35 3 0 z TM Maxwell r - E r z - H z + E z r = ε E r t = μ H t rh = ε E z r t + σe z 3 + σe z 4 Fig ΔrΔz Δt Maxwell H n+0 5 i + 0 5 j + 0 5= H n-0 5 +

35 3 0 9 JOURNAL OF NANJING NORMAL UNIVERSITYNatural Science Edition Vol 35 No 3 Sept 0 0003 FDTD TL LEMP TM863 A 00-466003-0043-05 Comparison of Two Lightning Return Stroke Models Yin Jie College of ScienceNanjing University of Posts and CommunicationsNanjing 0003China AbstractTwo lightning return stroke models are usedand they are transmission line model TLand thin wires model This paper uses finite difference time-domain FDTDmethod to calculate the lightning channel current and lightning electromegnetic pulse The calculation of two models is discussed and tested with other author s resultsand some useful conclusions are obtained Key wordslightning electromegnetic pulsereturn stroke modelfdtd Lightning Lightning Electromagnetic Pulse LEMP LEMP LEMP 94 C E R Bruce R H Golde TL FDTD TL Uman Mclain t z' Iz' t t z' = 0 I0 t Iz' t= I0 t - z' /v f v f Maxwell 0-03-9 E-mailyinjie@ njupt edu cn 43

35 3 0 z TM Maxwell r - E r z - H z + E z r = ε E r t = μ H t rh = ε E z r t + σe z 3 + σe z 4 Fig ΔrΔz Δt Maxwell H n+0 5 i + 0 5 j + 0 5= H n-0 5 + Δt μ 0 Δr E n i + j + 0 5- zz En z i j + 0 5 - Δt μ 0 Δz E n r i + 0 5 j + - E n r i + 0 5 j E n+ ε - σδt z i j + 0 5= ε + σδt En z i j + 0 5+ Δt ε + σδtδ r [ r i +0 5 H n+0 5 r i 5 i + 0 5 j + 0 5- r i -0 5 H n+0 5 r i E n+ ε - σδt Δt r i + 0 5 j= ε + σδt En r i + 0 5 j H n+0 5 i + 0 5 j - 0 5 E z E n+ ε - σδt z 0 j + 0 5= ε + σδt En z 0 j + 0 5+ E n+ ε - σδt z 0 j + 0 5= ε + σδt En z 0 j + 0 5+ ε + σδtδz Hn+0 5 图 8Δt ε + σδtδr Hn+0 5 8Δt ε + σδtδr Hn+0 5 z 轴 TL 模 型 雷 电 通 道 示 意 图 Configuration of lightning channel based on TL model i - 0 5 j + 0 5 ] 6 0 5 j + 0 5- i + 0 5 j + 0 5-0 5 j + 0 5 7 8 4Δt πεδr I0 j + 0 5 Mur Δt Courant 图 细 导 线 模 型 雷 电 通 道 示 意 图 r Fig Configuration of lightning channel based on thin wire model 9 Δt minδr Δz 0 c z 轴 TL TL Maxwell TL CP /r 44 z Maxwell

H n+ j + = H n- j + - Δt μ 0 Δz Δt ( μ 0 Δz ) ( lnδr /r 0 ) En z [ ] E n z j + - E n z j + r 0 E r E z FDTD FDTD 3 4 3 4 4 3 = 0 ka α = 3 0 4 s - β = 0 7 s - = 0 8 m /s I 0 i0 t= I 0 e -αt - e -βt v f TL 00 m 6 m 4 σ = 0 - s /m ε r = 0 3 i0 t= exp - β t - [ τ0 ] 3 τ β = 5= 00 ns τ 0 0 图 3 文 献 [4] 中 的 通 道 底 部 电 流 波 形 Fig3 Waveform of channel base current, the same as Nucci, et al [4] 图 4 Fig4 Er/(V/m) TL 模 型 计 算 距 雷 电 通 道 00 m 地 面 上 6 m 处 水 平 电 场 波 形 Waveform of horizontal electric field at a distance of 50 m and a height of 6 m above ground based on TL model 3 5 6 Ez/(kV/m) 图 5 细 导 线 模 型 计 算 的 雷 电 通 道 中 的 电 流 波 形 Fig5 Waveforms of lightning channel current based on thin wire model Fig6 图 6 细 导 线 模 型 计 算 的 通 道 周 围 的 垂 直 电 场 波 形 Waveforms of vertical electric fields around lighting channel based on thin wire model 45

35 3 0 6 A5 A50 B50 B00 0C75 C50 m TL 3 4 3 TL Heidler Fig7 图 7(a) i0 t= I 0 TL 模 型 雷 电 通 道 中 的 电 流 波 形 Waveforms of current at different heights based on TL model I 0 = 3 5 ka I 0 = 8 95 ka τ = t τ e - t τ + I 0 ( e - t τ3 - e - t τ4 ) 4 t + τ Fig7 Ez/(V/m) 图 7(b) 细 导 线 模 型 雷 电 通 道 中 的 电 流 波 形 Waveforms of current at different heights based on thin wire model 0 07 us τ = 6 67 us τ 3 = 00 us τ 4 = 0 5 us v f = 5 0 8 m /s σ = 0 - s /m ε r = 0 Δz = Δr = 0 5 m Δt = Δz c r 0 = 5 cm FDTD 7a 7b 50 m 00 m E z 8 r=50 m 实 线 :TL 模 型 虚 线 : 细 导 线 模 型 r=00 m TL 7a 图 8 两 种 模 型 在 地 面 同 一 点 的 垂 直 电 场 波 形 7b Fig8 Waveforms of vertical electric fields at ground 8 TL 46

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