Wouldn't be surprised if you told me that's where the idea for warp drive came from...even if not it made a lot more people drive to figure out a way to make it work...
Star Trek is chock full of inaccuracies and is completely barren of any scientific credibility. A spaceship remaining intact after skimming the surface of a star by using a magnetic field? Fat chance. Red matter? The idea is closer to anti-matter than exotic particles. And I'd like an explanation of how vertical gravity works on a spacecraft.
I did some research on Star Trek's warp drive, and the fundamental idea of it transcends from impossible to complete fantasy.
Matter-Antimatter interactions do not produce plasma, they produce energy outbursts. Potentially, the heat output could warm an outside gas to ionize into a plasma. Judging by the description given on the Star Trek Wiki, the plasma created is quark-gluon plasma, which is, to my knowledge, impossible to create just from smaller-scale matter-antimatter explosions.
Correct me if I'm wrong.