Electrode Erosion Phenomena in a High-Energy Pulsed Discharge

IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 1, MARCH 1984 28 [161 E. M. Honig, "Progress in developing repetitive pulse systems utilizing inductive energy storage," in Proc. 4th IEEE Pulsed Power Conf. (Albuquerque, NM), June 1983. [171 E. M. Honig, "Dual 30-kA, HVDC interrupter test facility," in Proc. 7th Symp. Eng. Problems Fusion Research (Knoxville, TN), Oct. 1977, IEEE Pub. 77CH1 267-4-NPS, pp. 1071-1075. [181 R. W. Warren, "Experiments with vacuum interrupters used for large DC-current interruption," Los Alamos National Laboratory, Los Alamos, NM, Informal Rep. LA-6909-MS, Oct. 1967, pp. 10-15. [191 E. M. Honig, "Repetitive opening switches, Final report, 9-30-83" Los Alamos National Laboratory, Los Alamos, NM, LA-UR-832926, Sept. 1983. [201 J. A. Rich, C. P. Goody, and J. C. Sofianek, "High-power triggered vacuum gap of rod array type," General ElectricRep. 81CRD321, Dec. 1981. [211 R. Carruthers, "Energy storage for thermonuclear research,"Proc. Inst. Elec. Eng. Pt. A, vol. 106, Suppl. no. 2, pp. 166-1 72, 1959. [221 H. Knoepfel, Pulsed High Magnetic Fields. Amsterdam, The Netherlands: North-Holland, 1970, pp. 144-150. Electrode Erosion Phenomena in a High-Energy Pulsed Discharge A. L. DONALDSON, M. 0. FELLOW, IEEE, HAGLER, FELLOW, IEEE, M. KRISTIANSEN, G. JACKSON, AND L. HATFIELD Abstract-The erosion rates for hemispherical electrodes, 2.5 cm in The purpose of this study was to measure the erosion rate of diameter, made of graphite, copper-graphite, brass, two types of cop- different electrode materials as a function of current in order per-tungsten, and three types of stainless steel, have been examined to generate a data base from which theoretical models dein a spark gap filled with air or nitrogen at one atmosphere. The elecprocesses could be developed and trodes were subjected to 50 000 unipolar pulses (25,lls, 4-25 kA, 5-30 scribing the complex erosion and insulator surfaces were electrode the In addition, verified. kV, 0.1-0.6 C/shot) at repetition rates ranging from 0.5 to 5 pulses per electrode erosion characthe define to in an effort in the examined resulting occurred, conditioning surface second (pps). Severe formation of several spectacular surface patterns (craters up to 0.6 cm teristics and to reduce the material parameter space used in in diameter and nipples and dendrites up to 0.2 cm in height). Surface further studies. damage was limited to approximately 80 ,m in depth and was considerably less in nitrogen gas than in air. Anode erosion rates varied from a slight gain (a negative erosion rate), for several materials in niEXPERIMENTAL APPARATUS trogen, to S ,ucm3/C for graphite in air. Cathode erosion rates of Gap Spark 0.4 gcm3/C for copper-tungsten in nitrogen to 25 Acm3/C for graphite in air were also measured. The spark gap shown in Fig. 1 was designed to facilitate fre- quent electrode and insulator replacement and to allow for accurate control over electrode alignment and gap spacing. The electrodes are composed of three parts: the brass support (which also serves as a channel for gas flow), the brass adapter, and the electrode tip. The hemispherically shaped electrode tips are 2.5 cm in diameter and are made from the various materials studied. The Lucite inserts provide protection for the main gap housing and also provide a surface which gives a permanent history of the discharge debris which is deposited on the walls. INTRODUCTION HIGH-ENERGY spark gaps with lifetimes of 108 shots are seen as one of the critical components in pulsed power systems used for particle beam systems, lasers, nuclear isotope separation, electromagnetic pulse simulation, and thermonuclear fusion reactors. The performance of a pressurized spark gap as a high-energy rep-rated switching device is typically characterized by its hold-off voltage, recovery time, delay time, and jitter [1]. The switch lifetime is determined by the electrode erosion, gas decomposition and disassociation, and insulator damage that occur as energy is dissipated in the Test Circuit and Conditions Numerous experimentors have measured erosion rates for switch [2]. high-current (10-800 kA) oscillatory discharges [3]-[7]. A Manuscript received May 18, 1983; revised December 14, 1983. few have studied erosion rates in high-current (<10 kA) uniThis work was supported by the Air Force Office of Scientific Re- polar discharges using brass and copper electrodes only [8], search. was A. L. Donaldson, M. 0. Hagler, and M. Kristiansen are with the [9]. A test circuit capable of delivering a unipolar pulse Plasma and Switching Laboratory, Department of Electrical Engineer- chosen for this stl iy, both to simplify separate investigations ing, Texas Tech University, Lubbock, TX 79409. of the erosion processes at the anode and the cathode and to G. Jackson is with the BDM Corporation, Huntsville, AL 35803. more closely. The circuit, shown L. Hatfi'eld is with the Department of Physics, Texas Tech University, simulate certain applications in Fig. 2, consists of a six-section Rayleigh pulse forming netLubbock, TX 79409. 0093-3813/84/0300-0028$01.00 © 1984 IEEE DONALDSON et al: ELECTRODE EROSION PHENOMENA 29 Rc L, L, Lb L4 L, L, SPARK GAP vc_ - : C' C2 1C, TC4 TC, Tc R..6a Lo- 200nH VgAX.. 30kV C-3.5$F each I,w,- 25kA L-L25,%H each Fig. 2. Test circuit for erosion studies. >W 44 tO is/div Fig. 3. Current pulse. Fig. 1. Spark gap for erosion studies. work (PFN) which is resistively charged to the self-breakdown voltage of the spark gap by a 30-kV 1-A constant voltage power supply. When the gap breaks down, the PFN is discharged into a matched 0.6-S2 high-power load. Further details of the test circuit and load design are discussed elsewhere [10]. The waveform of the discharge current is shown in Fig. 3. The test conditions are summarized below: voltage <30 kV <25 kA total capacitance 21 ,F charge/shot <0.6 C energy/shot <9 kJ 25 Ms pulse width current rep-rate 0.5-5 pps gas pressure air or N2 I atm (absolute) 1 gap volume every <0.8 cm. flow rate spacing gap 5 s Materials Tested The electrode materials tested were: brass (SAE 660), stainless steel (304, 2OCb-3, 440-C) [11], copper-tungsten (K-33 [12], 3W3 [13], graphite (ACF-IOQ), and copper-graphite (DFP-1C) [14]. This combination of materials allowed for: 1) a comparision with existing data for brass and stainless steel [3], [4], [8], [15], 2) utilization of materials which experimentally have given good spark gap performance [3], [6], [16], 3) the testing of several new materials, namely coppergraphite, and the stainless steels 20Cb-3 (previously used in highiy corrosive environments in MHD generators) and 440-C (a high strength stainless steel). The thermophysical properties of these materials are given in Table I. EXPERIMENTAL RESULTS Erosion Characteristics The change in mass of the spark gap electrodes after 50 000 shots was measured with an analytical balance with a precision of ±5 mg. The individual test conditions and resulting erosion rates are given in Table 11. Although many authors report erosion rates in micrograms per coulomb, the actual factor determining lifetime is the volume eroded, hence the units microcubic centimeters per coulomb (jucm3/C). The results for brass are discussed later because of the failure of the electrodes due to gross material extraction. Material: A ranking of the volume erosion rate for each material investigated, from smallest to largest, is: Cathode: CT-3W3(N2), CT-K-33(N2), CT-3W3 (air), CT-K33(air), SS-304(N2), SS-304(air), SS-440-C(air), SS-20Cb-3(air), CG(air), CG(N2), G(N2), G(air); Anode: CT-3W3(air), CT-K-33(air), SS-440-C(air),CG(N2), SS-304(air), SS-2OCb-3(air), G(air). (The rest of the anodes showed no net erosion.) 30 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 1, MARCH 1984 TABLE I ELECTRODE MATERIAL PROPERTIES Material Canposition r1. (T) d (kq/m3) k (W/'n °K) (kJ/kq °K) c p I0-b Q cm) Brass Cu 83%, Pb 7% Sn 7%, Zn 3% 980 8700 120 0.36 6.7 Stainless steel (SS) (304) Fe 69%, Cr 19% Ni 9%, Mn 2% 1430 8000 16 0.56 72 Stainless steel (SS) (2OCb-3) Fe 41%, Ni 33% Cr 19%, Cu 3% 1370 8100 13 0.50 108 Stainless steel (SS) Fe 79%, Cr 17% C 1%, Mn 1% 1370 7600 24 0.44 6U Copper-tunqsten (CT) W 67%. Cu 33% Ci] 1080 W 3400 14000 270 0.25 3.4 Copper-tungsten W 68%, Cu 32% " 230 NA 3.4 1830 87 0.80 2700 2970 175 0.84 178 (440-C) (K-33) (3W3) (CT) of Graphite (ACF-10Q) (G) C 100% Copper-graphite (CG) 4200* C 84%, Cu 16% (OFP- iC) Cu 1080 Tmp: melting temperature, d: density, k: thermal conductivity, c: specific heat p; resistivity, *: graphite sublinies. TABLE II ELECTRODE EROSION RATES Electrode Gas V Q CE AE Stainless steel (304) Air 10.3 0.21 1.8 1.2 Stainless steel Air 10.6 0.22 1.5 1.0 " [1]1 Air 18.0 0.37 1.6 1.5 Stainless steel (440-C) Air 12.4 0.26 1.8 0.5 Air 10.0 N2 2.5 0.7 1.2 1.2 1.2 Stainless steel Stainless steel (20Cb-3) Air 18.0 0.21 0.16 0.20 0.24 0.37 Copper-tungsten (3W3) Air 15.8 0.32 0.8 0.2 Copper-tungsten (K-33) (31 N2 14.8 0.31 0.4 0.4 0.4 + 0.0 Stainless steel (304) (2,31 Air 7.8 9.5 Copper-tungsten " Air 11.5 Copper-tungsten " Copper-tungsten (K-33) 0.9 + 0.0 0.4 0.3 0.5 Copper-tunqsten (3W3) N2 16.4 0.34 Copper-qraphite (DFP-1C) Air 8.3 0.17 8.5 0.4 Copper-graphite Air 16.2 0.34 8.6 + 0.0 Copper-graphite Copper-graphite [3] n3] Air 11.4 0.24 7.2 0.0 N2 14.8 0.31 13.5 0.8 3.5 Graphite (ACF-1OQ) Air 9.2 0.19 24.1 Graphite Air 10.6 0.22 24.6 3.6 Graphite Air 16.0 0.33 23.5 5.0 N2 12.9 0.27 15.7 0.0 Graphite [3] V. average voltage, kV; Q: charge/shot, coulombs; CE: cathode erosion, ,cm3/C; AE: anode erosion, ,ucm3/C; [11- 32 000 shots, [2]22 000 shots, [3]-experiment performed at approximately 85 percent of maximum power, + indicates that an increase in mass was measured. As expected, the copper-tungsten composites gave the lowest volume erosion rate. Somewhat surprising, however, was the excellent performance of the stainless steels (304 and 440-C) and the poor performances of the graphite materials as cathodes. From the results obtained for stainless steel in a pulsed discharge, it is seen that the high erosion rate reported by Gruber and Suess [3], for an oscillatory discharge, was possibly a result of using a stainless steel which, according to the work reported here, is a poor anode material. Previous studies [6], [15], which indicated that graphite was highly resistant to erosion were done at a much slower repetition rate (0.03 pps) and, therefore, gave a significantly lower erosion rate (<l ,ucm3/C). More recent results by Bickford [16] at 1000 pps gave an erosion rate of 41 ,cm3/C which is reasonably close to the value of 25 ,ucm3/C measured in this experiment. A summary of the erosion rates found by other investigators is given in Table III. If one takes into account the lower values of current used in this study, then the results obtained in this experiment are in generally good agreement with the measurements of other investigators. Polarity: Unlike previous experiments, where oscillatory current conditions masked any polarity effect, a distinct difference in the cathode and anode erosion rate and, most likely, the erosion mechanisms themselves were observed using a unipolar pulse. The ratio of cathode to anode erosion, for those materials which had significant anode erosion, varied from 1.5 in stainless steel (304) to 16 in copper-graphite. Carder [8] reported ratios of 2.5 to 5 for brass under similar conditions. Previous experiments, which gave cathode to anode erosion ratios less than one, were done at much higher pulse repetition rates (10-1000 pps) [15] -[18]. In addition, the results obtained by Petr [18] were done with smaller anode diameters and gap spacings (both <2.5 mm). In general, anode erosion rates were somewhat scattered, and thus general trends were hard to obtain, given the limited data base. However, some agreement with an anode erosion rate proportional to Q1.S was observed for graphite. A similar dependence has been found experimentally and derived theoretically by numerous other investigators [19] -[21] . Some anodes actually gained mass, which indicated that material was being transferred from the cathode to the anode and/or chemical reactions were forming compounds on the anode. The material transfer was demonstrated experimentally when a stainless steel cathode was found to deposit molten material on a graphite anode. Gray and Pharney [22] 31 DONALDSON et al.: ELECTRODE EROSION PHENOMENA TABLE III SUMMARY OF COMPARABLE EROSION RESULTS Investigator Erosion Rate (Icn3/coul) Affinito [15] 1 Belkin [17] 0.7-1.4 Bickford [16] Carder [8] Gruber and Suess [3] Gas Current Wavefonm Graphite N2 (2 atm) 100 Oscillatory Brass Helium (1 atm) 40 Oscillatory (kA) 5 Copper-tunqsten CO (1 atn) 6 Stainless-steel 41 Burden and James [4] Material 1.5 t0 Graphite (0.03 pps) Unipolar (1000 pps) it n 5 Brass Air (1.25 atm) 400 Oscillatory 3-5 Brass N2 (2 atm) 10-22 Unipolar (1 pps) 40-170 Oscillatory 2-10 5-40 20-40 Copper-tunqsten Air (1 atm) 80 Copper-tungsten SF6 (4 atm) Kawakita [7] Brass Stainless-steel " " " 100 " 0- A, _ 0 - 01000 :1X Graphite (ACF-1OQ) Copper-graphite (DFP-IC) Stainless steel (304) 11 (20Cb-3) o4 (440-C) Copper-tungsten (K-33) 11 ,, - ,, ((3W3) it AvN2 ON, 100 .-I 0 0 a., +N 10 O~2 1. I 7.5 - Q __- 15 10 = fidt (C x 10') Fig. 4. Total cathode erosion versus total charge transfer for different electrode materials in air. proposed a reasonable model for this effect at low currents, which is based upon the reduction of the ion bombardment force on the molten cathode material during the fall of the current pulse. Cathode erosion rates are plotted in Fig. 4 as a function of the total charge transferred in 50 000 shots (f i dt)l The actual experimental variable used to change the current was the gap spacing. Thus, from these data, there is no way to isolate the effect of increasing gap spacing and increasing current. . 1Note that the constant slope shown implies constant erosion rate per Coulomb. For a given cathode material these results indicate a linear dependence of the erosion rate on the quantity Q = f i dt over the entire range of currents. Since the energy in the arc is equal to f V,ar i dt, this seemed to indicate that the main source of energy producing molten material and subsequent vaporization and droplet ejection is in the cathode fall region of the arc (ion impact heating) and not the localized i2R losses (Joule heating) in the material. (A similar statement by Belkin [5] touched off a heated debate in the literature [23], [24].) Although both experimental [25] and theoretical results [26] exist which support this conclusion it will be shown that you can obtain erosion rates proportional to any reasonable function of current, even f i dt, with Joule heating. Also, it should be mentioned that cathode and anode fall voltages are not known for short-pulse high-current arcs which make it hard to check the erosion dependence on f Varc i dt. Current: In order to understand the erosion dependence on current one should consider the following: the high-current arc in both vacuum and pressurized gaps is known [9], [27] to consist of many individual filaments, each of which is attached to the electrode and forms a microscopic crater. Even if the erosion at each crater site is due to Joule heating [21], [28] the total erosion is a function of the filament current and the temporal history of each attachment site. For example, under certain circumstances it has been shown [9], [27] that the current per filament and the attachment lifetime are approximately constant. Thus regardless of the erosion dependence on current at each individual attachment site, the total erosion would be a function of I i dt since the total number of sites would be a linear function of current. This also explains why no clear dependence of erosion on the thermophysical properties [Tmp, d, k, c, p] has been consistently measured in experiments. Thus to understand the erosion process correctly, one not only has to model the erosion mechanism occurring at each filament attachment site correctly, which will certainly depend on Tmp, d, k, c, and p [21], but also a model must exist which specifies the filament current and the temporal history of its attachment site. Excellent models exist for filament motion in low-current low-pressure ~ ~IMm:E IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 1, MARCH 1984 32 (a) Imm F-4 50 cim | I Fig. 5. Cross section of stainless steel (304) cathode in air. (b) Fig. 7. Surface of brass electrodes in air; (a) anode, (b) cathode. 50 pm Fig. 6. Cross section of stainless steel (304) cathode in nitrogen. [28], and high-current arcs in vacuum [27], but it is not anticipated that any one model will suffice for the wide range of conditions encountered in high-energy switches. Gas: The erosion rate for copper-graphite was slightly higher in nitrogen than in air, whereas the rates for most of the other materials were smaller in nitrogen by a factor of 2-3. In addition, the cross sections of the electrodes, shown in Figs. 5 and 6, show a significant reduction in the depth and amount of damage when the gas is nitrogen rather than air. The gas may affect the erosion in one or more of the following ways: 1) by forming chemical compounds on the electrode surface which alter: a) the thermal stability [29], b) the current density at individual attachment sites in the arc [30], c) the lifetime of each attachment [30] 2) by producing accelerated chemical reactions at the electrode surface [311 particularly at impurity sites or at the magnesium sulfide stringer locations in stainless steel [32]; and 3) by altering the cathode and anode fall voltages, particularly at higher pressures. arcs , SURFACE CONDITIONS The surface of the electrode tips and the insulator inserts were examined after 50 000 shots. The analysis techniques utilized were Auger electron spectroscopy (AES), scanning electron microscopy (SEM), and optical microscopy. Brass: The surfaces of the brass electrodes are shown in Figs. 7 and 8. Large-scale melting is evident, with dendrites or metallic protrusions up to 0.2 cm long existing on the surface. The self-breakdown voltage for these electrodes dropped from 20 to 3 kV in approximately 2000 shots as a result of macroscopic field enhancements. In addition, the voltage self-breakdown distribution was characterized by a series of 'jumps" thought to be due to large particles being "blown" off the ends of the protrusions. Originally it was thought that the material being "pulled out" of the bulk electrode was lead, but the results of the AES analysis shown in Fig. 9 indicate the surface consists primarily of carbon, copper, and oxygen, with a notable absence of zinc and lead. From these results and those found by Marchesi and Maschio [6], it is obvious that brass has only limited use in repetitive operation at higher levels of charge transfer. Although the mechanism for the material extraction is not completely understood, Belkin [33] showed that the electromagnetic J X B force resulting from the discharge can play an important role at large currents. In addition, Fitch and Mc- DONALDSON et al.: I LLCTRODE EROSION PHENOMENA 33 (a) (b) Fig. 8. Surface of brass electrodes in nitrogen; (a) anode, (b) cathode. (a) (a) (b) (b) Fig. 9. Auger electron spectroscopy surface analysis of brass electrodes; (a) catlode. (b) Auger spectrum. Cormick [34] ohseived gross material extraction from stainless steel electrodeS Li a result of asymmetrical current con- Fig. 10. (a) Graphite and (b) copper-graphite cathode surfaces in air. nections. and copper-tungsten cathodes show evidence of severe meltCathode: The citlhodes lor most of the remaining materials ing. Although it is not easy to see in the photographs, all cathare shown in Figs. 10-1'. Considerable erosion has taken odes showed a distinct tendency to form a large-scale crater place, especially on1 the graplhite materials. The stainless steel whose diameter increases with increasing gap spacing and cur- 34 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 1, MARCH 1984 (a) (b) Fig. 11. (a) Stainless steel (304) and (b) copper-tungsten (K-33) cathode surfaces in air. (a) (b) Fig. 12. (a) Stainless steel (304) and (b) copper-tungsten (K-33) cathode surfaces in nitrogen. rent. Similar macroscopic cratering was observed by Watson [35] who explained the results with the use of a hydromagnetic flow model. The idea of using a cathode cup in spark gaps is not new [36] , [371, but it is interesting that the electrode erosion produces this shape. The location of the current attachment at the cathode should depend on the minimum electrical path length seen by the electron avalanche prior to breakdown. Thus the erosion pattern and the corresponding erosion rate may be highly geometry dependent. Anode: The anodes, corresponding to the cathodes shown in Figs. 10-12, are shown in Figs. 13-15. The graphite and copper-graphite anode erosion occurs primarily in a band, 0.8 cm wide, with the inner radius located 0.3 cm from the center of the electrode. This pattern is consistent with the results of Johnson and Pfender [38] which showed that an annular-shaped attachment region of high current density can exist at the anode. The copper-tungsten and stainless steel anodes indicate that melting and vaporization have taken place over the entire surface. Like the pattern at the cathode, the diameter of the anode erosion region increases with increasing current. Insulator: A typical insulator insert, for eight of the possible combinations of electrode material and gas, is shown in Figs. 16 and 17. The insulator surfaces are covered by a coating of recondensed electrode material. The one notable exception was graphite electrodes in air, in which case no coating was found on the insulator surface. A dramatic difference is seen in Fig. 16, in the case of a graphite electrode run in nitrogen. The entire insulator surface is covered with a thick coating of fluffy black material which is thought to consist of monoatomic layers of amorphous carbon [31 1. All insulators were covered with solid particles, 10-100 gm in size, distributed within a 5-cm band centered on a plane passing through the center of the gap and parallel to the electrode surfaces. This indicates that a considerable portion of the solid or molten material is ejected parallel to the electrode DONALDSON et al.: ELECTRODE EROSION PHENOMENA 35 (a) (b) Fig. 13: (a) Graphite and (b) copper-graphite anode surfaces in air. pr _ (a) (b) Fig. 14. (a) Stainless steel (304) and (b) copper-tungsten (K-33) anode surfaces in air. (a) (b) Fig. 15. (a) Stainless steel (304) and (b) copper-tungsten (K-33) anode surfaces in nitrogen. IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. PS-12, NO. 1, MARCH 1984 36 (a) (b) Fig. 16. Insulator inserts exposed to (a) graphite and (b) copper-graphite electrodes in air and nitrogen. I;: v (b) Fig. 18. Scanning electron microscope picture of stainless steel (304) electrode surface; (a) outer edge, (b) outer edge enlarged. Nitrogen Air (a) L~~~~~~~~~~~ Air 1 Nitrogen (b) Fig. 17. Insulator inserts exposed to (a) stainless steel (304) and (b) copper-tungsten (K-33) electrodes in air and nitrogen. surfaces. Daalder [39] has reported similar results for vacuum arcs and McClure [40] has developed a model which shows that the ion recoil pressure of a vacuum arc plasma is sufficient to remove molten material from a cathode spot crater with velocities of 2 X 103 to 2 X 104 cm/s parallel to the electrode surface. The values of velocity from McClure's model are in good agreement with the experimental findings of Udris [41 ]. Recent studies in vacuum arcs by Farrall [42] and Shalev [43], which have characterized the size and flux of the ejected particles as a function of current, indicate that the maximum number of particles are released at, or just following, the current maximum. Since the arc attachment region will reach its maximum diameter at the current maximum, then one would expect droplets of material to separate from the electrode at the crest or edge of the macroscopic crater. An SEM examination of the surface of the stainless steel (304) electrodes shows considerable agreement between the size and shape of the electrode surface features existing at the edge of the macroscopic crater, which is shown in Fig. 18, and a 50-,m stainless steel 37 DONALDSON et aLt: ELECTRODE EROSION PHENOMENA lowing objectives are being considered for future work. 1) Measure the erosion rate as a function of pressure (10-2 to 4 atm), rep-rate (1-1000 pps), and gas flow rate for a few of the more promising electrode-gas-insulator combinations. 2) Study the attachment of the arc to the electrode surface for a single shot as a function of pulse shape and peak current. 3) Compare the relative erosion rates for oscillatory and unipolar pulses which have different peak currents but transfer the same net charge. 4) Measure the voltage drop in the arc for pulsed currents in order to calculate the energy dissipated in the gap region. 5) Measure energy delivered to electrodes as a function of pulse shape, previously done by Carder [8], and compare these results with those computed from the arc voltage measurements in 4). Fig. 19. 50-pm stainless steel (304) particle on Lucite insulator. (304) particle found on the insulator and shown in Fig. 19. A thorough characterization of the particles found on the insulators used in this experiment is given by Jackson et al. [44]. The presence of similar particles has been shown to have serious effects on the flashover potential of the insulator at high pressures for particles bigger than 35 ,um and densities of 20 particles/mm [451. Thus the electrode erosion mechanism affects the switch lifetime, not only as a result of the erosion itself, but also by coating the insulating materials with conductive particles. CONCLUSIONS The erosion rate and surface damage of the electrodes was determined for several materials utilized in a high-energy spark gap. The results from these preliminary studies have led to the following conclusions. 1) The electrode erosion rates and mechanisms are highly polarity dependent and thus results for oscillatory and unipolar discharges can be considerably different. 2) A large amount of the erosion is in the form of solid and molten material removed parallel to the electrode surface and, apparently, from the edge of the macroscopic craters found on the cathode. 3) Cathode erosion rates are proportional to the total amount of charge transferred for a fixed repetition rate and pulse width. 4) Stainless steel (304) may be an economical replacement for copper-tungsten composites as a cathode material for the conditions studied. 5) Anode erosion rates were quite scattered, but, in general, were considerably less than the cathode erosion rates for all materials tested except stainless steel. 6) No distinct correlation was found between the thermophysical properties of the electrode materials and the amount of erosion. In order to develop a more precise understanding of the effects of electrode erosion on switch performance, the fol- ACKNOWLEDGMENT The authors wish to express their sincere appreciation to the following people for their various contributions to this work and its preparation: A. Bowling, M. Byrd, J. Clare, B. Conover, J. Davis, B. Maas, C. Mueller, R. Ness, S. Prien, K. Rathbun, A. Shaukat, and A. Williams. REFERENCES [1] T. R. Burkes et al., "A critical analysis and assessment of high power switches," NSWC Dahlgren Lab., Rep. NP 30/78, pp. 189-202, 1978. [2] L. B. Gordon et al., "Material studies in a high energy spark gap," IEEE Trans. Plasma Sci., vol. PS-10, pp. 286-293, 1982. [3] J. E. Gruber and R. Suess, "Investigation of the erosion phenomenon in high current, high pressure gas discharges," Max Planck Inst. fur Plasmaphysik, Garching bei Munchen, IPP 4/72, Dec. 1969. [4] R. A. Burden and T. E. 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Jackson et al., "Surface studies of dielectric materials used in spark gaps," J. Appl. Phys., vol. 55, pp. 262-268, 1984. B. F. Hampton and S. P. Fleming, "Impulse flashover of particle contaminated spacers in compressed sulfur hexafluoride," Proc. Inst. Elec. Eng., vol. 120, pp. 514-522, 1973. Transport Properties of Ablated Vapors of PTFE, Alumina, Perspex, and PVC in the Temperature Range 5000-30 000 K Thermodynamic and P. KOVITYA Abstract-Values of density, specific heat, enthalpy, sonic velocity, viscosity, thermal, and electrical conductivities have been calculated for the plasmas of PTFE, alumina, Perspex, and PVC for temperatures from 5000 to 30 000 K. Equilibrium particle concentrations and degrees of ionization are calculated using the minimization of Gibbs free energy, and transport properties are calculated using the Chapman-Enskog approximations. I. INTRODUCTION MXATERIAL FUNCTIONS of high-temperature plasmas have been reported for well-known gases such as air and nitrogen [1], SF6 [2], and argon [3]. However, very little Manuscript received February 15, 1983. The author is with the Commonwealth Scientific and Industrial Research Organization (CSIRO), Division of Applied Physics, Sydney, Australia 2070. has been reported recently on material functions of plasmas formed from ablated-wall vapors of plastics and ceramic materials which are found in arcs burning in fuses, lightning arrestors, and circuit breakers. Such plasmas are produced by PTFE (polytetrafluoroethylene, also known as Teflon), PVC (polyvinylchloride), Perspex (polymethylmethacrylate), and alumina. When fuses, lightning arrestors, and circuit breakers operate, high-current arcs are formed and ablation of wall materials can occur. Theoretical analyses of such arcs are possible [4], [5], but require material functions of the ablated vapors. Material properties of a plasma mixture can be divided into two distinct types: (a) thermodynamic properties such as density, entropy, enthalpy, heat capacity, and sonic velocity, and (b) transport properties such as viscosity, and thermal and electrical conductivities. For the calculation of the thermodynamic 0093-3813/84/0300-0038$01.00 © 1984 IEEE