# Could chemical energy quicken ion propulsion?

## Background

Tsiolkovski's rocket equation says that change of speed is proportional to the exhaust velocity. Chemical propulsion seems to have a strictly limited and since long achieved maximum exhaust velocity in its combustion products. But applied ion propulsion today already has tens of times higher exhaust velocity and, I think, theoretically has no distinct upper limit. The problem with ion propulsion is that it is electric, and solar and nuclear power plants do not produce power at all at such high effect as chemical combustion/explosion does. (Such is my uneducated understanding.)

## Question

Could chemical combustion be used to power an ion engine to shorten travel times? That instead of gradually capturing the rays of the Sun or the decay of plutonium, an interplanetary spacecraft could accelerate to high speed in minutes instead of during months, by suddenly combusting hydrogen and oxygen, in some kind of thermal chemical power plant on the spacecraft, into electric power for ion acceleration? Joining the suddenness of chemics with the efficiency of ions.

Hydrogen-oxygen fuel cells, such as SOFC, have maximum specific energy density of ~ 17.9 MJ/kg (using 142 MJ/kg for compressed hydrogen and including oxygen at 1:7.93 2H-O mass fraction yielding water at a stoichiometrically perfect air to fuel ratio). Other chemical components yield lower specific energy density since they're using higher molar mass fuels. Incidentally, this is also the reason why LOX/LH2 achieve highest specific impulse among chemical rockets. Now, theoretically highest fuel cell efficiency, assuming heat recapture, is at 85–90%. So we're down to maximum theoretical specific energy density of ~ 16 MJ/kg.

Conversely, plutonium (Pu-238) powered RTGs have specific energy density of 2,239,000 MJ/kg. If we assume they generate sufficient power for one quarter its half-life of 87.7 years, let's round it up to 20 years, we've made use of 14.6% of its total power density, and efficiency of 7% (pretty good for a RTG, most of its energy ends up as waste heat), we end up with our system power density of 22,916 MJ/kg. That's over 1,400 times more than our best chemical fuels when it comes to power density (which is what matters when it comes to moving mass around).

And it's not that RTGs are that much more efficient, they're not, it's just that chemical energy doesn't come in very mass efficient form. Fuel cells will have some advantages over RTGs, such as being able to dump no longer needed reaction products overboard or even find its use elsewhere (coolant, potable water, biological shielding,...), not having to shield against own fuel's radioactive decay, and so on, but it will also come with disadvantages, such as still requiring thick-walled or heavily heat shielded pressure vessels not to lose too much of it to space due to fuel boil-off, energy efficient fuel cells will still generate a lot of excess heat that needs to be efficiently radiated away, etc. Not that RTGs don't need that, but fuel cells won't have so many advantages over them to offset those 1,400 times the difference in power density.

And since we're already discussing nuclear, RTGs are completely overshadowed by nuclear fission reactors with specific energy density of 79,420,000 (thorium) to 80,620,000 (uranium). And there are compact, space application ready nuclear fission reactor designs, like SAFE, SP-100, SNAP-10A, HOMER-15 to name a few, mostly using Heatpipe Power Systems (HPS) design. We just have to overcome our aversion to anything nuclear and start regulating their development, testing and use so they're as much of an option as they're safe to use.

• I like the details, but he is referring to the trade-off between Isp and thrust -- can chemical-based reactions be used to generate high power for higher thrust ion propulsion? – Brian Lynch Nov 4 '15 at 4:09
• @BrianLynch However you turn it, you'd do better with a chemical rocket then, since there's less power conversion loss, uses stored energy mass directly as reaction mass, and advects away most of excess heat of exothermic process. Ion propulsion has its own losses, mainly in first ionization potential being lower with high molar mass exhaust, which is inefficient due to the nature of kinetic energy ($0.5mv^2$). It's again all about energy density, it's just a bit different how stored energy is converted to kinetic one and where inefficiencies are. I intentionally remained with the basics. – TildalWave Nov 4 '15 at 4:21
• BTW Ion thrusters are more mass efficient than chemical rockets, but not nearly as energy efficient, which is actually pretty low and governed by the Child-Langmuir law. So if you use stored chemical energy to power an ion thruster, you're combining worst of the two, not best of them. You get low energy density, low conversion efficiency, and likely rather poor thrust (unless you use stuff like C-60 fullerene) at slightly worse than chemical rocket's mass efficiency. That's also why SEP makes sense. Well, kinda. – TildalWave Nov 4 '15 at 4:37
• Certainly, I am not disagreeing with you (hence my +1), but again, the question is referring to the actual thrust. Two competing designs: (1) scale up an RTG or solar powered system to achieve enough power to get thrust levels as high as chemical rockets, or (2) exploit chemical reactions to achieve the same power (via fuel cell, combustion, any option). Of course both solutions mean scaling up the ion thruster itself, but assume that is independent and the same scaled-up engine can be used for both (1) and (2). – Brian Lynch Nov 4 '15 at 5:17

The idea of using a high-power source of electricity to increase the thrust of an ion thruster is definitely sound, but inefficiency in transforming chemical energy to electrical energy is really the limiting factor. Add to that the complexity of the propulsion system, which translates into increased mass and hence lower overall Delta-V for the same amount of propellant, and you diminish the benefits of using ion propulsion in the first place.

At the moment, ion thrusters depend on solar or nuclear power supplies for electricity, and those sources have limits on the amount of power available -- therefore limiting your thrust. Larger power supplies could be used to provide higher thrust, so if your hydrogen fuel cell (or other chemical energy converter) can provide higher power at a manageable mass then it would be feasible. However, carrying the chemical propellants to generate that electricity is a major problem -- so maybe your idea would be more suitable for futuristic interstellar spacecraft that could harvest hydrogen and oxygen along the way.