My family has had a closer call with ALS than I would ever have wished for, so the news of Stephen Hawking’s death stays with me as I write this morning. I want to finish up my thoughts on antimatter from the last few days, but I have to preface that by noting how stunning Hawking’s non-scientific accomplishment was. In my family’s case, the ALS diagnosis turned out to be mistaken, but there was no doubt about Hawking’s affliction. How on Earth did he live so long with an illness that should have taken him mere years after it was identified?
Hawking’s name will, of course, continue to resonate in these pages — he was simply too major a figure not to be a continuing part of our discussions. With that in mind, and in a ruminative mood anyway, let me turn back to the 1950s, as I did yesterday in our look at Eugen Sänger’s attempt to create the design for an antimatter rocket. Because even as Sänger labored over the idea, one he had been pursuing since the 1930s, Les Shepherd was looking at the antimatter prospect, and coming up with aspects of the problem not previously identified.
Getting a Starship Up to Speed
Shepherd isn’t as well known as he should be to the public, but within the aerospace community he is something of a legend. A specialist in nuclear fusion, his activities within the International Academy of Astronautics (he was a founder) and the International Astronautical Federation (he was its president) were legion, but this morning I turn to “Interstellar Flight,” a Shepherd paper from 1952. This was published just a year before Sänger explained his antimatter rocket ideas to the 4th International Astronautical Congress in Zurich, later published in Space-Flight Problems (1953).
Remember that neither of these scientists knew about the antiproton as anything other than a theoretical construct, which meant that a ‘photon rocket’ in the Sänger mode just wasn’t going to work. But Shepherd saw that even if it could be made to function, antimatter propulsion ran into other difficulties. Producing and storing antimatter were known problems even then, but it was Shepherd who saw that “The most serious factor restricting journeys to the stars, indeed, is not likely to be the limitation on velocity but rather limitation on acceleration.”
This stems from the fact that the matter/antimatter annihilation is so mind-bogglingly powerful. Let me quote Shepherd on this, as the problem is serious:
…a photon rocket accelerating at 1 g would require to dissipate power in the exhaust beam at the fantastic rate of 3 million Megawatts/tonne. If we suppose that the photons take the form of black-body radiation and that there is 1 sq metre of radiating surface available per tonne of vehicle mass then we can obtain the necessary surface temperature from the Stefan-Boltzmann law…
Shepherd worked this out as:
5.7 x 10-8 T4 = 3 x 1012 watts/metre2
with T expressed in degrees Kelvin. So the crux of the problem is that we are producing an emitting surface with a temperature in the range of 100,000 K. The problem with huge temperatures is that we have to find some way of dissipating them. We’d like to get our rocket operating at 1 g acceleration so we could tour the galaxy, using relativistic time dilation to send a crew to the galactic center, for example, within a human lifetime. But we have to dispose of waste heat from the extraordinarily hot emitting surfaces of our spacecraft, because with numbers like these, even the most efficient engine is still going to produce waste heat.
Image: What I liked about the ‘Venture Star’ from James Cameron’s film Avatar was that the design included radiators, clearly visible in this image. How often have we seen the heat problem addressed in any Hollywood offering? Nice work.
Now we can look at Robert Frisbee’s design — an antimatter ’beamed-core’ starship forced by its nature to be thousands of kilometers long and, compared to its length, incredibly thin. Frisbee’s craft assumes, as I mentioned, a beamed-core design, with pions from the annihilation of protons and antiprotons being shaped into a stream of thrust by a magnetic nozzle; i.e., a superconducting magnet. The spacecraft has to be protected against the gamma rays produced in the annihilation process and it needs radiators to bleed off all the heat generated by the engine.
We also need system radiators for the refrigeration systems. Never forget that we’re storing antimatter within a fraction of a degree of absolute zero (-273 C), then levitating it using a magnetic field that takes advantage of the paramagnetism of frozen hydrogen. Thus:
…the width of the main radiator is fixed by the diameter of the superconductor magnet loop. This results in a very long main radiator (e.g., hundreds of km in length), but it does serve to minimize the radiation and dust shields by keeping the overall vehicle long and thin.
Frisbee wryly notes the need to consider the propellant feed in systems like this. After all, we’re trying to send antimatter pellets magnetically down a tube at least hundreds of kilometers long. The pellets are frozen at 1 K, but we’re doing this in an environment where our propellant feed is sitting next to a 1500 K radiator! Frisbee tries to get around this by converting the anti-hydrogen into antiprotons, feeding these down to the engine in the form of a particle beam.
Frisbee’s 40 light-year mission with a duration of 100 years is set up as a four-stage antimatter rocket massing millions of tons, with radiator length for the first stage climbing as high as 7500 kilometers, and computed radiator lengths for the later stages still in the hundreds of kilometers. Frisbee points out that the 123,000 TW of first-stage engine ‘jet’ power demands the dumping of 207,000 TW of 200 MeV gamma rays. Radiator technology will need an extreme upgrade.
And to drop just briefly back to antimatter production, check this out:
The full 4-stage vehicle requires a total antiproton propellant load of 39,300,000 MT. The annihilation (MC2) energy of this much antimatter (plus an equal amount of matter) corresponds to ~17.7 million years of current Human energy output. At current production efficiencies (10-9), the energy required to produce the antiprotons corresponds to ~17.7 quadrillion  years of current Human energy output. For comparison, this is “only” 590 years of the total energy output of sun. Even at the maximum predicted energy efficiency of antiproton production (0.01%), we would need 177 billion years of current Human energy output for production. In terms of production rate, we only need about 4×1021 times the current annual antiproton production rate.
Impossible to build, I’m sure. But papers like these are immensely useful. They illustrate the consequences of taking known theory into the realm of engineering to see what is demanded. We need to know where the showstoppers are to continue exploring, hoping that at some point we find ways to mitigate them. Frisbee’s paper is available online, and repays a close reading. We could use the mind of a future Hawking to attack such intractable problems.
The Les Shepherd paper cited above is “Interstellar Flight,” JBIS, Vol. 11, 149-167, July 1952. The Frisbee paper is “How to Build an Antimatter Rocket for Interstellar Missions,” 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, 20-23 July 2003 (full text).