Guys,
Really sorry about the trouble you are having! However, no matter how much it sounds like a good idea and the certainty these A$$holes deserve anything they get my advice is to avoid anything that someone might even remotely get hurt on or by! It's absolutely amazing how quickly the law turns to be on the side of the injured, no matter how stupid or deserving of their plight.
The best methods of stopping what is happening is to adopt the suggestion mentioned earlier of a couple of concealed game cameras that cover the field, several well prepared signs that declare the use of the field to be for Model airplane flying only with the name of the authority that so designates the field, and close coordination with the local law enforcement to explain your problem and potential solution. Then when you get an identity of the vehicle in question the police will have a reason to enforce and at least warn the individual causing the problem and or arrest or at least warn the guilty individual of a trespassing violation. Not sure of what it takes there to press a trespassing violation. It usually varies by county, state, etc. You will have to consult the local constabulary or DA's office to see what if anything can legally be done to the JERK!
Randy Cuberly