587, 1986. [2] T.H.Lee & A. Greenwood : Theory for the cathode mechanism in metal vapor arcs, J.Appl.Phys., 32, 916, 1961 [3] O.Morimiya, S. Suzuki and K. Watanabe, An analysis of the in stability phenomena of a low current vacuum arc, Trans. IEE of Japan.,vol. 119-A, No. 2, 1999. [4] Smeets, R.P.P.; Kaneko, E.; Ohshima, Experimental characterization of arc instabilities and their effect on current chopping in low-surge vacuum interrupters, IEEE Trans. Plasma Sci, vol. 2, pp. 439-446, Aug. 1992 [5] K. Tsuruta, N. Tanaka, H. Kido, K.Hirai, and T. Yanagidai, Ignition and instability of lowcurrent DC vacuum arcs ignited by the opening of the electrodes, IEEE Trans. Plasma Sci., vol. 29, pp. 671-674, Oct. 21 [6] C. Ding and S. Yanabu, Effect of parallel circuit parameters on the instability of a lowcurrent vacuum arc, IEEE Trans.Plasma Sci., vol. 31, pp. 877-883, Oct. 23 [7] J. Smithhells, Metal reference book, p. 14, 137 [8] N. Mungkung, O. Morimiya and T. Kamikawaji, An analysis of the instability phenomena of a low-current vacuum arc for copper cathodes, IEEE Trans. Plasma Sci., vol. 31, No. 5, pp. 963-967, Oct. 23