Folks , since this topic is quite crucial for success in our Hollow Planet research , I am posting some information I found on the reddit site about relevant sources for building a comprehensive theoretical framework for the Electric Universe Concept . As can be expected , most of the clues will come from the cutting edge of Physics - Plasma Cosmology .
It must also be said however , that to understand how nature works , the common sense approach is that - "Mathematics must follow where the observation leads and not the other way round" :-
https://www.reddit.com/r/plasmacosmology/comments/b6ugff/resources_and_mathematical_models_describing_the/
Resources and mathematical models describing the Electric Universe and Plasma Cosmology theory

Some of the first few questions that most people ask about Electric Universe/Plasma Cosmology theory is who developed the model(s), what available resources describe it, and what are the mathematical models that EU/PC is based upon? I've compiled a short list of some of the available authors and resources that are helpful when trying to learn about and understand EU/PC theory. I would strongly encourage others to add to this list as they see fit.
Kristian Birkeland
I suppose that I'll start with Kristian Birkeland because Birkeland and his team were the first scientists to study the concept of an electric universe in a systematic and scientific way, Birkeland and his friends risked life and limb collecting magnetic field measurements during solar storms from some of the most inhospitable environments on the planet in an effort to understand the Earth's aurora. They also conducted a series of very important laboratory experiments related to solar physics and planetary aurora a little over a century ago. I would say that Kristian Birkeland easily knew more about solar atmospheric physics than most astronomers know to this day. From his laboratory experiments, BIrkeland correctly predicted, and simulated in his lab, that the sun emitted both types of charged particles, polar jets, coronal loops, cathode rays (electron beams), which resulted in a hot solar corona, and planetary aurora, along with a whole host of observations that have since been confirmed by satellites in space. I'll start with a quick video that explains his basic solar and planetary models and his early work on electric universe theory:
Birkeland also produced some of the very first mathematical models to describe the trajectory of charged particles and plasma as they flowed from the sun, long before most people even realized that 99+ percent of the universe is made of plasma and most of the mass of the universe is found in the particles between the stars, rather than the stars themselves. A simplified explanation of his beliefs can be found in a New York Times article published in 1913. Pick the "Download PDF" option to read the full article.
Birkeland wrote an encyclopedia sized volume entitled The Norwegian Aurora Polaris Expedition 1902–1903 (158 MB) describing his data collection efforts and his laboratory experiments which you can download freely. His book is full of mathematical models related to charged particle trajectories from the sun at the end of the volume. You can also order a copy of his book here if you are so inclined.
Hannes Alfven
Hannes Alfven won the Nobel Prize for inventing and developing MHD theory. He was also one of the first scientists to apply circuit theory to high energy plasma events in space, and he is credited with developing one of the first comprehensive cosmology models based upon circuit theory and plasma physics. His book "Cosmic Plasma" is one of the defining books on this topic. It contains many mathematical models from his numerous published papers on a host of assorted topics related to plasma cosmology theory. Unlike Birkeland, Alfven lived in a "post Hubble" world when the universe was understood to be composed of many galaxies, not just one. Alfven was a prolific writer on this topic.
Dr. Anthony Peratt
Dr. Anthony Peratt was a student of Alfven and worked at Los Alamos Labs and in the field of plasma physics for most of his career. His book entitled "Physics Of The Plasma Universe" is by far the most comprehensive mathematical presentation of the plasma cosmology model. It's not exactly light reading due to it's emphasis on mathematics, but the material is presented in organized, simple and professional manner. It contains an excellent mathematical explanation of virtually every aspect of EU/PC theory. If you're primarily interested in the mathematical models associated with EU/PC theory, this is the book for you. It's well worth the money IMO. Without a doubt, this book will be read by future astronomers long after the big bang model has been forgotten. Peratt has put together a great website explaining plasma cosmology theory, and like his mentor, Peratt has been a prolific writer of published papers. He wrote an excellent introductory paper which you can find here.
Dr. Charles Bruce
Dr. Charles Bruce wrote a number of excellent papers related to electrical discharge theory as it's applied to solar physics and various events in space. His landmark paper entitled "Successful Predictions of the Electrical Discharge Theory of Cosmic Atmospheric Phenomena and Universal Evolution" is an amazing paper, and well worth reading. It outlines many of the key successes of EU/PC theory.
James Dungey
James Dungey wrote a number of papers on the topic of electrical discharges processes involved in solar flares.
Dr. Donald Scott
Dr. Donald Scott continues to be very active within the Electric Universe community. Dr. Scott wrote an excellent book entitled "The Electric Sky" that is a wonderful introduction to the EU/PC topic. Unlike several of the books previously mentioned, Scott's book is very light reading and it's designed for a general audience. It not a mathematical presentation of this topic, rather it's a well organized conceptual orientation to the EU/PC model. In contrast to his book Dr. Scott's revolutionary 2015 paper entitled Birkeland Currents: A Force-Free Field-Aligned Model is a comprehensive mathematical model of the primary energy distribution mechanism of the electric universe. This paper is probably one of the most important papers ever written on this topic, both in terms of the mathematical model of electrical currents in space, and in terms of the conceptual energy distribution system of our universe on every scale. If you're interested in understanding the mathematical models of EU/PC theory, this paper is a "must read". Scott has written another more recent paper entitled "Birkeland Currents and Dark Matter" which mathematically explains how Birkeland Currents wire galaxies together and eliminate the need for "dark matter" when describing the rotation patterns of galaxies. If you're only going to read a couple of papers on this topic, those two papers would be an excellent place to start.
Eric Lerner
Eric Lerner was also a student of Hannes Alfven. His book entitled "The Big Bang Never Happened" will forever change your beliefs about the dominant theory of cosmology today. Lerner has also written several papers explaining the evidence that demonstrates that we live in a static universe, and which demonstrates that cosmological redshift is a result of inelastic scattering/tired light, not because of expansion. FYI, it is a little known fact that even Edwin Hubble himself ultimately rejected the expansion interpretation of cosmological redshift.
Wal Thornill & Dave Talbott
Wal Thornhill and Dave Talbott have been two of the primary "movers and shakers" within the Electric Universe community for many years. They are the creators of The Thunderbolts Project website, and have been instrumental in organizing and putting together Electric Universe conventions as well as helping to create a plethora of high quality and informative Youtube videos on this topic. They also wrote fantastic introductory books to the EU/PC concept called The Electric Universe and Thunderbolts Of The Gods. Like Scott's book, their videos and their beautifully illustrated books are targeted and aimed at a more general audience. You don't have to have a strong mathematical background to appreciate their books or their videos. Their importance to the EU/PC community in terms of organization and vision cannot be overstated. Without their ceaseless public efforts, the EU/PC community would not be the growing and vibrant community that it is today.
I know that I've missed a few important contributors to the EU/PC model, like Halton Arp, Ralph Juergens and others, but I think I'll stop here for now since it's getting late. Suffice to say there are ample mathematical models and resources to support the EU/PC paradigm as the links listed above will demonstrate.
Anyone who would like to add to this list is certainly encouraged to do so. It's much easier and better to refer new readers to a resource thread than to reinvent the wheel and roundup the various links each time someone asks the same questions. My hope is that this thread will serve the purpose of providing someone who's interested in this topic with the relevant background information to give them a jump start in their investigation of our electric universe. 
Regards