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 j + 0 5= H n-0 5 +

Size: px

Start display at page:

Download "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 +"

连麴
7 years ago
Views:

1 JOURNAL OF NANJING NORMAL UNIVERSITYNatural Science Edition Vol 35 No 3 Sept FDTD TL LEMP TM863 A 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 yinjie@ njupt edu cn 43

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

2 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 j + 0 5= H n Δt μ 0 Δr E n i + j zz En z i j Δt μ 0 Δz E n r i j + - E n r i j E n+ ε - σδt z i j + 0 5= ε + σδt En z i j Δt ε + σδtδ r [ r i +0 5 H n+0 5 r i 5 i j r i -0 5 H n+0 5 r i E n+ ε - σδt Δt r i j= ε + σδt En r i j H n+0 5 i j E z E n+ ε - σδt z 0 j + 0 5= ε + σδt En z 0 j E n+ ε - σδt z 0 j + 0 5= ε + σδt En z 0 j 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 j ] j i j j Δt πεδr I0 j 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

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 +

3 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 = 0 ka α = 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 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

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

4 A5 A50 B50 B00 0C75 C50 m TL 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 = 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

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

5 Bruce C EGolde R H The lightning discharge J J Inst Elect Pt Rakov V A Uman M A Review and evaluation of lightning return stroke models including some aspects of their application J IEEE Trans Electromag Compat Baba YRakov V A On the transmission lines model for lightning return stroke representantion J Geophydical Recearch Letters doi0 09 /003GL Marcos Rubinstein An approximate formula for the calculation of the horizontal electric field from lightning at close intermediateand long range J IEEE Trans Electromag Compat Moini RKordi BRaif G Zet al A new lightning return stroke model based on antenna theory J J Geophys Res D ( 上接第 4 页 ) κ LL < Casati GChirikov B VFord Jet al Stochastic behavior of a quantum pendulum under periodic perturbation J Lect Notes Phys Wintgen DMarxer H Level statistics of a quantized cantori system J Phys Rev Lett Kilbane DCummings AO Sullivan Get al Quantum statistics of a kicked particle in an infinite potential well J ChaosSolitons and Fractals Heller E JO Connor P WGehlen J The eigenfunctions of classical chaostic systems J Physica Scripta J Izrailev F M Simple models of quantum chaosspectrum and eigenfunctions J Phys Rep Casti GChirikov B VGuarneri I Energy-level statistics of integrable quantum systems J Phys Rev Lett Honig AWintgen D Spectral properties of strongly perturbed Coulomb systemsfluctuation properties J Phys Rev A J

4Marcos Rubinstein An approximate formula for the calculation of the horizontal electric field from lightning at close intermediateand long range J IEEE Trans Electromag Compat996383 53-535 5Moini

南京师大学报自然科学版第 35 卷第 3 期 0 年因有两个第一这是一个经典简并系统 KAM 定理的条件不满足文献上非 KAM 系统研究的很少第二由于该系统数值处理上较困难本征值本征态能谱统计等方面的研究结果还没有看到过报导系统的经典动力学一维周期受击简谐振子系统的哈密顿量

南京师大学报自然科学版第 35 卷第 3 期 0 年因有两个第一这是一个经典简并系统 KAM 定理的条件不满足文献上非 KAM 系统研究的很少第二由于该系统数值处理上较困难本征值本征态能谱统计等方面的研究结果还没有看到过报导系统的经典动力学一维周期受击简谐振子系统的哈密顿量 35 3 0 9 JOURNA OF NANJING NORMA UNIVERITYNatural cience Edition Vol 35 No 3 ept 0 0046 κ Poisson κ = 30 κ = 0 3 6 0 6 < 0 > 0 κ = 0 3 Σ γ γ κ 043 A 00-466003-0037-06 Classical Dynamics and Quasi-Energy