No. Electric propulsion works by bringing ions to very high energies/speeds. This isn't practical in a dense atmosphere, because ions make too many collisions with air molecules. Their energy is dissipated almost immediately, as heat.
Moreover, it's not useful for escaping a planet's gravity well, atmosphere or not. Ion thrusters are extremely weak. E.g. the Dawn probe has a thrust/weight ratio of 0.000007. At the earth's surface, the gravity pulling it down would be 135,000 times stronger than the thrusters pushing it up. It can't fly.
Hmm, maybe you can help with my math? (and keep an open mind)
Here's what I was thinking. Float an ion thruster powered ship tethered to a weather balloon with solar panels up to 53km altitude (world record) and fire up the thrusters gradually reaching orbital velocity.
Here are my calculations:
altitude = 53 km
Air density = 5.3 kg/m^3
max speed =7 km/s
Coefficient of drag = .02
Cross section area = 130 meters
I used this equation to calculate the drag:
(aird/2) * (speed2) * coeffdrag * area
And I got around 340 newtons of drag. If an Ion thruster could produce something greater than that, we might be in business.
Your calculation is off by 10^6 -- I think you mixed up m/s with km/s? Also the air density should be far lower -- at your altitude (53 km) it's 7.2e-4 kg/m^3 or so. I don't think streamlining makes much difference at hypersonic speeds -- air molecules will hit your craft regardless of how it's shaped, there's no time push them out of the way. So a drag coefficient of 0.02 isn't likely; it's probably at least 1. You could look up stuff on spacecraft reentry to find more accurate figures.
Put together, I get something like 2 million Newtons or 200 tonnes force. This is about half the thrust of SpaceX's Falcon 9, so clearly this won't work.
Right, but helium doesn't just magically "go up". It provides lift in proportion to the difference in density between the gas in the balloon and the surrounding atmosphere.
As the atmosphere thins, the amount of lift capable of generated by a helium balloon decreases to the point where, at the altitude you've mentioned, it could lift a total of about 0.8kg (according to GP's calculations). The point being that you wouldn't be able to have much of a payload lifted to those heights.
They're mass ejection thrusters, so yes. But the amount of thrust produced is minuscule compared to a hydrocarbon burning rocket. So I don't think they'd be useful so deep into earths gravity well.
Absolutely. Hayabusa and Dawn (among others) have already demonstrated the efficiency of ion propulsion systems.
http://en.wikipedia.org/wiki/Ion_thruster