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Radio emission structure of cloud-to-ground lightning discharge
Physics Letters A 375 (2011) 1128–1134
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Radio emission structure of cloud-to-ground lightning discharge A.V. Gurevich a,∗ , A.N. Karashtin b a b
P.N. Lebedev Physical Institute, Moscow, Russia Radiophysical Research Institute, Nizhny Novgorod, Russia
a r t i c l e
i n f o
Article history: Received 10 December 2010 Accepted 20 December 2010 Available online 28 December 2010 Communicated by V.M. Agranovich Keywords: Lightning discharge Radio emission
a b s t r a c t Cloud-to-ground lightning discharge radio frequency emission is analysed on the base of measurements with high temporal resolution allowed to fully resolve its structure. Discharge radio emission mainly consists of independent random bi-polar pulses. Pulse length, amplitude and interpulse period distributions are studied at different stages of lightning discharge. The significant change of radio frequency emission structure during discharge development is demonstrated. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Radio interferometry was widely used for thunderstorm discharge studies during last years allowing to observe the spatiotemporal evolution of the lightning. Directions to the sources of radiation and electric field waveforms (C.T. Rhodes et al. [1]), spacial and temporal development of lightning initiation process (X. Shao and P. Krehbiel [2], W. Rison et al. [3]), correlations of radio interferometric measurements with high-speed video (V. Mazur et al. [4]) and electric field data (T.C. Marshall et al. [5], M. Stolzenburg et al. [6]), leader velocities (S.A. Behnke et al. [7]), preliminary breakdown and leader initiation (G.S. Zhang et al. [8]) were studied in details. Combination of radio studies with other methods allowed to extend the knowledge about the details of thunderstorm discharge development. At the same time previously used radio interferometric methods had rather low temporal resolution (about 1 μs). Such resolution did not allow to resolve temporal structure of radio emission fully. Our wide band radio frequency receiving system (see A.V. Gurevich et al. [9], A.N. Karashtin et al. [10]) was specially designed to short pulse detection. Its temporal resolution of about 16 ns allowed us to resolve fine structure of radio emission during all stages of lightning discharge. In this Letter we study the development of cloud-to-ground (CG) discharge including preliminary breakdown and leader phase up to the return stroke. We demonstrate that the radio frequency emission of discharge mainly consists of independent pulses. Radio pulse lengths, amplitudes and interpulse periods are analyzed at various stages of discharge. Presented observations
*
Corresponding author. E-mail addresses: [email protected] (A.V. Gurevich), tolk@nirfi.sci-nnov.ru (A.N. Karashtin). 0375-9601/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.12.053
give the full description of the radio emission pulse structure during the lightning initiations process. 2. Lightning radio emission Radio emission of lightning was investigated at SURA facility of Radiophysical Research Institute located near Vasil’sursk at about 120 km to the east from Nizhny Novgorod using special installation described in details in [9,10]. This installation was designed to detect short electromagnetic pulses in the HF frequency range (actually from 50 kHz to 30 MHz) allowing to record pulse waveform with 16 ns temporal resolution, and to find direction to the source of radio emission. In this Letter we present a case study of the HF radio emission structure for rather distant one-stroke cloud-to-ground lightning discharge took place on August 06, 2008 at 12:05:47 local summer time. It is known that horizontal extent of the active region of lightning discharge could reach several kilometers in the thundercloud at the preliminary stage. Rather distant lightning was chosen to diminish possible influence of the range variations from the receiver to the sources of radiation during discharge development on the observed radio emission intensity. The distance to the particular discharge was estimated as few ten kilometers based on the sudden change of measured quasi-static electric field on the ground. So radio emission intensity in our case practically corresponds to the source strength only slightly varying due to range variations. Temporal behavior of received lightning radio emission for the considered case is shown in Fig. 1(a), and quasi-static electric field record is shown in Fig. 1(b). Sudden beginning of radio emission should be noted. As it was shown earlier [10] this emission consists of a series of short bi-polar pulses up to the return stroke. Several stretched out time 1 ms scans of radio emission are pre-
A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
sented in Fig. 1(c), (d), (e) clearly showing its pulsed structure. Pulse amplitude does not show any growth from the very beginning of the lightning discharge. First of all let us examine time dependence of lightning discharge radio frequency emission in more details. To characterize average intensity of the emission one can introduce two parameters: root mean square (rms) and median amplitudes. The ratio between these amplitudes can provide information about the character of radiation. Its obvious that for monochromatic signal this ratio should be equal to unity, while for rare pulses median amplitude should be close to zero independently from pulse amplitudes. For normal Gaussian noise rms/median amplitude ratio is about 1.5. Therefore the combined behaviour of rms and median amplitudes can serve as an indicator of pulse and continuous fractions of radio emission. Rms and median amplitudes taken on 100 μs intervals are shown in Fig. 2, and their ratio — in Fig. 3. Lightning discharge radio emission began at about 133.2 ms before the return stroke. It is clear from Fig. 3 that the rms/median amplitude ratio is close to 1.5 out of the discharge mentioned above. This means that background is a normal noise resulted from mixing of emission from a lot of radio stations. The last are clearly seen in the spectra of received background radio emission. It should be mentioned that comparison of actual values with theoretical estimations should be accomplished taking into account discrete character of the record and low level of the background signal.
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Discharge radio emission begins with radical enhancement of rms amplitude while median one remains approximately the same that means pulsed character of emission. This character remains the same with considerable variations of rms amplitude till about 30 ms before the return stroke. Rms amplitude variations can be explained by rather rare occurrence of pulses when only few pulses fall into each 100 μs interval. As from about 30 ms before the return stroke median amplitude shows a steady excess above its background magnitude, and it continuously increases started in 10 ms before the return stroke. At the same time variations of rms amplitude becomes less while its (rms amplitude) maximum magnitude remains approximately the same as in the previous period. Such behavior can be caused by the appearance of quasi-continuous component of radiation on the one hand, and more frequent occurrence of pulses on the other. At the return stroke that actually lasted about 150 μs, both radio emission averaged amplitudes (rms and median) grow up by one order approximately, and their ratio falls to about 2 that indicates the presence of both pulsed and continuous components of comparable intensity. 3. Pulsed component structure Let us analyse now pulsed component of lightning discharge radio emission. We will consider pulses with amplitudes large enough to prevent occasional missing low amplitude pulses on the noise background. In terms of input voltage we choose pulses
Fig. 1. Radio emission (a) and quasi-static electric field (b) temporal behaviour during the lightning discharge. Several stretched out one millisecond time scans of radio emission — (c) at the very beginning of the emission, (d) in the middle of the discharge, (e) at the return stroke.
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Fig. 1. (continued)
with amplitude exceeded 20 mV while rms background amplitude is about 2 mV with standard deviation of the same order. In the whole discharge we found 8373 pulses with amplitudes above 20 mV. Pulse amplitude distribution is shown in Fig. 4, and distribution of interpulse intervals — in Fig. 5. Both distributions were obtained over the whole discharge. The last distribution seems to be a sum of two (or more) logarithmic distributions with different time scales that could be caused by mixing of different distributions at different stages of discharge development. Let us remind
that logarithmic distribution of interpulse intervals indicates independence of pulses in the series. Pulse length (actually a length of the first part of bi-polar pulse calculated using parabolic approximation around its maximum at the half-maximum level) distribution obtained over the whole discharge is shown in Fig. 6. The length of the main part of pulses lies between 40 and 150 ns, and there is no pulses with lengths less than 30 ns (temporal resolution of our measurements was about 16 ns that guaranteed detection of such pulses if they are in the emission).
A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
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Fig. 2. Root mean square (top) and median (bottom) amplitudes of lightning radio emission in 100 μs intervals.
Fig. 3. Ratio of RMS to median amplitude in 100 μs intervals.
Consider now temporal behaviour of pulse rate counting pulses in 1 ms intervals. The result is shown in Fig. 7. Pulse rate is approximately 40 1/ms during about 50 ms from the discharge radio emission beginning, then it is slightly reducing coming back to the previous level to 30 ms before the return stroke. Next
10 ms it grows to 120 1/ms remaining the same about 10 ms after that. About 10 ms before the return stroke pulse rate begins to grow rapidly reaching about 300 1/ms. At the last millisecond before the return stroke it falls abruptly. At the same time the mean amplitude of pulses varies weakly all the time till
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A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
Fig. 4. Pulse amplitude distribution over the whole discharge (for pulses with amplitude exceeded 20 mV).
Fig. 5. Interpulse interval distribution over the whole discharge (for pulses with amplitude exceeded 20 mV).
Fig. 6. Pulse length distribution over the whole discharge (for pulses with amplitude exceeded 20 mV).
A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
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Fig. 7. Temporal behaviour of pulse rate during the discharge.
Fig. 8. Pulse amplitude distributions at different stages of discharge development.
10 ms before the return stroke significantly falling to the return stroke. We can distinguish 5 characteristic time intervals based on the time dependence of pulse amplitude and rate: (I) −132 to −87 ms, (II) −82 to −42 ms, (III) −27 to −17 ms, (IV) −12 to −7 ms, and (V) −7 to −2 ms regarding to the return stroke. Pulse emission parameter varies weakly at each interval. Examine now pulse characteristics independently at each interval. Pulse amplitude distributions are shown in Fig. 8. At three first intervals they are practically the same while at the forth one can mark some deficit of high amplitude pulses that becomes distinct at the last interval immediately before the return stroke. Distributions of interpulse intervals are shown in Fig. 9. All these distributions are close to logarithmic, but have different characteristic time: it is approximately the same at first two intervals and then decreases considerably with discharge development. Logarithmic law of distributions indicates independence of pulse occurrence. Pulse length (first part of bi-polar pulse) distributions are shown in Fig. 10. Again, at first two intervals they are practically the same varying at later intervals. Characteristic length of the pulses decreases from about 75 ns at intervals I, II to about 55 ns at interval V. At the same time distribution becomes more narrow with discharge development due to lessening of longer pulses.
4. Conclusion Let us summarize the main results as follows. 1. The radio emission during the preconditioning and initiating stages of the cloud-to-ground lightning consists of a large number (several thousands) radio pulses. 2. The characteristic growth time of the radio pulse is less than 100 ns. The full time is few hundred ns. 3. The pulses are random and independent. 4. The pulses have random amplitude. The pulse amplitude distribution is falling with amplitude growth. 5. The time interval between pulses is random. The average interval in the preliminary (I and II period) part of discharge is about 30–40 μs, close to the return stroke it is rapidly diminishing up to 10–3 μs. 6. The larger is the pulse amplitude the wider is the time interval between pulses. Note the significant difference in the pulse behavior at the preliminary (I and II period) and concluding (III–V periods) parts of the discharge. At the first two periods the radio emission characteristics have no considerable differences except of some diminution of pulse amplitude and frequency of occurrence at II period.
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Fig. 9. Interpulse interval distributions at different stages of discharge development.
Fig. 10. Pulse length (first part of bi-polar pulse) distributions at different stages of discharge development.
Characteristics of radio emission at subsequent intervals in the concluding part are varying significantly in the following manner.
• Intensity of lightning HF radio emission varies insignificantly except of return stroke.
• Relative part of continuous component increases during lightning discharge development.
• Pulse amplitude distribution becomes more narrow at the expense of large amplitude pulses.
• Pulse rate grows significantly. • Interpulse period distributions are logarithmic at all intervals, characteristic time of distributions decreases in accordance to pulse rate growing. • Characteristic length of first part of bi-polar pulses decreases notably, and its distribution narrows at the expense of longer pulses.
References [1] C.T. Rhodes, X.M. Shao, P.R. Krehbiel, R.J. Thomas, C.O. Hayenga, J. Geophys. Res. 99 (1994) 13059. [2] X. Shao, P. Krehbiel, J. Geophys. Res. 101 (1996) 26641. [3] W. Rison, R.J. Thomas, P.R. Krehbiel, T. Hamlin, J. Harlin, Geophys. Res. Lett. 26 (1999) 3573. [4] V. Mazur, P. Krehbiel, X.-M. Shao, J. Geophys. Res. 100 (1995) 25731. [5] T.C. Marshall, M. Stolzenburg, C.R. Maggio, L.M. Coleman, P.R. Krehbiel, T. Hamlin, R.J. Thomas, W. Rison, Geophys. Res. Lett. 32 (2005) L03813. [6] M. Stolzenburg, T.C. Marshall, W.D. Rust, E. Bruning, D.R. MacGorman, T. Hamlin, Geophys. Res. Lett. 34 (2007) L04804. [7] S.A. Behnke, R.J. Thomas, P.R. Krehbiel, W. Rison, J. Geophys. Res. 110 (2005) D10207. [8] G.S. Zhang, Y.X. Zhao, X.S. Qie, T. Zhang, Y.H. Wang, C.P. Chen, Sci. China, Ser. D: Earth Sci. 51 (2008) 694. [9] A.V. Gurevich, L.M. Duncan, A.N. Karashtin, K.P. Zybin, Phys. Lett. A 312 (2003) 228. [10] A.N. Karashtin, Y.V. Shlyugaev, A.V. Gurevich, Radiophys. Quantum Electron. 48 (2005) 711.
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Radio emission structure of cloud-to-ground lightning discharge A.V. Gurevich a,∗ , A.N. Karashtin b a b
P.N. Lebedev Physical Institute, Moscow, Russia Radiophysical Research Institute, Nizhny Novgorod, Russia
a r t i c l e
i n f o
Article history: Received 10 December 2010 Accepted 20 December 2010 Available online 28 December 2010 Communicated by V.M. Agranovich Keywords: Lightning discharge Radio emission
a b s t r a c t Cloud-to-ground lightning discharge radio frequency emission is analysed on the base of measurements with high temporal resolution allowed to fully resolve its structure. Discharge radio emission mainly consists of independent random bi-polar pulses. Pulse length, amplitude and interpulse period distributions are studied at different stages of lightning discharge. The significant change of radio frequency emission structure during discharge development is demonstrated. © 2010 Elsevier B.V. All rights reserved.
1. Introduction Radio interferometry was widely used for thunderstorm discharge studies during last years allowing to observe the spatiotemporal evolution of the lightning. Directions to the sources of radiation and electric field waveforms (C.T. Rhodes et al. [1]), spacial and temporal development of lightning initiation process (X. Shao and P. Krehbiel [2], W. Rison et al. [3]), correlations of radio interferometric measurements with high-speed video (V. Mazur et al. [4]) and electric field data (T.C. Marshall et al. [5], M. Stolzenburg et al. [6]), leader velocities (S.A. Behnke et al. [7]), preliminary breakdown and leader initiation (G.S. Zhang et al. [8]) were studied in details. Combination of radio studies with other methods allowed to extend the knowledge about the details of thunderstorm discharge development. At the same time previously used radio interferometric methods had rather low temporal resolution (about 1 μs). Such resolution did not allow to resolve temporal structure of radio emission fully. Our wide band radio frequency receiving system (see A.V. Gurevich et al. [9], A.N. Karashtin et al. [10]) was specially designed to short pulse detection. Its temporal resolution of about 16 ns allowed us to resolve fine structure of radio emission during all stages of lightning discharge. In this Letter we study the development of cloud-to-ground (CG) discharge including preliminary breakdown and leader phase up to the return stroke. We demonstrate that the radio frequency emission of discharge mainly consists of independent pulses. Radio pulse lengths, amplitudes and interpulse periods are analyzed at various stages of discharge. Presented observations
*
Corresponding author. E-mail addresses: [email protected] (A.V. Gurevich), tolk@nirfi.sci-nnov.ru (A.N. Karashtin). 0375-9601/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.12.053
give the full description of the radio emission pulse structure during the lightning initiations process. 2. Lightning radio emission Radio emission of lightning was investigated at SURA facility of Radiophysical Research Institute located near Vasil’sursk at about 120 km to the east from Nizhny Novgorod using special installation described in details in [9,10]. This installation was designed to detect short electromagnetic pulses in the HF frequency range (actually from 50 kHz to 30 MHz) allowing to record pulse waveform with 16 ns temporal resolution, and to find direction to the source of radio emission. In this Letter we present a case study of the HF radio emission structure for rather distant one-stroke cloud-to-ground lightning discharge took place on August 06, 2008 at 12:05:47 local summer time. It is known that horizontal extent of the active region of lightning discharge could reach several kilometers in the thundercloud at the preliminary stage. Rather distant lightning was chosen to diminish possible influence of the range variations from the receiver to the sources of radiation during discharge development on the observed radio emission intensity. The distance to the particular discharge was estimated as few ten kilometers based on the sudden change of measured quasi-static electric field on the ground. So radio emission intensity in our case practically corresponds to the source strength only slightly varying due to range variations. Temporal behavior of received lightning radio emission for the considered case is shown in Fig. 1(a), and quasi-static electric field record is shown in Fig. 1(b). Sudden beginning of radio emission should be noted. As it was shown earlier [10] this emission consists of a series of short bi-polar pulses up to the return stroke. Several stretched out time 1 ms scans of radio emission are pre-
A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
sented in Fig. 1(c), (d), (e) clearly showing its pulsed structure. Pulse amplitude does not show any growth from the very beginning of the lightning discharge. First of all let us examine time dependence of lightning discharge radio frequency emission in more details. To characterize average intensity of the emission one can introduce two parameters: root mean square (rms) and median amplitudes. The ratio between these amplitudes can provide information about the character of radiation. Its obvious that for monochromatic signal this ratio should be equal to unity, while for rare pulses median amplitude should be close to zero independently from pulse amplitudes. For normal Gaussian noise rms/median amplitude ratio is about 1.5. Therefore the combined behaviour of rms and median amplitudes can serve as an indicator of pulse and continuous fractions of radio emission. Rms and median amplitudes taken on 100 μs intervals are shown in Fig. 2, and their ratio — in Fig. 3. Lightning discharge radio emission began at about 133.2 ms before the return stroke. It is clear from Fig. 3 that the rms/median amplitude ratio is close to 1.5 out of the discharge mentioned above. This means that background is a normal noise resulted from mixing of emission from a lot of radio stations. The last are clearly seen in the spectra of received background radio emission. It should be mentioned that comparison of actual values with theoretical estimations should be accomplished taking into account discrete character of the record and low level of the background signal.
1129
Discharge radio emission begins with radical enhancement of rms amplitude while median one remains approximately the same that means pulsed character of emission. This character remains the same with considerable variations of rms amplitude till about 30 ms before the return stroke. Rms amplitude variations can be explained by rather rare occurrence of pulses when only few pulses fall into each 100 μs interval. As from about 30 ms before the return stroke median amplitude shows a steady excess above its background magnitude, and it continuously increases started in 10 ms before the return stroke. At the same time variations of rms amplitude becomes less while its (rms amplitude) maximum magnitude remains approximately the same as in the previous period. Such behavior can be caused by the appearance of quasi-continuous component of radiation on the one hand, and more frequent occurrence of pulses on the other. At the return stroke that actually lasted about 150 μs, both radio emission averaged amplitudes (rms and median) grow up by one order approximately, and their ratio falls to about 2 that indicates the presence of both pulsed and continuous components of comparable intensity. 3. Pulsed component structure Let us analyse now pulsed component of lightning discharge radio emission. We will consider pulses with amplitudes large enough to prevent occasional missing low amplitude pulses on the noise background. In terms of input voltage we choose pulses
Fig. 1. Radio emission (a) and quasi-static electric field (b) temporal behaviour during the lightning discharge. Several stretched out one millisecond time scans of radio emission — (c) at the very beginning of the emission, (d) in the middle of the discharge, (e) at the return stroke.
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Fig. 1. (continued)
with amplitude exceeded 20 mV while rms background amplitude is about 2 mV with standard deviation of the same order. In the whole discharge we found 8373 pulses with amplitudes above 20 mV. Pulse amplitude distribution is shown in Fig. 4, and distribution of interpulse intervals — in Fig. 5. Both distributions were obtained over the whole discharge. The last distribution seems to be a sum of two (or more) logarithmic distributions with different time scales that could be caused by mixing of different distributions at different stages of discharge development. Let us remind
that logarithmic distribution of interpulse intervals indicates independence of pulses in the series. Pulse length (actually a length of the first part of bi-polar pulse calculated using parabolic approximation around its maximum at the half-maximum level) distribution obtained over the whole discharge is shown in Fig. 6. The length of the main part of pulses lies between 40 and 150 ns, and there is no pulses with lengths less than 30 ns (temporal resolution of our measurements was about 16 ns that guaranteed detection of such pulses if they are in the emission).
A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
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Fig. 2. Root mean square (top) and median (bottom) amplitudes of lightning radio emission in 100 μs intervals.
Fig. 3. Ratio of RMS to median amplitude in 100 μs intervals.
Consider now temporal behaviour of pulse rate counting pulses in 1 ms intervals. The result is shown in Fig. 7. Pulse rate is approximately 40 1/ms during about 50 ms from the discharge radio emission beginning, then it is slightly reducing coming back to the previous level to 30 ms before the return stroke. Next
10 ms it grows to 120 1/ms remaining the same about 10 ms after that. About 10 ms before the return stroke pulse rate begins to grow rapidly reaching about 300 1/ms. At the last millisecond before the return stroke it falls abruptly. At the same time the mean amplitude of pulses varies weakly all the time till
1132
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Fig. 4. Pulse amplitude distribution over the whole discharge (for pulses with amplitude exceeded 20 mV).
Fig. 5. Interpulse interval distribution over the whole discharge (for pulses with amplitude exceeded 20 mV).
Fig. 6. Pulse length distribution over the whole discharge (for pulses with amplitude exceeded 20 mV).
A.V. Gurevich, A.N. Karashtin / Physics Letters A 375 (2011) 1128–1134
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Fig. 7. Temporal behaviour of pulse rate during the discharge.
Fig. 8. Pulse amplitude distributions at different stages of discharge development.
10 ms before the return stroke significantly falling to the return stroke. We can distinguish 5 characteristic time intervals based on the time dependence of pulse amplitude and rate: (I) −132 to −87 ms, (II) −82 to −42 ms, (III) −27 to −17 ms, (IV) −12 to −7 ms, and (V) −7 to −2 ms regarding to the return stroke. Pulse emission parameter varies weakly at each interval. Examine now pulse characteristics independently at each interval. Pulse amplitude distributions are shown in Fig. 8. At three first intervals they are practically the same while at the forth one can mark some deficit of high amplitude pulses that becomes distinct at the last interval immediately before the return stroke. Distributions of interpulse intervals are shown in Fig. 9. All these distributions are close to logarithmic, but have different characteristic time: it is approximately the same at first two intervals and then decreases considerably with discharge development. Logarithmic law of distributions indicates independence of pulse occurrence. Pulse length (first part of bi-polar pulse) distributions are shown in Fig. 10. Again, at first two intervals they are practically the same varying at later intervals. Characteristic length of the pulses decreases from about 75 ns at intervals I, II to about 55 ns at interval V. At the same time distribution becomes more narrow with discharge development due to lessening of longer pulses.
4. Conclusion Let us summarize the main results as follows. 1. The radio emission during the preconditioning and initiating stages of the cloud-to-ground lightning consists of a large number (several thousands) radio pulses. 2. The characteristic growth time of the radio pulse is less than 100 ns. The full time is few hundred ns. 3. The pulses are random and independent. 4. The pulses have random amplitude. The pulse amplitude distribution is falling with amplitude growth. 5. The time interval between pulses is random. The average interval in the preliminary (I and II period) part of discharge is about 30–40 μs, close to the return stroke it is rapidly diminishing up to 10–3 μs. 6. The larger is the pulse amplitude the wider is the time interval between pulses. Note the significant difference in the pulse behavior at the preliminary (I and II period) and concluding (III–V periods) parts of the discharge. At the first two periods the radio emission characteristics have no considerable differences except of some diminution of pulse amplitude and frequency of occurrence at II period.
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Fig. 9. Interpulse interval distributions at different stages of discharge development.
Fig. 10. Pulse length (first part of bi-polar pulse) distributions at different stages of discharge development.
Characteristics of radio emission at subsequent intervals in the concluding part are varying significantly in the following manner.
• Intensity of lightning HF radio emission varies insignificantly except of return stroke.
• Relative part of continuous component increases during lightning discharge development.
• Pulse amplitude distribution becomes more narrow at the expense of large amplitude pulses.
• Pulse rate grows significantly. • Interpulse period distributions are logarithmic at all intervals, characteristic time of distributions decreases in accordance to pulse rate growing. • Characteristic length of first part of bi-polar pulses decreases notably, and its distribution narrows at the expense of longer pulses.
References [1] C.T. Rhodes, X.M. Shao, P.R. Krehbiel, R.J. Thomas, C.O. Hayenga, J. Geophys. Res. 99 (1994) 13059. [2] X. Shao, P. Krehbiel, J. Geophys. Res. 101 (1996) 26641. [3] W. Rison, R.J. Thomas, P.R. Krehbiel, T. Hamlin, J. Harlin, Geophys. Res. Lett. 26 (1999) 3573. [4] V. Mazur, P. Krehbiel, X.-M. Shao, J. Geophys. Res. 100 (1995) 25731. [5] T.C. Marshall, M. Stolzenburg, C.R. Maggio, L.M. Coleman, P.R. Krehbiel, T. Hamlin, R.J. Thomas, W. Rison, Geophys. Res. Lett. 32 (2005) L03813. [6] M. Stolzenburg, T.C. Marshall, W.D. Rust, E. Bruning, D.R. MacGorman, T. Hamlin, Geophys. Res. Lett. 34 (2007) L04804. [7] S.A. Behnke, R.J. Thomas, P.R. Krehbiel, W. Rison, J. Geophys. Res. 110 (2005) D10207. [8] G.S. Zhang, Y.X. Zhao, X.S. Qie, T. Zhang, Y.H. Wang, C.P. Chen, Sci. China, Ser. D: Earth Sci. 51 (2008) 694. [9] A.V. Gurevich, L.M. Duncan, A.N. Karashtin, K.P. Zybin, Phys. Lett. A 312 (2003) 228. [10] A.N. Karashtin, Y.V. Shlyugaev, A.V. Gurevich, Radiophys. Quantum Electron. 48 (2005) 711.