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Fractal modeling of lightning


Please use this identifier to cite or link to this item: http://hdl.handle.net/1928/12039

Fractal modeling of lightning

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Title: Fractal modeling of lightning
Author: Greninger, Paul
Advisor(s): Gilmore, Mark
Committee Member(s): Jeffery, Chris
Taylor, Gregory
Department: University of New Mexico. Dept. of Physics & Astronomy
Subject: Lightning, Fractal, Hausdorff, sprite,Valdivia, Vecchi, Mandelbrot, QE model, EMP model, run away electron, non-Maxwellian, power spectrum, Koch curve, fractal antenna, channel lightning, characteristic frequency, Folker-Plank, Niemeyer, Pasko
LC Subject(s): Lightning--Computer simulation.
Degree Level: Masters
Abstract: A program has been developed that portrays the fractal modeling of lightning, which subsequently calculates the fields from a fractal antenna. Nodal currents are weighted with branch length. The Hausdorff dimension for various growth parameters η, agree with those in the literature. Electric fields in the far zone have been calculated by weighting the branch currents with an overall damped sinusoidal current. The current waveform for each element is evaluated at retarded times based upon the speed the discharge propagates along the fractal. At scale lengths of 100 m an interference pattern becomes noticeable. We have investigated the slope of the power spectrum for spider lightning. For f < fthreshold the slope is between -1.6 to -2.6 with a standard deviation of ~ 2. In the case of channel lightning this slope would be -2. For f > fthreshold the average slope varies between -3.4 and -3.5. In the case of channel lightning this slope would be -4. The lesser slope is attributed to more interference between radiating elements in this model. For f > fthreshold the slope appears to be independent of the growth parameter. Observations show for inter-cloud lightning the threshold frequency is 50 kHz, with zero slope for f < fthreshold and -1.6 slope for f > fthreshold.
Graduation Date: December 2010
URI: http://hdl.handle.net/1928/12039

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