Would an ionocraft have better or worse performance in the upper atmosphere?

The ionocraft produces lift by accelerating ions in the air downward by the use of two meshes held at a large relative voltage difference.

With a cursory look at the physical principle, it seems like it could have advantages over other methods of propulsion in sub-orbital high altitude flight. It's not limited by having to take reaction mass on board, it doesn't have to deal with high drag because it can be functionally stationary, and higher altitude might not force it to scale up size like balloons.

Only problem is that the idea isn't practical. Wikipedia notes power requirements of 1 Watt per gram.

However, ions are more available in the higher atmosphere. Qualitatively, more ions for an ionocraft would seem to imply that you would get more force with less power input. The lift equation for an ionocraft is:

$$F = \frac{Id}{k}$$

$k$ is "ion mobility coefficient of air". I'm confused about the meaning of that so I can't answer this myself. Should this be lower or higher at very high altitudes? And considering the entire picture, might an ionocraft (which is non-viable at sea level) become viable if you flew it up to high altitudes first?

This paper from 1970 makes some progress to answering the question. It gives the following graph:

This gives the ion mobilities for different altitudes, and for both positive and negative charges. Considering that the units match as well, I'm going to identify this as $k$ in the equation with fairly good confidence.

The correlation is from applying physical principles to the atmosphere, so there is no expectation that this would be correct in real life. Actually, there are several confounding factors in real life, including a significant difference between day and night. Attempts at a real real measured curve are much more messy, and even has a global maximum. However, this global max is far above the 100 km mark, and up to that point, this exponential relationship looks like it could hold fairly well. For a straightforward order-of-magnitude estimation (which is what this question wants), this seems perfectly sufficient.

Now, to compare values, the above graph's value for sea-level can be roughly estimated by observation:

$$k|_{h=0} = 1.5 - 2.0 \frac{ cm^2 }{ V s} = 1.5 - 2.0 \times 10^{-4} \frac{ m^2 }{ V s}$$

Let's compare to the Wikipedia article on ionocraft:

k is the ion mobility coefficient of air, measured in dimension M−1 T2 I (Nominal value 2·10−4 m2 V−1 s−1).

$$k|_{h=0} = 2.0 \times 10^{-4} \frac{ m^2 }{ V s}$$

These numbers look to be in fairly good correspondence. This gives a little more credibility to the graph's numbers. If they are correct, we're looking at a change in the value from sea-level to higher altitudes of around:

$$\frac{ k|_{h=70 km} }{k|_{h=0}} \approx 2 \times 10^4$$

It is clear enough that the ionocraft equation would benefit from the difference in the k value. The real question is if a detriment to the other independent variables would also exist? Perhaps electrical arcing would happen at a lower voltage, which would further constrain the I and d tradeoffs. That's still unclear to me.

It's also unclear if a factor of 10,000 would be sufficient to move from non-viable to viable. Or if this would be sufficient to compensate for the cost of running wires from the ground to a high-altitude craft. You could still go higher. The global minimum looks closer to maybe 200 or 300 km in altitude. By pushing the 70 km to maybe 100 or 150 km you could certainly buy yourself several more orders of magnitude in k.

• I might be wrong here, but I have looked at the article referenced by AlanSE and, as he mentioned, the ion mobility increases with altitude (as expected I would add). However I don't understand how this helps the ionocraft as the force is inversly proportional to the ion mobility (F=Id/k), so if k increases the force would decrease, no? I know that drag would decrease as well but with the current efficiency of lifters I doubt that a ionocraft at higher altitudes would perform considerably better. – user4653 Jun 26 '14 at 10:30

It is nice to see these equations about ionocrafts however, the first equation shown, that everyone has been going by, is wrong.

The thrust of an ionocraft correlates primarily with the voltage not current. 1 watt at 100kV produces far more ion wind than 1000 watts at 10 volts for instance. 1000 watts at the same voltage will produce more wind than 1 watt at that voltage, but it is not at all a linear increase. All of this of course depends very much on the geometry of the system producing the ions. Lower currents at higher voltages can be much more efficient. At higher altitudes the air is thinner and provides less electrical resistance between the collector and emitter therefore, the device will draw more current according to Ohms law(counter intuitively lower resistance loads draw more current). Since there are less particles per unit length in thinner air, there will be less thrust. If the emitter to collector distance is increased at higher altitudes, the resistance will return and the particle count will also return therefore, also according to ohms law the current draw will return. Since the energy and current transfer will be the same, the thrust should return. There are no thorough tests of this yet as of early 2019 though. Since the ions would have more time to accelerate in the high altitude case, it might turn out to be more efficient. It is surprising no one has thoroughly tested this in a vacuum chamber yet.

• What you've written might apply to an ion engine in vacuum, but the equation given for the ionocraft applies to dense air where there mean free path for ions is very short (order of microns) and so the ions never build up a large kinetic energy. The process is more of an electric field driven diffusion than an acceleration, so even if you used a 100 kV potential difference, the speed of the ions; their drift velocity will be stay in the meters per second range. The thrust comes from the momentum being transferred to all of the neutral atoms. – uhoh Oct 20 '19 at 0:53
• This section of the Wikipedia article linked in the question explains this somewhat. – uhoh Oct 20 '19 at 0:54
• What I wrote applies to real results experimenting with ion propulsion in air for 19 years mostly full time. I am also the inventor of the Self Contained Ion Powered Aircraft, videos are on Google. Large numbers of charged particles do continue below ionocrafts although they are short lived and it is rarely mentioned in the literature. The path of many of the particles is from the emitter to the collector. I am correct that the accepted equation is wrong. Ion propulsion in air correlates way better with voltage than with current. – Ethan Krauss Oct 21 '19 at 2:09
• The actual effect correlates somewhat with the current but then rapidly drops off. People imagine intense coronas but ideally it is more like a low temperature electrostatics like effect. It is more efficient with lower current. – Ethan Krauss Oct 21 '19 at 2:09