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I have also seen papers recently proposing the use of a sort of tesla
coil circuit as a portion of a ns rise time EMP generator
There are better ways to generate precisely formed HV and High current
pulses for EMP testing. A Marx generator for instance.
A search of the IEEE database should shed some useful light on EMP use.
Marx generators are useful for generating precisely controlled rise and
fall times, yes, but not necessarily capable of the high rep-rate which
some applications call for.
Some papers show that energy density, mass and reliability are
advantages found in Tesla transformers. EMP generation is certainly
achieved by Marx and by Tesla techniques.