GIThruster wrote:That's right, and the kinetic energy gain of an M-E powered craft cannot exceed the energy consumed either. ...
It should be obvious your example applies equally as well to a Hall thruster as it does to an M-E thruster, and you are thus doing the math wrong.
Not at all. These devices will run out of substance to thrust before the maths becomes compromised, because they have to eject some of the mass of the craft. They are figuratively dependent on their rest mass before they commenced the acceleration. The power consumed will be exactly related to the kinetic energy content ejected, and/or gathered en route.
State which line the error of premise occurs:
1) A 1 kg test thruster is subjected to a 1 W, 130 uN of thrust.
2) It accelerates for 10 years (call it 300 Ms) from a given rest frame at which it was at 0 m/s.
3) 300 MJ has been expended.
4) The test thruster is travelling at 39,000m/s (it'll have reached 3.6 bn miles by then ... a trip to Neptune!)
5) Its kinetic energy wrt the given rest frame is then 760 MJ, which is greater than the 300 MJ expended.