## Radiation from a current filament driven by a traveling wave |

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1.5 km long 10t 9 Figure 10t 9 FREQUENCY 240 OBSERVER angle approximate solution behavior of exact center 4 km complete solution coplanar current element current filament driven current wave current waveform distance ejkR electric field end points equations 11 equations 31a exact and approximate exact solution exponential far-field approximation far-field solution field components fields radiated Figure 17 Figure 28 filament center following form Fourier transform fraunhofer region frequency dependence FREQUENCY Hz geometry image filament low frequencies Low-frequency behavior LOWER END PT magnetic fields magnetic vector potential magnitude minima nonradiation terms Note observer located orientation oscillates plotted position vector previously in figure radiated fields radiation component radiation from lightning radiation terms return stroke rotation source and image spectra speed of light stepped leader surface three-exponential waveform transfer function unit vector UPPER END PT velocity of propagation vertical element z-axis