What about ion drive propulsion?
Also, wouldn't a constant force of energy cause the vessel to continuously accelerate faster in space? If there's no counter-active force, wouldn't said vessel accelerate infinitely?
It would continously accelerate, not accelerate faster, and in fact, as EponiCo pointed out, when getting closer to lightspeed it will start to accelerate slower when the force propelling it remains constant.
Actually the energy is far higher since acceleration becomes more expensive the faster you are. The formula is something with
sqrt(n / (1- v²/c²)). Reaching speed of light would require infinite energy. Also, nitpick, but you are confusing gigawatt-hours with gigawatt/hour.
You are right, my knowledge sadly does not exceed simple Newtonian physics. Of course what we know now dictates that reaching lightspeed is theoretically impossible as well.
