Electromagnetic missiles from currents on fractal sets

John M. Myers; Tai Tsun Wu; Howard E. Brandt

doi:10.1117/12.18567

1 April 1990 Electromagnetic missiles from currents on fractal sets

John M. Myers, Tai Tsun Wu, Howard E. Brandt

Proceedings Volume 1226, Intense Microwave and Particle Beams; (1990) https://doi.org/10.1117/12.18567
Event: OE/LASE '90, 1990, Los Angeles, CA, United States

Abstract

Electromagnetic pulses of finite total radiated energy can deliver energy to a distant receiver that decreases with distance much more slowly than the usual r exp -2. Such electromagnetic missiles can be generated by any of a class of current distributions over one or another set of points contained in a bounded region of a two-dimensional or three-dimensional space. For a given currrent-bearing set of points as a transmitter, one can explore various time and space dependencies of the transmitting current. Over some classes of dependencies, the energy reaching the receiver decreases as r exp -epsilon, where epsilon is a positive number that can vary from one current to another. Current-bearing sets so far explored have dimension 0, 1 or 2. For these, the requirement of finite total radiated energy establishes a greatest lower bound on epsilon, dependent on the dimensions of both the set and the space in which it resides. This infimum defines what can be called the pulse index of a set relative to the space containing it. One might conjecture that the pulse index can be defined for sets of fractional Hausdorff dimension. It will be shown that this is so, and that for certain sets of fractional dimension, the index is related to the dimension just as it is for integral dimensions.

Citation Download Citation

John M. Myers, Tai Tsun Wu, and Howard E. Brandt "Electromagnetic missiles from currents on fractal sets", Proc. SPIE 1226, Intense Microwave and Particle Beams, (1 April 1990); https://doi.org/10.1117/12.18567

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