Physical Mechanism of Initial Breakdown Pulses in Lightning Discharges

Talk presented at 2014 AGU Fall Meeting, San Francisco, CA, December, 2014

Transcript

1. Introduction Model Formulation Results Summary Physical Mechanism of Initial Breakdown Pulses in Lightning Discharges Caitano L. da Silva and Victor P. Pasko Communications and Space Sciences Laboratory Department of Electrical Engineering Penn State University University Park, PA 16802, USA AGU Fall Meeting San Francisco, CA, USA 15 – 19 December 2014 C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 1 / 19
2. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 1 / 19
3. Introduction Model Formulation Results Summary Preliminary Breakdown Stage [e.g., Karunarathne et al., JGR, 119, 14, 2014] C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 2 / 19
4. Introduction Model Formulation Results Summary Initial Breakdown Pulses (IBPs) [e.g., Karunarathne et al., JGR, 119, 14, 2014] E-change (V/m) E-change (V/m) (a) (b) (c) (d) C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 3 / 19
5. Introduction Model Formulation Results Summary Narrow Bipolar Events (NBEs) [e.g., Eack, GRL, 31, 20, 2004] (a) (b) C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 4 / 19
6. Introduction Model Formulation Results Summary Previous Modeling Efforts Transmission Line (TL) Models Runaway Electron Avalanches Seeded by Cosmic Ray Extensive Air Showers (RREA–EAS) I(z, t) = f (z) I h1 , t − z−h1 v Pros Reproduce a wide range of observed sig- natures and allow one to retrieve source parameters Propose a physical origin to the NBE source Cons Do not explain the physical origin of the channel or the injected current pulse Require unrealistically large (1) energy for the initial cosmic ray and (2) strong thunderstorm electric fields References [e.g., Watson and Marshall, GRL, 34(4), L04816, 2007; Nag and Rakov, JGR, 115, D20102, 2010; Karunarathne et al., JGR, 119, 14, 2014] [e.g., Gurevich et al., PLA, 254, 1-2, 2002; Tierney et al., JGR, 110, D12109, 2005; Arabshahi et al., JGR, 119, 1, 2014] C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 5 / 19
7. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 5 / 19
8. Introduction Model Formulation Results Summary Pulse Types and Source Locations in the Thundercloud Region Type IBPs in +ICs IBPs in –CGs Polarity +NBEs –NBEs –18 C +57 C –50 C +11 C E- eld threshold −6 −4 −2 0 2 4 6 0 2 4 6 8 10 12 14 16 −150 −100 −50 0 50 100 150 IBPs [Karunarathne et al., JGR, 118, 13, 2013; Marshall et al., JGR, 118, 19, 2013]. NBEs [Smith et al., RS, 39(1), RS1010, 2004; Wu et al., JGR, 117, D05119, 2012]. C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 6 / 19
9. Introduction Model Formulation Results Summary Physical Mechanism of IBP and NBE Sources (a) Electric Potential (b) Linear Charge Density (c) Problem Geometry Eamb Ground z 0 step U(z) Stage 1: Before Stepping Stage 2: After Stepping Range of likely values G0 (S·m) 0 (m) τstep (µs) step (m) 0.01–1 200–2000 1–100 50–1500 C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 7 / 19
10. Introduction Model Formulation Results Summary Model of Charges and Currents in the Developing Lightning Leader                            U(z, t) = Uamb (z) + 1 4πε h2 h1 q(z , t ) R(z, z ) dz A(z, t) = µ 4π h2 h1 I(z , t ) R(z, z ) dz ∂A ∂t + ∂U ∂z + I G = 0 ∂q ∂t + ∂I ∂z = 0 R(z, z ) = (z − z )2 + a2 and t = t − R(z, z )/c. ε = 5.3ε0 and µ = µ0 [Moini et al., JGR, 105, D24, 2000]. Equations are solved with method of moments applied to time-domain antenna theory [e.g., Miller et al., JCP, 12(1), 24, 1973; Carlson et al., JGR, 115, A10324, 2010]. Region of Uniform Charge Density Numerical Discretization i − 1 i i + 1 ∆z qi , zq,i , Ui Ii , zI,i , Ei z C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 8 / 19
11. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 8 / 19
12. Introduction Model Formulation Results Summary Dynamics of Charges and Currents in the IBP Source −100 −50 0 5 5.5 6 6.5 −2 −1 0 1 2 5 5.5 6 6.5 0 10 20 30 5 5.5 6 6.5 0 0.2 0.4 0.6 0.8 5 5.5 6 6.5 (a) (b) (c) (d) Parameters to match observation by Karunarathne et al. [2014] Event Label IBP-4 h0 (km) 6 G0 (S·m) 0.85 0 (m) 700 τstep (µs) 28 step (m) 480 C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 9 / 19
13. Introduction Model Formulation Results Summary Dynamics of Source Currents and Comparison to Previous Work 0 20 40 60 5 5.5 6 6.5 0 20 40 60 5 5.5 6 6.5 0 10 20 30 40 This work Karunarathne et al. [2014] (a) (b) Dashed lines show the conductor’s length, emphasizing the stepping at t = 0 in panel (a). C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 10 / 19
14. Introduction Model Formulation Results Summary Dynamics of Source Currents and Comparison to Previous Work 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 0 20 40 5 5.5 6 6.5 (a) (d) (c) (b) (e) (h) (g) (f) This work Karunarathne et al. [2014] C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 11 / 19
15. Introduction Model Formulation Results Summary Simulation of IBP Waveforms [Karunarathne et al., JGR, 119, 14, 2014] E-change (V/m) E-change (V/m) (a) (b) (c) (d) C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 12 / 19
16. Introduction Model Formulation Results Summary Simulation of IBP Waveforms −40 −20 0 20 40 −50 −40 −30 −20 −10 0 10 20 30 20 40 60 80 100 −30 −20 −10 0 10 20 120 140 160 180 200 −15 −10 −5 0 5 10 160 180 200 220 240 −10 −5 0 5 10 (a) (b) (c) (d) Parameters to match observation by Karunarathne et al. [2014] Event Label IBP-4 h0 (km) 6 G0 (S·m) 0.85 0 (m) 700 τstep (µs) 28 step (m) 480 C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 13 / 19
17. Introduction Model Formulation Results Summary Simulation of NBE Waveforms [Watson and Marshall, GRL, 34(4), L04816, 2007] (a) (b) C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 14 / 19
18. Introduction Model Formulation Results Summary Simulation of NBE Waveforms −60 −40 −20 0 20 40 60 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 −60 −40 −20 0 20 40 60 −4 −2 0 2 4 6 8 10 (a) (b) Observation h0 (km) G0 (S·m) 0 (m) τstep (µs) step (m) Eack [2004] 7.2 0.65 830 17 800 C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 15 / 19
19. Introduction Model Formulation Results Summary Effects of Leader Properties on IBP/NBE Waveforms −20 0 20 40 60 0 −20 0 20 40 60 −10 0 10 20 30 40 (a) Case 1 (b) Label h0 (km) G0 (S·m) 0 (m) τstep (µs) step (m) Case 1 8 0.65 800 8 50–1500 Case 2 8 0.65 800 16 50–1500 Case 3 8 0.65 1600 16 50–1500 C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 16 / 19
20. Introduction Model Formulation Results Summary Effects of Leader Properties on NBE Waveform Parameters 50 500 1000 1500 0 10 20 30 40 50 500 1000 1500 0 2 4 6 8 10 50 500 1000 1500 0 5 10 15 50 500 1000 1500 10 20 30 40 50 60 Case 1 Case 3 Case 2 (a) (b) (c) (d) Shaded bands are average ± one standard deviation as measured by Nag et al. [JGR, 115, D14115, 2010]. C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 17 / 19
21. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 17 / 19
22. Introduction Model Formulation Results Summary Summary We propose that IBPs and NBEs are generated by the same processes inside the thundercloud. IBPs and NBEs are the electromagnetic response to a sudden elongation (or stepping) of the negative leader tip during the initial stages of the bidirectional lightning leader tree development. We have developed a model to retrieve the full dynamics of charges and currents in the bidirectional lightning leader (and demonstrate the above hypothesis). IBP and NBE pulse amplitudes and durations are directly related to step length. C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 18 / 19
23. Introduction Model Formulation Results Summary Thank you for your attention! Acknowledgments This research was supported by NSF AGS-1332199 grant to Pennsylvania State University. Contact C. L. da Silva and V. P. Pasko, Communications and Space Sciences Laboratory, Department of Electrical Engineering, Pennsylvania State University, 227 EE East, University Park, PA 16802-2706, USA (caitano.dasilva@psu.edu; vpasko@psu.edu). C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 19 / 19
24. Discussion Qualitative dependence of electric field amplitude on leader parameters. Charge Moment Change: ∆MQ ∝ 0 step Eamb [Pasko, GRL, 41, 179, 2014] Current Moment: MI ≈ ∆MQ τstep Radiation Field: E1 ∝ − 1 D ∂MI ∂t ≈ − 1 D MI τstep            |E1 | ∝ 0 step|Eamb| Dτ2 step C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 1 / 3
25. Comparison of Current Moment Simulation of an IBP Source 0 20 40 60 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 (a) 0 20 40 60 −5 0 5 10 15 20 25 30 (b) 0 20 40 60 −0.02 −0.015 −0.01 −0.005 0 0.005 0.01 0.015 0.02 This work Karunarathne et al. [2014] (c) C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 2 / 3
26. Comparison of Current Moment Simulation of a NBE Source 0 20 40 60 80 −0.7 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 (a) 0 20 40 60 80 −45 −40 −35 −30 −25 −20 −15 −10 −5 0 (b) 0 20 40 60 80 −6 −5 −4 −3 −2 −1 0 1 2 This work Watson and Marshall [2007] (c) C. L. da Silva and V. P. Pasko Mechanism of IBPs and NBEs 3 / 3