Musk calls the Hyperloop a "fifth mode" of transportation (after planes, trains, cars and boats) that is, in the right application, better than all the others. That specific case is between major cities that are less than 900 miles apart. The system relies on tubes built between the cities that would be traversed by pods that have an "electric compressor fan [mounted] on the nose of the pod that actively transfers high pressure air from the front to the rear of the vessel. This is like having a pump in the head of the syringe actively relieving pressure," Musk wrote, and will help the Hyperloop overcome the Kantrowitz Limit (the top-speed law for a given tube-to-pod area ratio).
To propel the pods, we just have to look at the Model S. Musk envisions an external linear electric motor, "which is simply a round induction motor (like the one in the Tesla Model S) rolled flat. This
"The Hyperloop can generate far in excess of the energy needed to operate" - Elon Musk
would accelerate the pod to high subsonic velocity and provide a periodic reboost roughly every 70 miles." The system would also be green as all get out. Thanks to solar panels on the top of the tube, "the Hyperloop can generate far in excess of the energy needed to operate. This takes into account storing enough energy in battery packs to operate at night and for periods of extended cloudy weather. The energy could also be stored in the form of compressed air that then runs an electric fan in reverse to generate energy, as demonstrated by LightSail," Musk wrote.
Musk first mentioned the Hyperloop a year ago, and there has been a lot of speculation as to what, exactly, the man who is forcing the auto industry to pay attention to electric vehicles and sending rockets into space can come up with. In a Tesla conference call last week, Musk admitted that the interest has been kind of intense and that, "I think I kind of shot myself in the foot by ever mentioning Hyperloop."
Musk's plan is to publish his "quite detailed design," let outsiders criticize and improve it, and then let it breathe as an "open source design that maybe you can keep improving and I don't have any plan to execute, because I must remain focused on SpaceX and Tesla." Today's proposal is called Hyperloop Alpha, after all. One of the people who may be able to take the idea further is John Gardi who, before the reveal, Musk said had "the best guess so far."
You can read Gardi's thoughts here and find Musk's ideas written out on the Tesla blog and you can find all of his details in this 57-page PDF.