Nuclear rockets, or as I like to think of them, "half way between a continuous small atomic explosion and reactor whose front fell off". There are many variants, and my aliens are using relative simple nuclear salt water rockets.
The Wikipedia page on EMPs shows that the strength of the EMP from a nuclear bomb is significantly affected by the environment, so a detonation in near-Earth space (400km) creates a much more powerful EMP than the same size detonation within the atmosphere.
How would the exhaust plume of a nuclear rocket interact with Earth's atmosphere, magnetosphere, and ionosphere? Is there any risk of inducing significant currents on or near the surface (effectively, if not literally, an EMP) when the engine is switched on?
On the assumption that engine size has some effect on the answer:
- Scout: About the same size as a space shuttle, give or take, but with a max delta-V of ~400 km per second. Can sustain 55.88 m/s² for ~30 minutes. This one goes into Earth orbit at $some_altitude. How far away does the ship have to be to not cause problems?
- Colony ship: I'm not sure exactly how large, and I suspect I will be vague when describing it, but large. 130,000 colonists (each about half the weight as a human, and crammed in like… perhaps not literally sardines, but they're not having much fun). Max delta-V 40 km per second. This vessel lands on Earth (well, on water). This ship is designed to land directly without waiting in orbit. How will the engines affect electronics in the surrounding continent, if at all? Assuming the engines must be turned off at some altitude (and they switch to chemical rockets for the remainder of the descent), what altitude would that be?
On the recommendation of comments, I'll accept [science-based] answers as well as [hard-science] answers. [hard-science] still preferable, if it's possible.