“It’s the Power Supply That Matters”

On the face of it, it seems attractive.  Everyone knows the term “specific impulse” (Isp), which is just impulse (thrust * time) divided by the reaction mass expelled … so “impulse per unit mass” is “specific impulse”.  For a rocket, in metric units, that’s the same as the exhaust velocity (N-s/kg simplifies to m/s – I love metric).   The rocket equation is: velocity gained = Isp * LN(Mass Ratio), and so if you want a high velocity, you need a high Isp (because mass ratio shows up inside the logarithm, it takes rather implausible mass ratios to get too large a multiple of Isp as net velocity).   Electric propulsion systems come in a bewildering array of flavors – gridded ion thrusters, hall effect thrusters, magnetoplasmadynamic systems, hot plasma expelled through a magnetic nozzle, and so on.  In every case, either they use higher temperatures than combustion reactions, or they use non-thermal processes to push the expelled reaction mass to higher velocities than chemical rockets can achieve.

The problem, well-known in the propulsion world, is that there’s more to the story – where does the power come from?  The joke that “we could get to Mars easily if we only had a long extension cord” goes back to the Von Braun and Stuhlinger days.  The ideal power for a rocket thruster (100% efficiency!) is Power = 0.5 * Thrust * Isp.   A useful metric to bear in mind then is “specific power” (Psp), which is simply the thrust power divided by the mass of the ship (after propellant is expelled), W/kg.  (For historical reasons, a lot of literature refers to “alpha” of a power supply (kg/kW), which is the inverse of Psp.)

Since acceleration is Thrust/Mass, the peak acceleration is simply: 2 * Psp / Isp

The fundamental problem is that if your acceleration is too low, you can’t shorten the trip time – the high achievable velocity of the electric thruster can’t be used!  After all, everyone has an electric thruster in their house that has an exhaust velocity of the speed of light – we call it a flashlight.   But we can’t get to Mars with a flashlight, because the thrust is negligibly small.  Consider a trip of 6×10^10 meters (which I’ll write in computer notation, 6E10) – not a bad first guess at the distance to Mars when in opposition (when the Earth is between Mars and the Sun).  If we want to get to Mars in a month (2.6E6 seconds), with constant acceleration (note that this is a simplification for illustrative purposes – acceleration is lower at the start of the trip than at the end), using the old d=0.5*a*t^2 formula, is about 0.036 m/s^2.   Velocity at midflight is then an impressive 46000 m/s – which we don’t get to enjoy, because we have to start braking immediately.   Doing that with a mass ratio of 2 requires an Isp of ~66000 m/s (in English units, an Isp of ~6800 ‘seconds’, which may be more familiar to some).   That’s a bit high for many electric thrusters but by no means out of reach. Peak acceleration would then have to be about .05 m/s^2 to get average acceleration high enough to make that trip.

To get that acceleration, then, at that Isp, Psp has to be 0.5*acceleration*Isp, which is 1650 W/kg.   Of course, that’s the Psp *for the entire ship*, which includes not only the power supply, but the tanks, the radiators, the electric thruster itself, and the payload.   We’d probably need a power supply of ~6000 W/kg taken just as a stand alone (or if you prefer, an “alpha” of 0.17 kg/kW).   And that, we don’t have – and we aren’t close.

Solar arrays used today in space missions, when you factor in the support and deployment structures, provide about 200 W/kg.   At Mars, you’re further from the sun, and that drops to ~100 W/kg.   There are higher performance options that have been demonstrated … thin-film arrays, arrays with inflatable solar concentrators, roll-out arrays … that can approach ~1000 W/kg at Earth orbit – 500 W/kg at Mars.   Another factor of two or so improvement is possible based on things in the laboratory.  That is still a far cry from 6000 W/kg.

What about nuclear sources?   The one nuclear reactor the U.S. flew in space, SNAP-10a, produced ~590 watts of electrical power and massed ~290 kg, or ~2 W/kg.   After many years, NASA is now nearing maturity on a more modern design, Kilopower (or KRUSTY), which uses Stirling cycle power to get more electricity from the reactor, and hopes to reach 10000 W in a 236 kg package (which still needs shielding mass added).   That’s a lot more impressive – 42 W/kg – and looks extremely promising for providing electrical power for deep space missions and Lunar or Mars surface systems.   But still, that’s nowhere *near* what it takes for high-speed flight.

There are designs for extremely high temperature reactors.  High temperature is really the key, because in space, there’s no good way to get rid of waste heat except by radiating it – and the area of a radiator scales inversely with the FOURTH power of temperature.   Energy conversion to electricity runs on a temperature difference, so if you want to reject waste heat at a nice high temperature, the source of heat has to be at an even *higher* temperature.   These designs tend to use gas-cores, running at temperatures so high that solid reactor elements would melt.   It’s important work, and I’d love to see it pushed forward faster with bigger budgets.   At the present time – it isn’t close.  No such reactor has ever been tested with fission fuel even in a laboratory (some pieces of it, like power conversion machinery, have been tested with electric heaters).   There are people who think we might one day get to ~1000 W/kg with such systems or even higher.   But we aren’t there yet and no one can say when, or even if, we will.

There are more promising routes – essentially, to use either fission or fusion reactions, both of which actually generate their energy in the form of high-speed charged particles, and instead of using those charged particles to make something hot, and drive a generator, to capture them directly in a “direct electric conversion” process.  Those processes side-step the temperature limits discussed above (or, if you prefer, are using the fact that a process running at 120 volts has an effective temperature of about 1.4 million Kelvin).   I think this is an encouraging route to a high Psp power supply – but there are practical challenges.  For fission, there are a lot of neutrons involved, and they have to go *somewhere* (ideally, back in to the fission reactor), and that takes mass and involves waste heat that has to be radiated.   For fusion, we have the ongoing problem that making a fusion reaction happen at all in a net-energy producing way remains a technological stretch unless we want to accept a very large reaction happening quickly, vaporizing the apparatus in the process (a fusion bomb).

Ironically, the old joke about the long extension cord is probably the most promising route.   Today we can see how to build beams – lasers, microwave beams, particle beams, and so on – which can beam power a long way.  We can’t beam all the way to Mars yet – but such a system isn’t out of reach, especially if built in space.   With supplied power, getting thousands of W/kg from a laser beam is credible – and the W/kg for a microwave or particle-beam receiver is extremely high (>10000 W/kg is definitely achievable).   There is some work going on at NASA for mission designs using laser beams to power high-intensity solar arrays and drive an electric thruster – presently just to accelerate because of the limited range of the beam.

So this is why I can’t get all that excited about the next breakthrough in electric thrusters.  It’s good and important work.  But we already have thrusters that are better by far than our power supplies can effectively use.  What we need is a better power supply!

Keywords: Power supply, electric thrusters, Jeff Greason, Tau Zero Foundation.