If you'd like a brief (2 minute) empirical introduction to Birkeland's cathode sun theory, this very short video presents a working (albeit slighly oversimplified) demonstration of both his cathode sun theories, and the sun's effect on the Earth's aurora as a result of the current flow process. Keep in mind it's not just a mathematical "theory" about the importance of current with relationship to events in space. It's a miniaturized working model of the sun and the planetary aurora which visually explains the excess heat of the sun's corona. As you'll see in the video, the corona around the cathode sphere glows in a light blue color due to the current flowing though the atmosphere around the cathode. The same current flow "glow" also occurs around the planetary sphere near the poles where the electrical currents are concentrated from the Earth's magnetic fields which power the aurora.
https://www.youtube.com/watch?v=m58-CfVrsN4
The Themis satellite in space has actually already confirmed the existence of 'magnetic ropes', AKA current carrying plasma filaments, which connect the Earth to the sun. Those plasma filaments, AKA magnetic ropes would take the place of the solid "wires" which were used in that particular lab experiment, but the concept and the solar and planetary physics is otherwise exactly the same process as you see in the video.
http://science.nasa.gov/science-news/sc ... ec_themis/
This second hour long video will introduce you to plasma cosmology/electric universe theory by real "experts" in the plasma cosmology community. It's a really good introduction to the whole plasma cosmology theory framework, and it explains very clearly how plasma cosmology/electric universe theory is vastly different from Lambda-CDM (big bang) theory. If you're at all into astronomy, IMO you owe it to yourself to check out this video.
https://www.youtube.com/watch?v=m-2uvQ_MJz8