In Tempest, you control a "shooter" that is moved around the outside of a fixed track. In many cases, this looks like a "tube" drawn in three dimensions. Enemies come up the tube, and you have to destroy them, and (hopefully) avoiding them if they make it all the way up to the top. You control your shooter with a spinner, shoot with a fire button, and you're given a "super-zapper" to use once on each level.
Tempest is one of the most collectible games. By many accounts, it is collected even more than games like Dragon's Lair and Pac-Man.
Later, a software (ROM change) was created that has new levels. It's called Tempest Tubes, and can be played by changing a few programmed ROMs.
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