the gas volume by the metastable and excited gas atoms or molecules. In fact, in large gaps the breakdown is governed by steamer formation in which photon emission from the avalanches plays a dominant role. Break down characteristics of gases are represented graphically in terms of the Paschen curves, which are plots of the breakdown voltage as a function of the product of gas pressure p and the electrode separation d Each gas is characterized by a well-defined minimum breakdown voltage at one particular value of the pd product. The breakdown process in liquids is perhaps the least understood due to a lack of a satisfactory theory on the liquid state. The avalanche theory has been applied with limited success to explain the breakdown in liquids, by assuming that electrons injected from an electrode surface exchange energy with the atoms or molecules of the liquid, ultimately causing the atoms and molecules to ionize and thus precipitating breakdown. Recent investigations, utilizing electro-optical techniques, have demonstrated that breakdown involves steamers with tree-or bushlike structures that propagate from the electrodes [Bartnikas, 1994]. The negative streamers due to free electrons in the liquid itself. The breakdown of liquids is noticeably affected by electrolytic impure emerging from the cathode form due to electron emission, while positive steamers originating at the anode as well as water and oxygen content; also, macroscopic particles may form bridges between the electrodes along which electrons may hop with relative ease, resulting in a lower breakdown. As in solids, there is a volume effect and breakdown strength decreases with thickness; a slight increase in breakdown voltage is also observed with viscosity In both solid and liquid dielectrics, the breakdown strength under dc and impulse fields is markedly greater than that obtained under ac fields, thus suggesting that under ac conditions the breakdown may be partially thermal in nature. Thermal breakdown occurs at localized hot spots where the rate of heat generated exceeds that dissipated by the surrounding medium. The temperature at such hot spots continues to rise until it becomes fficiently high to induce fusion and vaporization, causing eventually the development of a channel along which breakdown ensues between the opposite electrodes. Since a finite amount of time is required for the heat buildup to occur to lead to the thermal instability, thermally induced breakdown is contingent upon the time of the alternating voltage application and is thus implicated as the leading cause of breakdown in many dielectrics under long-term operating conditions. However, under some circumstances thermal instability may develop over a very short time; for example, some materials have been found to undergo thermal breakdown when subjected to very short repetitive voltage pulses. In low-loss dielectrics, such as polyethylene, the occur rence of thermal breakdown is highly improbable under low operating temperatures, while glasses with signif icant ionic content are more likely to fail thermally, particularly at higher frequencies The condition for thermal breakdown may be stated as KA△T=oeE2tan6 where the left-hand side represents the heat transfer in J s- along a length I(cm)of sectional area A(cm)of the dielectric surface in the direction of the temperature gradient due to the temperature difference AT in C such that the units of the thermal conductivity constant K are in JC -cm-s. The right-hand side of Eq (55.18)is equal to the dielectric loss dissipated in the dielectric in J s-I, where E is the external field, e the real value of the permittivity, and tan& the dissipation factor at the radial frequency o Other causes of extrinsic breakdown are associated with particular defects in the dielectric or with the nvironmental conditions under which the dielectric material is employed. For example, some dielectrics ma contain gas-filled cavities that are inherent with the porous structure of the dielectric or that may be inadvert- ntly introduced either during the manufacturing process or created under load cycling. If the operating electrical field is sufficiently elevated to cause the gas within the cavities to undergo discharge, the dielectric will be subjected to both physical and chemical degradation by the partial discharges; should the discharge process be sustained over a sufficiently long period, bi ensue. With overhead line insulators or bushings of electrical equipment, breakdown may occur along the surface rather than in the bulk of the material Insulator surfaces consisting of porcelain, glass, or polymeric materials (usually elastomers), may become contaminated by either industrial pollutants or salt spray near coastal areas, leading to surface tracking and breakdown below the normal flashover voltage. Surface tracking is enhanced in the presence of moisture, which increases the surface conductivity, particularly in the presence of ionic contaminants Bartnikas, 1987]. The latter is measured in S or n2- and must be distinguished from the volume c 2000 by CRC Press LLC© 2000 by CRC Press LLC the gas volume by the metastable and excited gas atoms or molecules. In fact, in large gaps the breakdown is governed by steamer formation in which photon emission from the avalanches plays a dominant role. Break￾down characteristics of gases are represented graphically in terms of the Paschen curves, which are plots of the breakdown voltage as a function of the product of gas pressure p and the electrode separation d. Each gas is characterized by a well-defined minimum breakdown voltage at one particular value of the pd product. The breakdown process in liquids is perhaps the least understood due to a lack of a satisfactory theory on the liquid state. The avalanche theory has been applied with limited success to explain the breakdown in liquids, by assuming that electrons injected from an electrode surface exchange energy with the atoms or molecules of the liquid, ultimately causing the atoms and molecules to ionize and thus precipitating breakdown. Recent investigations, utilizing electro-optical techniques, have demonstrated that breakdown involves steamers with tree- or bushlike structures that propagate from the electrodes [Bartnikas, 1994]. The negative streamers emerging from the cathode form due to electron emission, while positive steamers originating at the anode are due to free electrons in the liquid itself. The breakdown of liquids is noticeably affected by electrolytic impurities as well as water and oxygen content; also, macroscopic particles may form bridges between the electrodes along which electrons may hop with relative ease, resulting in a lower breakdown. As in solids, there is a volume effect and breakdown strength decreases with thickness; a slight increase in breakdown voltage is also observed with viscosity. In both solid and liquid dielectrics, the breakdown strength under dc and impulse fields is markedly greater than that obtained under ac fields, thus suggesting that under ac conditions the breakdown may be partially thermal in nature. Thermal breakdown occurs at localized hot spots where the rate of heat generated exceeds that dissipated by the surrounding medium. The temperature at such hot spots continues to rise until it becomes sufficiently high to induce fusion and vaporization, causing eventually the development of a channel along which breakdown ensues between the opposite electrodes. Since a finite amount of time is required for the heat buildup to occur to lead to the thermal instability, thermally induced breakdown is contingent upon the time of the alternating voltage application and is thus implicated as the leading cause of breakdown in many dielectrics under long-term operating conditions. However, under some circumstances thermal instability may develop over a very short time; for example, some materials have been found to undergo thermal breakdown when subjected to very short repetitive voltage pulses. In low-loss dielectrics, such as polyethylene, the occur￾rence of thermal breakdown is highly improbable under low operating temperatures, while glasses with signif￾icant ionic content are more likely to fail thermally, particularly at higher frequencies. The condition for thermal breakdown may be stated as KA DT/l = ve¢E2 tand (55.18) where the left-hand side represents the heat transfer in J s–1 along a length l (cm) of sectional area A (cm2 ) of the dielectric surface in the direction of the temperature gradient due to the temperature difference DT, in °C, such that the units of the thermal conductivity constant K are in J °C –1 cm–1 s–1. The right-hand side of Eq. (55.18) is equal to the dielectric loss dissipated in the dielectric in J s–1, where E is the external field, e¢ the real value of the permittivity, and tand the dissipation factor at the radial frequency v. Other causes of extrinsic breakdown are associated with particular defects in the dielectric or with the environmental conditions under which the dielectric material is employed. For example, some dielectrics may contain gas-filled cavities that are inherent with the porous structure of the dielectric or that may be inadvert￾ently introduced either during the manufacturing process or created under load cycling. If the operating electrical field is sufficiently elevated to cause the gas within the cavities to undergo discharge, the dielectric will be subjected to both physical and chemical degradation by the partial discharges; should the discharge process be sustained over a sufficiently long period, breakdown will eventually ensue. With overhead line insulators or bushings of electrical equipment, breakdown may occur along the surface rather than in the bulk of the material. Insulator surfaces consisting of porcelain, glass, or polymeric materials (usually elastomers), may become contaminated by either industrial pollutants or salt spray near coastal areas, leading to surface tracking and breakdown below the normal flashover voltage. Surface tracking is enhanced in the presence of moisture, which increases the surface conductivity, particularly in the presence of ionic contaminants [Bartnikas, 1987]. The latter is measured in S or V–1 and must be distinguished from the volume