For trains, linear induction motors have usually been paired with magnetic levitation, as in the Transrapid system. But they don't have to be. Many roller coasters with a linear induction motor launch system have been built; Flight of Fear at King's Dominion, by Premiere Rides, was the first, in 1996. For a 1-mile test track, outsourcing the whole job to Premiere Rides or Intamin would be a good move. Intamin, which mostly makes amusement park rides, also has a transportation division. They build monorail systems. Intamin would just have to combine the car design from their P8 monorail[1] with their linear induction motor launch system.[2] By Intamin standards, a fast 1 mile loop with no hills is easy. ("We can put in a vertical loop for a small extra charge...")
[1] http://www.intaminworldwide.com/transportation/Home/news/Sha... [2] http://www.intaminworldwide.com/amusement/RollerCoasters/LSM...