Mathematical and Physical Principles of PI Technology

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I am starting this thread to serve as a dedicated space for deep-diving into the foundational physics and mathematical modeling behind Pulse Induction (PI) technology. While there are plenty of excellent threads on specific DIY builds and schematics, I wanted a place where we can collectively break down the core principles that govern PI performance from the ground up.
My goal is to pull together and synthesize the wealth of information scattered across the web. I intend to aggregate technical theory from existing forum threads, academic articles, and all relevant patents to build a truly comprehensive repository here.
Let's demystify the math behind the magic. Looking forward to your insights!

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Here is detailed article on 'Optimizing Target Responses' that models and analyzes how non-ideal RLC networks behave during pulse induction turn-on and turn-off events."

This was a series of posts written by Carl-NC consisting of 5 parts from this thread https://www.geotech1.com/forums/foru...rget-responses. I have compiled them into a single document.

Note on formatting: Please be aware that some of the mathematical characters and subscripts may not have rendered with perfect accuracy due to character encoding conversion from the original. Refer to the original thread.