IX International Symposium on Lightning Protection th
th
26 -30 November 2007 – Foz do Iguaçu, Brazil
THE EARLY STREAMER EMISSION PRINCIPLE DOES NOT WORK UNDER NATURAL LIGHTNING !! Marley Becerra
Vernon Cooray
Division of Electricity and Lightning Research, Uppsala University, Sweden
[email protected] [email protected] The Ångström Laboratory, Box 534, SE 751 21, Uppsala, Sweden Abstract - An appropriate evaluation of the efficiency of air terminals is a key factor for the discussion of the claimed advantages of the Early Streamer Emission devices ESE compared to the conventional Franklin rods. In order to discuss the physical basis and validity of the ESE claim, a self-consistent physical model is used to simulate the performance of an air terminal under laboratory and under natural lightning conditions. It is theoretically shown that the early initiation of streamers can indeed lead to the sooner initiation of a self-propagating positive leader in a laboratory long air gap under switching voltages. However, this is not the case for positive leaders initiated from the same terminal under the influence of the electric field produced by the descent of a downward moving lightning leaders. The time evolution of the leader development under natural conditions is different to the case in laboratory, where the leader inception condition is closely dependant upon the streamer inititation. This is mainly because of the differences in the time variation of the electric field applied in laboratory and that produced by the approach of the downward leader. Therefore, it is found that the claimed similarity between the switching electric fields applied in laboratory and the electric field produced by the descent of a negative downward leader, used in the literature to extrapolate the early streamer emission principle to natural lightning, is not true.
1 INTRODUCTION Since the very moment when the use of air terminals was proposed by Franklin [1], the efficiency of sharp and blunt rods to attract lightning flashes has remained open to question. With time, new different kinds of air terminals have been introduced in the market, including the Early Streamer Emission devices ESE [2-6]. The manufacturers of these devices claim that their terminals have a larger lightning protection zone than the one offered by a conventional Franklin rod. These claims are based on the fact that an earlier initiation of streamers in a laboratory air gap under switching voltages leads to the reduction of the leader inititation time and therefore to a shorter time to breakdown. Since the breakdown in laboratory air gaps is usually associated with the attachment of the upward and downward leaders in lightning, this results has been extended to the natural case. The main assumption of this
extrapolation is that the switching electric fields applied in laboratory “fairly approximates” the electric fields produced by the descent of a negative downward moving leader [2-4]. Consequently, the ESE devices are equipped with a discharge triggering device to increase the probability of streamer initiation upon the approach of the downward leader. This supposedly would enhance the efficiency of lightning attraction and therefore extend the area of protection above that of a conventional Franklin rod. However, the discussion of the efficiency of such air terminals has been subject of much controversy. This is because the conditions in the laboratory experiments are apparently not the same as in the case of natural lightning, particularly in terms of dimensions [5, 6]. Even though the best way to evaluate the efficiency of air terminals is to test them under natural conditions, there are several practical limitations that make difficult to gather conclusive experimental evidence from such tests. Thus, there is a lack of scientific and technical bases either to reject or to accept these devices [6]. Due to the fact that all the ESE devices have the common characteristic that they enhance ionization of the air in the immediate vicinity of the terminal, a major question that need to be solved is how this additional ionization acts to enhance the upward leader initiation [6]. This question has to be answered based on the time lag to leader inititiation and electrical breakdown in laboratory and the time span between the streamer initiation and the connection between the downward and the upward leaders in natural lightning. Given the existing doubts about the validity and proper interpretation of results of laboratory experiments regarding the efficiency of ESE devices, the theoretical simulation of electrical discharges both in laboratory and in natural lightning is one of the best available tools for this purpose. Unfortunately, the problem of time variation of the electrical discharge and the statistical time lags have been avoided in existing computer numerical models of discharges [6]. In this paper, a recently proposed physical model for the evaluation of the inception and propagation of leader discharges has been used to study the above presented
question. Hence, the initiation and development of positive leaders considering the time variation of the electric fields applied in laboratory and those produced by the descent of the downward leader are simulated. Since this model also takes into consideration the space charge created by streamers and aborted leaders, the influence of the streamer initiation condition on the leader development is evaluated in this paper. In this way, the physical characteristis of positive leaders in laboratory and in lightning are compared. 2 THE MODEL The development of a positive leader discharge from an air terminal under laboratory and natural lightning conditions is simulated with the model described in [7, 8]. This model predicts the initiation and propagation of positive leaders considering time variations of the existing background electric field as well as the space charge created by streamers and aborted leaders. Thus, the main physical parameters of the leaders, namely the charge per unit length, potential gradient, channel radius, injected current and propagation velocity, are self-consistently computed. The model used in this paper has been successfully applied to estimate the unstable and stable leader inception times [7] as well as the times to breakdown [8] in laboratory long gaps under switching impulses. In addition, its predictions regarding upward connecting lightning leaders have been validated with the results of an altitude rocket triggered lightning experiment [9]. A good agreement between the results of the model and the measured upward leader current, the upward initiation time and the interception point between both leaders was found in [7, 8]. In order to take into account the effect of the statistical variation of the streamer initiation time on the development of positive leaders, the probability density pi(t) for streamer inception is evaluated as in [11, 12]. Figure 1 shows the volume around the rod tip in which the production of an electron leads to corona at two different applied voltages. Due to the fact that the rate of electron production in the critical volume changes with humidity [13], lower values than the ones reported in [12] are used in this paper in order to consider an extreme case with high humidity. 3 EARLY STREAMER EMISSION IN LABORATORY In order to simulate the conditions under which the early streamer principle was discovered, an electrode configuration similar to the one used in [2-4] to compare a conventional Franklin rod and an ESE device is considered. It consists of a grounded air terminal 3.5 m tall and a plane at height 13 m above the ground plane.
Fig. 1. Critical volume for streamer inception of the considered rod, when 0.5MV (dot-dash line) and 0.8MV (dashed lines) are applied to the upper plane. The red lines correspond to the electric field lines.
Since details about the geometry of the tested Franklin rod are not reported in [2-4], a hemispherically capped rod with radius of 0.015 m is analysed. For the simulation of the leader development in laboratory, a switching voltage impulse waveform with 3.2 MV peak value and 350 µs risetime is chosen to roughly reproduce the conditions reported in [2-4]. Figure 1 shows the simulated streak image of a positive leader propagating in the gap under a switching voltage impulse. In order to consider the statistical time lag for streamer inception and its effect on the time to breakdown, two extreme cases for the streamer inception times are simulated. The lower extreme (Fig. 1.a) correspond to the minimum possible streamer inception time ti(min) given by the streamer inception criterion [13]. The upper limit (Fig. 1.b) is the probabilistic maximum streamer inception time ti(max) where the probability to produce an electron to initiate the streamer is close to one t max
pi (t ) ⋅ dt ≈ 1 . Thus, the streamer inception times for the
0
considered air terminal range between those limits according to the probability distribution function pi(t) shown in Figure 1. a. It is found that the the unstable and stable leader inception times t1’ and t1, as well as the time to breakdown tB, decrease when the streamer inception takes place earlier (Fig. 1). The unstable leader inception corresponds to the moment when the stem of the produced streamer burst is thermalized and the first leader segment is created. The stable leader inception condition is given by the moment when the continuous propagation of the newly created leader is self-maintained by the existing electric field. Thus, if a streamer is “triggered” earlier by either lowering the minimum streamer inception time or by narrowing the streamer inception probability distribution function, a reduction of the leader inception and breakdown times is obtained.
Fig. 2. Simulated streak image of the leader propagation under a switching voltage impulse for different streamer inception times: a) the minimum possible streamer inception time, b) the probabilistic maximum streamer inception time
The reduction of the time to breakdown obtained by triggering an early streamer agrees with the time-tobreakdown probability distributions of a conventional Franklin rod and an ESE device obtained by Berger [4]. In the same manner, the predicted improvement of the leader inception time in laboratory air gaps under switching electric fields by reducing the streamer initiation time, agrees with the streak images shown in [4]. It was observed in the laboratory that the leaders initiated from an ESE device “starts very early, well under the inception times of the Franklin rod leader” [2]. This fact was found based on streak images of positive leaders initiated from an ESE device and from a conventional Franklin rod, as the one shown in Fig. 3. However, the evaluation of the leader initiation time in laboratory experiments has to be carefully analysed [14]. For instance, observe that the initiation of the leader from the Franklin rod (Fig. 3.b) does not take place at the moment when the leader propagation looks continuous (at about 300 µs). Even though the discharge in the Franklin rod looks like intermittent bursts of discharge growth during the initial stage [14], the leader has already started its continuous propagation. This is because laboratory leaders under long time to crest have been observed to grow continuously in length despite of several steps in charge and light emission [12], as in Fig. 3.b. Unfortunately it is not possible to make direct comparison between our predictions (Fig. 2) and the streak image of the Franklin rod studied in [2-4] (Fig. 3.b). This is because the simulated case does not exactly corresponds to the experimental conditions in [2-4], since neither the geometry of the rod or the voltage waveform were reported. However, note that some features of the leader propagation in the Franklin rod are consistent with our predictions, although the steps in light observed in the experiment cannot be predicted by the model.
Fig. 3. Streak image of the leader propagation in laboratory, adapted from [2] for a) an ESE device and b) a conventional Franklin rod. The time scale was estimated from the current waveforms reported in [2] and the dotted lines show the estimated position of the leader tip.
Regarding the ESE device, it is interesting to observe in Fig. 3 that the leader corona from the Franklin rod extends further than in the case of the ESE device [14]. For the same leader length, the corona zone in front of the leader tip is longer for the Franklin rod than for the ESE terminal. This difference could be produced by the presence of the triggering circuit in the ESE device or by differences in the applied voltage in both cases shown in Fig. 3. Due to the lack of information about the internal circuit of the ESE terminal used in [4], the authors did not intend to exactly simulate the leader development from such device. Nonetheless, similar leader characteristics as the ones predicted in Fig. 2 can be expected from the ESE device, given the fact that only a low voltage (up to 15 kV) is applied to the ESE terminal tip by the triggering unit used in [2-4]. 4 POSITIVE LEADERS UNDER LIGHTNING ELECTRIC FIELDS As it was observed in the previous section, the triggering of an early emitted streamer from an air terminal in the laboratory under swiching voltages can lead to the reduction of the time to leader initiation and to breakdown. However, this result has been extrapolated to the natural conditions of lightning [2-4], arguing that the leaders in laboratory resemble the upward connecting lightning leaders. Hence, this reduction on the leader inception time in the laboratory under switching waveforms is assumed to be reflected on an early initiation of upward connecting leaders when the terminal is exposed to downward lightning leaders. The main assumption considered in this claim is that the applied electric field “fairly approximates” the rising electric field produced by the downward moving leader [2, 4].
In order to evaluate if the switching electric fields applied in laboratory reproduce a leader propagating under natural conditions, the simulations are repeated considering the electric field produced by the descent of a downward moving leader. For the analysis, a straight negative downward leader channel descending with an average velocity Vdown of 2 x 105 m s-1 directly overhead the terminal is considered. The charge density of the downward leader channel is computed a function of the prospective return stroke peak current according to Cooray et al. [10]. Figure 4 shows the comparison between the switching electric field applied in laboratory and the electric fields produced by downward leaders with different prospective return stroke currents. As suggested in [4], the waveforms are aligned in time such that the natural and simulated electric fields coincide at the moment where ionization processes at the tip of the terminal take place. The simulated streak images of the leaders propagating in the studied laboratory air gap, under background electric fields corresponding to the approach of a downward leader with prospective return stroke current of 3, 5 and 10 kA (Fig. 4), are shown in Fig. 5. Note that the predicted propagation of the leader under the lightning electric fields have some different features compared with the leaders under a switching waveform (Fig. 2). In first place, note that the leader length in the laboratory is shorter under lightning electric fields than for the “equivalent” switching waveform. The leader length under the electric field produced by a downward leader with prospective return stroke current of 5 kA (Fig. 5.b) is about 1 m long at the moment of the final jump, while the leader for the “equivalent” switching waveform in Figure 2.b is three times longer. Secondly, the unstable leader inception time ti’ under lightning electric fields takes place a long time after the inception of the first streamer ti (ti’- ti is about 120 µs, 200 µs and 350 µs for prospective return stroke currents of 3, 5 and 10 kA respectively) compared with the switching case (ti’- ti is only about 25 µs in Fig. 2.b). Moreover, more than one streamer burst can be produced before the initiation of the bridging leader under lightning electric fields. Thirdly, the time difference between breakdown tB and stable leader inception t1 in the gap is significantly shorter when lightning-like electric fields are applied (Fig. 5) than when laboratory switching electric fields are used (Fig. 2). In the former case, the time span tB- t1 is shorter than 40 µs for the three prospective return stroke currents considered in this paper, while in the latter case this time spam takes more than 150 µs.
Fig. 4. Comparison between the laboratory switching electric field and the electric field produced by the descent of a downward leader with different prospective return stroke current.
Fig. 5. Simulated streak images of leaders under the electric field produced by the descent of a downward leader with different prospective return stroke current a) 3 kA, b) 5 kA, c) 10 kA
These basic differences are mainly caused by the differences in the rate of change of the switching impulses and the lightning electric fields (Fig. 4). After the streamer inception time ti, the lightning electric fields increase slowly, making the dark period (time where no streamers are produced) longer in comparison with the switching case. This dark period ends when the applied electric field is high enough to restore the electric field at the tip of the rod, which is shielded by the space charge injected by the first streamer. After the dark period, a new streamer is produced. Nevertheless, an aborted streamer/leader burst can be produced if the lightning electric field is still changing slowly (Fig. 5.b and 5.c) as to compensate the voltage drop at the tip of the newly created leader segment. Otherwise, a continuously leader is incepted. After the initiation of the self-propagating leader, the lightning electric fields derivative continues increasing quickly, enlarging the extension of the streamer corona at the tip of the leader channel. Since the streamer corona
zone is continously increasing, the breakdown of the gap tB takes place soon after the leader inception. Hence, the time for the propagation of the leader is shorter, and the gap is bridged by the streamers even if the leader channel is not long. Thus, it can be clearly seen by comparing the results of Figs. 2 and 5 that switching voltage waveforms DO NOT “fairly approximate” the electric fields produced by the descent of a downward leader, as claimed in [2-4]. Due to the fact that the rate of increase of the lightning electric fields changes from slow to fast, while the switching electric field derivative changes from fast to slow (Fig. 4), the development of leaders from air terminals under both conditions is different. Moreover, the early streamer principle does not apply for the case of lightning waveforms in laboratory either. Figure 6 shows the simulated streak image of a positive leader propagating in the laboratory air gap under lightning-like electric fields, considering the statistical streamer inception time. A downward leader with a prospective return stroke current is used in this case. Observe that despite of the fact that the probability to produce an electron to initiate the streamer from the terminal extends up to about 180 µs, the time to breakdown tB is not affected by the streamer inception time ti. In other words, there is not any change at all in the time to breakdown in this case even if a streamer is triggered earlier, contrary to the case of a leader propagating under a switching voltage waveform. Thus, if an early streamer is triggered from an air terminal under lightning-like electric fields in laboratory (Fig. 6.a), further bursts of aborted streamers and leaders are produced, but there is not any significant change in the stable leader inception time t1 compared with the case of a late streamer (Fig. 6.b).
Fig. 6. Simulated streak image of the leader propagation in the laboratory under the electric field produced by a downward leader with prospective return stroke current of 5 kA for different streamer inception times: a) the minimum possible streamer inception time, b) the probabilistic maximum streamer inception time
In the same way, the streamer emission principle does not produce any improvement in the stable leader inception time when the air terminal is exposed to the direct influence of a downward moving leader. Figure 7 shows our predictions of the development of an upward positive leader connecting a downward moving negative leader with prospective return stroke current of 10 kA. Similar features of the leader initiation and propagation as the ones discussed for lightning-like electric fields are obtained. Also, there is not any change in the time tfj or in the length of the upward leader at the moment of the interception of the downward leader when a streamer is initiated earlier. In this case, the connection of both leaders takes place at the same instant regardless the time of inception of the first streamer, even if the time difference of the streamer inception times evaluated in Fig. 7 is about 300 µs. Therefore, the results presented in this section clearly show that the early streamer principle DOES NOT work under lightning conditions. Even though the early streamer principle applies for leaders propagating in the laboratory under switching waveforms, it does not influence leaders propagating under the electric fields produced by the descent of a downward moving leader. Thus, the early emission of streamers from air terminals DOES NOT lead to longer upward leaders at the moment of the attachment of the downward leader and consequently to longer lightning protection zones.
Fig. 7. Simulated streak image of the leader propagation under the electric field produced by a downward leader with prospective return stroke current of 10 kA for different streamer inception times: a) the minimum possible streamer inception time, b) the probabilistic maximum streamer inception time
4 CONCLUSION From the results of the simulations presented in this paper it can be concluded that an early streamer triggered from an air terminal tested under a switching impulse waveform leads to the quicker initiation of the leader, and consequently to a shorter time to breakdown. However, this early emission principle does not apply for air terminals under lightning conditions. Due to the fact that the rate of increase of the lightning electric fields changes from slow to fast, while the switching electric field derivative changes from fast to slow, the development of leaders from air terminals under both conditions is different. Thus, the length of the upward connecting leader at the moment of attachment of the downward leader is not affected by the time of initiation of the first streamer. This fact clearly shows that the early streamer emission principle does not work for air terminals exposed to the influence of downward moving leaders and that the claimed enlarged lightning protection area of ESE devices is physically not plausible. At best, the ESE terminals perform similar to a conventional Franklin rod.
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