Streamer-to-Leader Transition in Gigantic Jets

Talk presented at 2nd TEA-IS Summer School, Collioure, France, June, 2014

Transcript

1. Introduction Model Formulation Results Summary Streamer-to-Leader Transition in Gigantic Jets 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 2nd TEA-IS Summer School Collioure, France 23 – 27 June 2014 C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 1 / 17
2. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 2 / 17
3. Introduction Model Formulation Results Summary Upward Jets from Thundercloud Tops (a) Blue starter Edens [GRL, 38, L17804, 2011] Wescott et al. [JGR, 106, A10, 2001] Soula et al. [JGR, 116, D19103, 2011] (b) Blue jet (c) Gigantic jet C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 3 / 17
4. Introduction Model Formulation Results Summary Motivation: Observed Acceleration in Gigantic Jets • What happens to a lightning leader propagating through regions of lower and lower air density? What is the reason for the observed acceleration in gigantic jets? Time (ms) Altitude (km) 50 100 150 200 250 20 30 40 50 60 70 80 90 Time (ms) Altitude (km) 80 100 120 140 160 180 20 30 40 50 60 70 80 90 (a) Pasko et al. [Nature, 416, 152, 2002] (b) Soula et al. [JGR, 116, D19103, 2011] 5.7x104 m/s ≥1.2x106 m/s 6.3x104 m/s ≥2.3x106 m/s Laboratory leaders: v ∼ 1–5×104 m/s [e.g., Andreev et al., PPR, 34, 7, 2008]. Lightning leaders: v ∼ 3–60×104 m/s [e.g., Saba et al., GRL, 35, L07802, 2008]. Laboratory streamers: v ∼ 1–40×105 m/s [e.g., Briels et al., JPD, 41, 23, 2008]. C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 4 / 17
5. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 5 / 17
6. Introduction Model Formulation Results Summary Schematics of Streamer-to-Leader Transition Region Streamer Zone Leader Channel Head or Stem e C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 6 / 17
7. Introduction Model Formulation Results Summary Model of Streamer-to-Leader Transition 1 Dynamics of neutral gas. Conservation of mass, momentum, and vibrational and translational energies. 2 Comprehensive plasma chemistry. Over 100 reactions including the most important processes in a gas discharge plasma. 3 Energy exchange between charged and neutral particles. Mechanism of fast air heating. 4 Delayed vibrational energy relaxation of nitrogen molecules. Vibrational-translational (VT) and vibrational-vibrational (VV) energy exchange. [da Silva and Pasko, JGR, 118, 13561, 2013] C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 7 / 17
8. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 8 / 17
9. Introduction Model Formulation Results Summary General Dynamics of Streamer-to-Leader Transition 10−9 10−8 10−7 10−6 10−5 103 104 Temperature (K) (d) 10−9 10−8 10−7 10−6 10−5 0 5 10 15 20 25 30 Electric Field (kV/cm) (e) 1010 1012 1014 1016 (b) 1011 1012 1013 1014 10−9 10−8 10−7 10−6 10−5 (f) 103 105 107 109 (c) (a) 0 1 2 3 4 5 6 I = const = 1 A, p = 1 atm. C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 9 / 17
10. Introduction Model Formulation Results Summary Radial Dynamics of the Channel ne (cm−3) −3 −2 −1 0 1 2 3 0 1 2 3 4 5 −3 −2 −1 0 1 2 3 0 0.5 1 1.5 2 0 0.5 1 1.5 2 2.5 3 3.5 4 −3 −2 −1 0 1 2 3 10 10 10 10 10 10 11 12 13 14 15 16 Hydrodynamic Expansion Lowering of Air Density Contraction of Current (a) (b) (c) C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 10 / 17
11. Introduction Model Formulation Results Summary Modeling of Leader Speeds vL (m/s) I (A) Model Popov [2009] Bazelyan and Raizer [1998] Andreev et al. [2008] 1 20 40 60 80 100 104 105 106 v L = ∆ls τh The size of the leader head is related to the length ∆ls of initial, still conducting, closely located streamer segments [Bazelyan et al., JPD, 40, 14, 2007]. C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 11 / 17
12. Introduction Model Formulation Results Summary Scaling of Streamer-to-Leader Transition Time τh and Leader Speed vL with Altitude Expansion Cooling 10−8 10−6 10−4 10−2 100 0 10 20 30 40 50 60 h (km) h (km) Time Scales (s) 1 2 3 5 10 20 40 (a) (b) 1 2 3 5 10 20 40 100 = 100 A ∆ls τc ∆ls τκT τh vL 103 104 105 106 107 0 10 20 30 40 50 60 Speed (m/s) Near ground pressure τh ∼ N−2 amb and deviation occurs for τh > τc , where τc is the gas dynamics time scale. Transition does not occur for τh > τκT , where τκT is the heat conduction time scale. C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 12 / 17
13. Introduction Model Formulation Results Summary Conceptual Model of Gigantic Jet Propagation (a) (b) Leader Channel Head or Stem Streamer Zone 0            US = hS hL Ecr,0 e−h/hN dh = hN (Ecr,L − Ecr,S ) LS = hN ln 1 − US hN Ecr,L −1 → hjump = hN ln(hN Ecr,0 /UL ) [Raizer et al., GRL, 33, L23801, 2006; da Silva and Pasko, GRL, 40, 12, 2013] C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 13 / 17
14. Introduction Model Formulation Results Summary Vertical Structuring of Gigantic Jets 0 50 100 150 200 250 300 20 30 40 50 60 70 80 90 Time (ms) Altitude (km) 1 MV 10 MV, Positive 10 MV, Negative 30 MV 60 MV 120 MV (a) (b) 0 10 20 30 40 50 60 101 102 103 104 The observed acceleration cannot be associated to an increase in leader speed. Sufficiently high leader potential and current can allow the GJ to dynamically extend (jump) all the way to the ionosphere. C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 14 / 17
15. Introduction Model Formulation Results Summary Outline 1 Introduction 2 Model Formulation 3 Results 4 Summary C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 15 / 17
16. Introduction Model Formulation Results Summary Summary At near-ground pressures, the streamer-to-leader transition time scales with air density close to τh ∼ N−2 amb , making leader speeds nearly independent of altitude (for a given current). The maximum altitude at which a leader can be formed in Earth’s atmosphere is determined by the interplay of air heating and channel expansion/cooling rates. The observed acceleration in gigantic jets cannot be associated to the rate of streamer-to-leader transition at reduced air densities. It is quite the opposite! A simple time-dynamic model shows that this observed acceleration is a consequence of the expansion of the leader streamer zone. C. L. da Silva and V. P. Pasko Streamer-to-Leader Transition 16 / 17
17. Introduction Model Formulation Results Summary Thank you for your attention! Acknowledgments This research was supported by NSF AGS-0652148, AGS-0836391, and AGS-1332199 grants to Pennsylvania State University. Reference da Silva, C. L., and V. P. Pasko (2013), Dynamics of streamer-to-leader transition at reduced air densities and its implications for propagation of lightning leaders and gigantic jets, J. Geophys. Res., 118, 24, 13,561–13,590, doi:10.1002/2013JD020618. 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 Streamer-to-Leader Transition 17 / 17