Calculation of triggered lightning current and electromagnetic fields based on spectral diagnosis and finite-difference time-domain method

SUO Yuhang; SHEN Xiaozhi; QI Qi; ZHANG Huaming

doi:10.7498/aps.74.20250448

Abstract

The channel plasma characteristics of an artificially triggered lightning in Guangdong, China, are analyzed using slit-free spectroscopy technology. Based on spectral diagnostic methods, the maximum and minimum values of the triggered lightning channel current are determined to be about 30.9 kA and 25.6 kA (minimum), respectively, and the current is simulated using a modified transmission line model with linear current decay (MTLL). To investigate the electric field distribution, the finite-difference time-domain (FDTD) method and transmission line (TL) model are employed. At a distance of 58 m, assuming a return stroke velocity of 1.3 × 10⁸ m/s, the TL-predicted radiation electric field deviates from experimental electric field, but is very close to the FDTD-simulation of the vertical electric field. Moreover, the analyses of magnetic fields at 58 m, 90 m, and 1.6 km are compared using FDTD simulations, dipole approximation, and charge magnetic field limit (CMFL) estimation. The discrepancies between calculated value and experimental values appear at 58 m and 90 m, which may be due to the near-field interference and measurement limitation. However, they become small at 1.6 km. This work is helpful for the study of lightning electromagnetic field properties and spectral diagnosis.

Keywords:

artificially triggered lightning /
spectroscopic diagnostics /
finite-difference time-domain (FDTD) method /
channel current /
electromagnetic field

Authors and contacts

1.
School of Science and Engineering, Hebei University of Engineering, Handan 056038, China
2.
State Key Laboratory of Severe Weather Meteorological Science and Technology/CMA Key Laboratory of Lightning, Chinese Academy of Meteorological Sciences, Beijing 100081, China
3.
School of Physics and Materials Science, Tianjin Normal University, Tianjin 300387, China
4.
Shanxi Meteorological Disaster Prevention Technology Center, Taiyuan 030002, China

Corresponding author: SHEN Xiaozhi, shenxz@tjnu.edu.cn ; ZHANG Huaming, zhanghuaming980@163.com

Funds: Project supported by the Open Research Program of Key Laboratory of Lightning Protection, China Meteorological Administration (Grant Nos. 2024KELL-B012, 2022LASWB21) and the Lightning Observation Research Project of Wutai Mountain Cloud Physics Base, Shanxi Meteorological Bureau, China (Grant No. SXKZDDW20217103).

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References

[1]	An Y Y, Shen X Z, Yuan P, Wu Z W 2023 Appl. Phys. Lett. 133 17 Google Scholar
[2]	Cai L, Li J, Wang J G, Zhou M, Xu F, Li Q X 2020 IEEE Trans. Electromagn. Compat. 63 811
[3]	Dong C X, Yuan P, Cen J Y, Wang X J, Mu Y L 2016 Atmos. Res. 178 1 Google Scholar
[4]	Yuan Y M, Shen X Z, Wang H Y, Zhang H M, Zhang Y J, Wang C M, An Y Y, Su M L 2022 Phys. Lett. A 452 128445 Google Scholar
[5]	Zhang Q L, Qie X S, Wang Z H, Zhang T L, Yang J 2009 Radio Sci. 44 1 Google Scholar
[6]	Zhang Y J, Yang S J, Lu W T, Zheng D, Dong W S, Li B, Chen S D, Zhang Y, Chen L W 2014 Atmos. Res. 135 330
[7]	Cai L, Li J, Wang J G, Zhou M, Li Q X, Fan Y D 2021 High Volt. 6 337 Google Scholar
[8]	Yang J, Qie X S, Zhang G S, Wang H B 2008 Radio Sci. 43 1
[9]	Pokharel R K, Ishii M, Baba Y 2003 IEEE Trans. Electromagn. Compat. 45 651 Google Scholar
[10]	Shen X Z, Su M L, Zhang H M, Gao Z G, Xu Y, Wei F 2024 Phys. Plasmas 31 103508 Google Scholar
[11]	Rubenstein M, Rachidi F, Uman M A, Thottappillil R, Rakov V A Nucci C A 1995 J. Geophys. Ress D: Atmos. 100 8863 Google Scholar
[12]	Schoene J, Uman M A, Rakov V A, Kodali V, Rambo K J, Schnetzer G H 2003 J. Geophys. Res. D: Atmos. 108(D6) 4192 Google Scholar
[13]	Li X, Lu G P, Fan Y F, Jiang R B, Zhang H B, Li D S, Liu M Y, Wang Y P, Ren H 2018 J. Geophys. Res. D: Atmos. 124 3168 Google Scholar
[14]	Yee K 1966 IEEE Trans. Antennas Propag. 14 302 Google Scholar
[15]	Cheng L, Zhu G X, Liu G N, Zhu L Q 2020 Mater. Res. Express 7 125009 Google Scholar
[16]	Piltyay S, Bulashenko A, Herhil Y, Bulashenko O 2021 IEEE 2nd International Conference on Advanced Trends in Information Theory Kyiv, Ukraine, November 25–27 2020, pp357–363
[17]	Su M L, Shen X Z, Wang H Y, Zhang H M, Yuan Y M, An Y Y 2023 Chem. Phys. Lett. 826 140664 Google Scholar
[18]	Shen X Z, Li J G, Jönsson P, Wang J G 2015 Astrophys. J. 801 129 Google Scholar
[19]	申晓志, 袁萍, 李冀光, 董晨钟, 颉录有, 师应龙 2007 物理学报 10 5715 Google Scholar Shen X Z, Yuan P, Li J G, Dong C Z, Ji L L, Shi Y L 2007 Acta Phys. Sin. 10 5715 Google Scholar
[20]	申晓志, 袁萍, 王杰, 郭逸潇, 乔红贞, 赵学燕 2008 物理学报 57 4066 Google Scholar Shen X Z, Yuan P, Wang J, Guo X Y, Qiao H Z, Zhao X Y 2008 Acta Phys. Sin. 57 4066 Google Scholar
[21]	Shen X Z, Yuan P, Liu J 2010 Chin. Phys. B 19 053101 Google Scholar
[22]	Shen X Z, Liu J, Zhou F Y 2016 Mon. Not. R. Astron. Soc. 462 1203 Google Scholar
[23]	Shen X Z, Liu J, Sang C C, Jönsson P 2018 Phys. Rev. A 97 012510 Google Scholar
[24]	Zhang X Y, Shen X Z, Yan P, Feng H 2020 Phys. Rev. A 102 042824 Google Scholar
[25]	邱德仁 2002 原子光谱分析(上海: 复旦大学出版社) 第63—64页 Qiu D R 2002 Atomic Spectrometry Analysis (Shanghai: Fudan University Press) pp63–64
[26]	Liu J, Shen X Z, Wang K, Sang C C 2020 J. Chem. Phys. 152 204303 Google Scholar
[27]	D’angola A, Colonna G, Gorse C, Capitell M 2011 Eur. Phys. J. D 65 453 Google Scholar
[28]	Devoto R S 1967 Phys. Fluids 10 2105 Google Scholar
[29]	D’angola A, Colonna G, Gorse C, Capitell M 2008 Eur. Phys. J. D 46 129 Google Scholar
[30]	Larsson A, Lalande P, Bondiou-Clergerie A, Lalande P, Delannoy A 2000 J. Phys. D: Appl. Phys. 33 1866 Google Scholar
[31]	马文蔚, 周雨清, 解希顺 2016 物理学教程(下册) (北京: 高等教育出版社) 第49页 Ma W W, Zhou Y Q, Xie X S 2016 A Course in Physics (Vol. 2) (Beijing: Higher Education Press) p49
[32]	Rakov V A 1998 J. Geophys. Res. D: Atmos. 103(D2) 1879
[33]	Yang C, Zhou B 2004 IEEE IEEE Trans. Electromagn. Compat. 46 133 Google Scholar
[34]	Rakov V A 1997 Proc. 12th Int. Zurich Symp. Electromagn. Compat Gainesville, FL, USA February 18–20, 1997 pp59–64
[35]	Bruce C E R, Golde R H 1941 J. Inst. Electr. Eng. -Part II: Power Eng. 88 487
[36]	Uman M A, McLain D K 1969 J. Geophys. Res. 74 6899 Google Scholar
[37]	Heidler F 1985 6th Symposium and Technical Exhibition on Electromagnetic Compatibility Zurich, Switzerland March 5–7, 1985 pp157–162
[38]	Diendorfer G, Uman M 1990 J. Geophys. Res. D: Atmos. 95 13621 Google Scholar
[39]	Shen X, Xu Y, Liu M, Zhang H M, Wang H Y 2025 J. Opt. Soc. Am. B: Opt. Phys. 42 773 Google Scholar
[40]	Rubinstein M, Uman M A 1989 IEEE Trans. Electromagn. Compat. 31 183 Google Scholar
[41]	Cai L, Hu Q, Wang J G, Zou X, Li Q X, Fan Y D 2021 J. Electrostat. 109 103537 Google Scholar
[42]	Wei F, Shen X Z, Yuan P, An T T, An Y Y, Su M L 2024 J. Opt. Soc. Am. B: Opt. Phys. 41 2033 Google Scholar
[43]	Kramida A, Ralchenko Y, Reader J, NIST ASD Team (2024) NIST Atomic Spectra Database (Ver. 5.12) [Online]. [2025, April 1]. National Institute of Standards and Technology, Gaithersburg, MD.
[44]	Qie X S, Zhang Q L, Zhou Y J, Feng G L, Zhang T L, Yang J, Kong X Z, Xiao Q F, Wu S J 2007 Sci. China Earth Sci. 50 1241 Google Scholar

Cited By

图 1 (a) 触发闪电测量装置示意图; (b) 触发闪电的实验场地; (c) 触发闪电通道示意图; (d) 数值计算模型. $\otimes $表示垂直指向纸上

Figure 1. (a) Schematic diagram of triggering lightning measurement device; (b) the experimental site; (c) schematic diagram of lightning channel; (d) numerical calculation model. $\otimes $: pointing vertically towards the paper.

DownLoad: Full-Size Img PowerPoint

图 2 2022年7月5日在中国广东拍摄的某次触发闪电的光谱　(a) 触发闪电通道和衍射光谱; (b) 为触发闪电的分析光谱

Figure 2. The spectrum of a triggered lightning captured on July 5th, 2022 in Guangdong, China: (a) Trigger lightning channel and its diffraction spectra; (b) spectral analysis for triggering lightning.

DownLoad: Full-Size Img PowerPoint

图 3 电流测量过程. X, Y, Z轴对应于电导率、通道半径、电流. 通道半径和电导率的交点位置对应的电流即为测量电流. Exp.Shen 2024引自文献[9]

Figure 3. Measurement process of Current. X, Y and Z axes correspond to electron conductivity, channel radius, and current. The current corresponding to the intersection of channel radius and electron conductivity is the measured current. Exp. Shen 2024 cites from Ref.[9].

DownLoad: Full-Size Img PowerPoint

图 4 MTLL电流模拟. F190611124401和Flash063002为两次实验电流. Exp.Cai引自文献[2,41]

Figure 4. MTLL numerical simulation. F190611124401 and Flash063002 are two measurements. Exp. Cai cites from Ref. [2,41]

DownLoad: Full-Size Img PowerPoint

图 5 (a), (b) FDTD模拟电场与实验电场对比; (c) $ {E}_{r} $分布; (d)电场对比. Exp.Cai 2021引自文献[41]

Figure 5. (a), (b) Comparison between FDTD simulated electric field and the experimental electric field; (c) E_r distribution; (d) electric field comparison. Exp. Cai 2021 quoted from Ref. [41].

DownLoad: Full-Size Img PowerPoint

图 6 (a), (b), (c) FDTD模拟磁场、偶极子方法计算磁场、电荷-磁场、实验磁场; (d) 磁场数据. Exp.Cai 2020引自文献[2]

Figure 6. (a), (b), (c) FDTD simulation of magnetic field, dipole method for calculating magnetic field, charge magnetic field, and (d) experimental magnetic field. Exp. Cai 2020 cited from reference [2].

DownLoad: Full-Size Img PowerPoint

表 2 基于实验电流得到的传输线模型和FDTD模拟的电场

Table 2. The electric fields for the transmission line model and FDTD simulation based on experimental currents.

	峰值电流/kA		距离/m	电场/(kV·m^–1)
类型	$i_{\text{p}}^{{\text{min}}}$	$i_{\text{p}}^{{\text{max}}}$	D	TL model		FDTD
类型	$i_{\text{p}}^{{\text{min}}}$	$i_{\text{p}}^{{\text{max}}}$	D	E_rad (v₁)^c	E_rad (v₂)^c	E_z	E_r
本文工作	25.6	30.9	38	18.2—21.9	33.6—40.7
			58	11.9—14.4	22.0—26.7	10.1—12.0	0.9—1.0
			78	8.8—10.7	16.4—19.8
			90	7.7—9.2	14.2—17.2
			102	6.7—8.2	12.5—15.1
			1000	0.4—0.7	1.3—1.5
			1600	0.4—0.5	0.8—0.9
			2200	0.3—0.4	0.6—0.7
Cai 2021^a	12.0	23.6	58	12.6—35.7
Qie 2007^b	11.9		60	18.0
注: ^{a, b} 引自文献[41]与[44]. ^c $v_1= 1.3\times10^8 $ m/s; ^d $v_2= 2.5\times10^8 $ m/s.

DownLoad: CSV

表 1 触发闪电特征谱线的光谱参数^[43]

Table 1. Spectral parameters of characteristic spectral lines for triggered lightning^[43].

	波长/nm	跃迁率	$ {E}_{k}/{{\mathrm{c}}{\mathrm{m}}}^{-1} $	谱线跃迁
	波长/nm	跃迁率	$ {E}_{k}/{{\mathrm{c}}{\mathrm{m}}}^{-1} $	上能级	下能级
N I	493.5	1.76×10⁶	106477	2s²2p²(³P)4p $\rm{}^2P^\circ_{1/2}$	2s²2p²(³P)3s ²P_3/2
N I	528.1	2.45×10⁵	107037	2s²2p²(³P)4p $\rm {}^4P^\circ_{1/2} $	2s2p⁴ ⁴P_5/2
N II	417.6	1.21×10⁸	210732	2s²2p4f F(5/2)₃	2s²2p3d $\rm{}^1D^\circ_2 $
N II	447.8	6.44×10⁶	188909	2s²2p3d $\rm{}^3P^\circ_1 $	2s²2p3d $\rm{}^1D^\circ_2 $
N II	498.7	6.98×10⁷	188937	2s²2p3d $\rm{}^3P^\circ_0 $	2s²2p3p ³S₁
N II	524.1	6.2×10⁵	221246	2s²2p5d $\rm{}^1P^\circ_1 $	2s²2p4p ¹P₁
N II	568.0	1.78×10⁷	166521	2s²2p3p ³D₁	2s²2p3s $\rm{}^3P^\circ_2 $

DownLoad: CSV

表 3 FDTD模拟、偶极子方法和电荷-磁场极限估算得到的磁场

Table 3. Magnetic field obtained from FDTD simulation, dipole method, and charge-magnetic field limit estimation.

	实验峰值电流/kA		距离/m	磁场/μT
类型	$i_{\text{p}}^{{\text{min}}}$	$i_{\text{p}}^{{\text{max}}}$	D	FDTD	偶极子方法	B_Q 估算
本文工作	25.6	30.9	38			95.3—115.3
			58	82.6—98.5	69.8—84.3	62.4—75.5
			78			46.4—56.2
			90	68.1—77.0	44.6—53.8	40.2—48.7
			102			35.5—42.9
			1000			3.6—4.4
			1600	2.3—2.8	2.3—2.7	2.3—2.8
			2200			1.6—2.0
实验测量
Cai^[2]	13.0		58	137.8
			90	84.9
			1600	1.4
Qie^[8]	28.1		60	66.3

DownLoad: CSV

[1]	An Y Y, Shen X Z, Yuan P, Wu Z W 2023 Appl. Phys. Lett. 133 17 Google Scholar
[2]	Cai L, Li J, Wang J G, Zhou M, Xu F, Li Q X 2020 IEEE Trans. Electromagn. Compat. 63 811
[3]	Dong C X, Yuan P, Cen J Y, Wang X J, Mu Y L 2016 Atmos. Res. 178 1 Google Scholar
[4]	Yuan Y M, Shen X Z, Wang H Y, Zhang H M, Zhang Y J, Wang C M, An Y Y, Su M L 2022 Phys. Lett. A 452 128445 Google Scholar
[5]	Zhang Q L, Qie X S, Wang Z H, Zhang T L, Yang J 2009 Radio Sci. 44 1 Google Scholar
[6]	Zhang Y J, Yang S J, Lu W T, Zheng D, Dong W S, Li B, Chen S D, Zhang Y, Chen L W 2014 Atmos. Res. 135 330
[7]	Cai L, Li J, Wang J G, Zhou M, Li Q X, Fan Y D 2021 High Volt. 6 337 Google Scholar
[8]	Yang J, Qie X S, Zhang G S, Wang H B 2008 Radio Sci. 43 1
[9]	Pokharel R K, Ishii M, Baba Y 2003 IEEE Trans. Electromagn. Compat. 45 651 Google Scholar
[10]	Shen X Z, Su M L, Zhang H M, Gao Z G, Xu Y, Wei F 2024 Phys. Plasmas 31 103508 Google Scholar
[11]	Rubenstein M, Rachidi F, Uman M A, Thottappillil R, Rakov V A Nucci C A 1995 J. Geophys. Ress D: Atmos. 100 8863 Google Scholar
[12]	Schoene J, Uman M A, Rakov V A, Kodali V, Rambo K J, Schnetzer G H 2003 J. Geophys. Res. D: Atmos. 108(D6) 4192 Google Scholar
[13]	Li X, Lu G P, Fan Y F, Jiang R B, Zhang H B, Li D S, Liu M Y, Wang Y P, Ren H 2018 J. Geophys. Res. D: Atmos. 124 3168 Google Scholar
[14]	Yee K 1966 IEEE Trans. Antennas Propag. 14 302 Google Scholar
[15]	Cheng L, Zhu G X, Liu G N, Zhu L Q 2020 Mater. Res. Express 7 125009 Google Scholar
[16]	Piltyay S, Bulashenko A, Herhil Y, Bulashenko O 2021 IEEE 2nd International Conference on Advanced Trends in Information Theory Kyiv, Ukraine, November 25–27 2020, pp357–363
[17]	Su M L, Shen X Z, Wang H Y, Zhang H M, Yuan Y M, An Y Y 2023 Chem. Phys. Lett. 826 140664 Google Scholar
[18]	Shen X Z, Li J G, Jönsson P, Wang J G 2015 Astrophys. J. 801 129 Google Scholar
[19]	申晓志, 袁萍, 李冀光, 董晨钟, 颉录有, 师应龙 2007 物理学报 10 5715 Google Scholar Shen X Z, Yuan P, Li J G, Dong C Z, Ji L L, Shi Y L 2007 Acta Phys. Sin. 10 5715 Google Scholar
[20]	申晓志, 袁萍, 王杰, 郭逸潇, 乔红贞, 赵学燕 2008 物理学报 57 4066 Google Scholar Shen X Z, Yuan P, Wang J, Guo X Y, Qiao H Z, Zhao X Y 2008 Acta Phys. Sin. 57 4066 Google Scholar
[21]	Shen X Z, Yuan P, Liu J 2010 Chin. Phys. B 19 053101 Google Scholar
[22]	Shen X Z, Liu J, Zhou F Y 2016 Mon. Not. R. Astron. Soc. 462 1203 Google Scholar
[23]	Shen X Z, Liu J, Sang C C, Jönsson P 2018 Phys. Rev. A 97 012510 Google Scholar
[24]	Zhang X Y, Shen X Z, Yan P, Feng H 2020 Phys. Rev. A 102 042824 Google Scholar
[25]	邱德仁 2002 原子光谱分析(上海: 复旦大学出版社) 第63—64页 Qiu D R 2002 Atomic Spectrometry Analysis (Shanghai: Fudan University Press) pp63–64
[26]	Liu J, Shen X Z, Wang K, Sang C C 2020 J. Chem. Phys. 152 204303 Google Scholar
[27]	D’angola A, Colonna G, Gorse C, Capitell M 2011 Eur. Phys. J. D 65 453 Google Scholar
[28]	Devoto R S 1967 Phys. Fluids 10 2105 Google Scholar
[29]	D’angola A, Colonna G, Gorse C, Capitell M 2008 Eur. Phys. J. D 46 129 Google Scholar
[30]	Larsson A, Lalande P, Bondiou-Clergerie A, Lalande P, Delannoy A 2000 J. Phys. D: Appl. Phys. 33 1866 Google Scholar
[31]	马文蔚, 周雨清, 解希顺 2016 物理学教程(下册) (北京: 高等教育出版社) 第49页 Ma W W, Zhou Y Q, Xie X S 2016 A Course in Physics (Vol. 2) (Beijing: Higher Education Press) p49
[32]	Rakov V A 1998 J. Geophys. Res. D: Atmos. 103(D2) 1879
[33]	Yang C, Zhou B 2004 IEEE IEEE Trans. Electromagn. Compat. 46 133 Google Scholar
[34]	Rakov V A 1997 Proc. 12th Int. Zurich Symp. Electromagn. Compat Gainesville, FL, USA February 18–20, 1997 pp59–64
[35]	Bruce C E R, Golde R H 1941 J. Inst. Electr. Eng. -Part II: Power Eng. 88 487
[36]	Uman M A, McLain D K 1969 J. Geophys. Res. 74 6899 Google Scholar
[37]	Heidler F 1985 6th Symposium and Technical Exhibition on Electromagnetic Compatibility Zurich, Switzerland March 5–7, 1985 pp157–162
[38]	Diendorfer G, Uman M 1990 J. Geophys. Res. D: Atmos. 95 13621 Google Scholar
[39]	Shen X, Xu Y, Liu M, Zhang H M, Wang H Y 2025 J. Opt. Soc. Am. B: Opt. Phys. 42 773 Google Scholar
[40]	Rubinstein M, Uman M A 1989 IEEE Trans. Electromagn. Compat. 31 183 Google Scholar
[41]	Cai L, Hu Q, Wang J G, Zou X, Li Q X, Fan Y D 2021 J. Electrostat. 109 103537 Google Scholar
[42]	Wei F, Shen X Z, Yuan P, An T T, An Y Y, Su M L 2024 J. Opt. Soc. Am. B: Opt. Phys. 41 2033 Google Scholar
[43]	Kramida A, Ralchenko Y, Reader J, NIST ASD Team (2024) NIST Atomic Spectra Database (Ver. 5.12) [Online]. [2025, April 1]. National Institute of Standards and Technology, Gaithersburg, MD.
[44]	Qie X S, Zhang Q L, Zhou Y J, Feng G L, Zhang T L, Yang J, Kong X Z, Xiao Q F, Wu S J 2007 Sci. China Earth Sci. 50 1241 Google Scholar

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Vol. 74, Issue 14 - 2025-07-20

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