Time lag to breakdown

P is the probability that a starter electron leads to breakdown and g(t) is the rate of injection of starter electrons in the stressed volume. In order to keep the conditions for all tests identical, the electrode surfaces and the liquid in the test gap should be changed after each breakdown event. Special attention has to be paid to the coupling of the high voltage pulse to the test gap in order to avoid voltage reflections (see Section 2.11). 

At longer gap distances, the distribution is characterized by two time lags which are summarized in Table 2. Analysis of the data with a single electron avalanche model (see Section 2.8) gave a first Townsend coefficient of a = 6.4 x 10 cm at 3.5 MV/cm (Arii et al, 1979). This value is one order of magnitude higher than data estimated by Haidara et al., (Haidara and Denat, 1991) for cyclohexane and propane (see Section 8.2). 

Data from Arii, K., Kitani, I., and Kawamura, M., /. Phys. D Appl. Phys., 12, 787, 1979. 

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In experiments with voltage pulses, the impedance matching of cable and test cell is of great importance in order to avoid voltage reflections (Arii et al, 1979). A test cell used for time lag to breakdown measurements and a typical oscilloscopic trace obtained are shown in Figure 46. 

Haidara and Denat (1991) investigated the onset of partial discharge pulses in a test cell with 50 D impedance consisting of a fine tip as cathode and a plane metal disk as anode. By comparing the threshold voltage in the vapor and in the liquid they were able to estimate values for a in the liquid phase as a function of applied field. Their data and for comparison the ionization rates reported for silicon are included in Figure 1. A crude estimation of a in liquid n-hexane obtained from time lag to breakdown measurements with thin liquid layers by Arii et al. (1979) is also included. 

Measurements of time lags to breakdown with n-hexane gave von Laue plots as depicted in Figure 9. At electrode separations below 40 pm, a behavior of P(t) as described by Equation 36 was observed. If the test gap is subjected to N step voltage pulses and breakdowns occurred at times greater than t, then P(t) becomes (assum-ing P = 1)... 

The application of pulse voltages and the measurement of time-lags to breakdown reveals a statistical feature of the breakdown process which is Influenced by conditions at the cathode. While the statistical time-lag can be as long as several microseconds, there is a formative time for the breakdown process which depends on overvoltage, electrode spacing and uniformity of field and can be very short. For example, breakdown of a 2 mm uniform-field gap in n-hexane at a field of 10 V cm can be completed in less than... 

When a voltage of sufficient magnitude (>Vs for dc) is suddenly applied to a gas-insulated electrode gap, or a gas-insulated conductor, breakdown does not occur instantaneously, but after a finite time t = ts T The 4 is called the statistical time lag and is the time that elapses between the application of the voltage V (>Vs) and the occurrence of a free electron in the stressed gas volume which initiates the breakdown process. The tf is called the formative time lag and is the time interval between the occurrence of the free electron and the collapse of the voltage (i.e., breakdown). 

Breakdown time-lag and successive steps leading to breakdown. 

The breakdown time-lag t corresponds to the following successive steps, in widely used and well-defined situations - divergent fields. 

The statistical study of breakdown time-lags in liquids has been the subject of numerous studies Lewis (1985) and his coworkers have proved the existence of a field-dependent "statistical time-lag", and showed how curves like the one of Fig. 1 could be predicted. The influence of the conditioning process of the electrodes and of the test method on the time-lag distribution density functions are extensively discussed in the book of Gallagher (1975). From breakdown time-lag measurements under rectangular voltage, it is possible to separate the initiation time (its statistical nature being questionable if it is field-dependent) from the so-called "formative time-lag", which is in fact the streamer propagation time (at least, in most of the experimental situations). With AC or DC, another aspect of initiation phenomena will be presented. 

As compared to other TPO, polypropylene is especially sensitive toward UV radiation [5]. The low stability of unstabilized PP exposed outdoors manifests itself by loss of gloss, formation of surface crazes, chalking, and breakdown of its mechanical properties. The same phenomena are observed in light stabilized PP too, but only after a more or less pronounced time lag [15, 16]. 

Movement of ions under the influence of an applied field will be very slow and subject to disruption by the thermal motion. Under the influence of such a field, movement of the atmosphere occurs in a direction opposite to that of the central ion, resulting in the continuous breakdown and re-formation of the atmosphere as the ion moves in one direction through the solution. The time-lag between the restructuring of the atmosphere and the movement of the central ion causes the atmosphere to be asymmetrically distributed around the central ion causing some attraction of the latter in a direction opposite to that of its motion. This is known as the asymmetry, or relaxation effect. In addition, central ions experience increased viscous hindrance to their motion on account of solvated atmosphere ions which, on account of the latter s movement in the opposite direction to the central ion, produce movement of solvent in this opposing direction as well. This is known as the electrophoretic effect. 

After administration of an antigen for the first time, there is an initial lag phase where antibodies are not produced. This is followed by a period in which the antibody titer rises logarithmically to a maximum and subsequently declines. The decline is due to either the breakdown or the clearance of the antibodies. 

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