Centauri Dreams

If you didn’t see this morning’s spectacular launch of the SpaceX Falcon 9, be sure to check out the video (and it would be a good day to follow @elonmusk on Twitter, too). As we open the era of private launches to resupply the International Space Station, it’s humbling to contrast how exhilarating this morning feels with the great distances we have to traverse before missions to another star become a serious possibility. We’ve been talking the last few days about the promise of antimatter, but while the potential for liberating massive amounts of energy is undeniable, the problems of achieving antimatter propulsion are huge.

So we have to make a lot of leaps when speculating about what might happen. But let’s assume just for the sake of argument that the problem analyzed yesterday — how to produce antimatter in quantity — is solved. What kind of antimatter engine would we build? If everything else were optimum, we’d surely try to master a beamed core drive, the pure product of the matter/antimatter annihilation sequence. Protons and antiprotons are injected into a magnetic nozzle, blowing out the back at a substantial percentage of the speed of light. This is the kind of rocket analyzed by Ronan Keane (Western Reserve Academy) and Wei-Ming Zhang (Kent State University) in the paper I’ve been skirting around the edges of these past few days.

Channeling Antimatter’s Energies

The paper, headed for publication in the Journal of the British Interplanetary Society, has the provocative title “Beamed Core Antimatter Propulsion: Engine Design and Optimization,” and it deals with the particle stream emerging from proton/antiproton collisions. What you get when you put the two together are gamma rays and pions, some of the latter charged and some neutral. Almost immediately the pions decay into positrons and electrons, which meet each other and produce gamma rays. But the tens of nanoseconds the pions take to decay gives us long enough to channel the charged pions through a magnetic nozzle to produce the needed thrust.

Image: Antimatter promises fast transportation throughout the Solar System and the opportunity for interstellar probes, but only if we can master its production and storage. New work is explaining how efficient an antimatter engine might be. Credit: Positronics Research, LLC.

The beamed core engine, then, is all about channeling the pions into a focused flow. Get this right and you’ve got a lot of energy to work with. In fact, Keane and Zhang note that the energy released per kilogram of annihilating antimatter and matter is 9 X 10¹⁶ joules, which is two billion times more than the thermal energy from burning a kilogram of hydrocarbon, and over a thousand times larger than burning a kilogram of fuel in a nuclear fission reactor. But while the beamed core engine is attractive because of the high relativistic velocities of the charged particles produced by the annihilation reactions, the situation is not ideal.

For one thing, much of the energy of the reaction goes into producing electrically neutral particles, which are impervious to the workings of a magnetic nozzle and thus cannot contribute to thrust. The other problem is that the nozzles we’ve been able to analyze have efficiency problems of their own in terms of creating the tight beam of thrust we’d like to produce. What Keane and Zhang do is to use software called Geant4 from the CERN accelerator laboratory to produce simulations of the interactions of particles with matter and fields. They want to bring previous studies of beamed core concepts up to date especially in terms of magnetic nozzles.

Robert Frisbee has performed rigorous studies of beamed core concepts in which magnetic nozzle efficiency is only about 36 percent, which means that while you’re dealing with pions that are initially moving at 90 percent of light speed and above, the exhaust velocity of the rocket would be just a third of that amount. Keane and Zhang derive an efficiency that is better than twice that, and manage to reach charged pion exhaust speeds of 69 percent of c. They also show that the initial speed of charged pions in a beamed core engine is actually closer to .81c than Frisbee’s 90 percent-plus. Despite the lower initial speed, the nozzle efficiencies make quite a difference depending on the kind of mission being attempted:

Frisbee’s papers explain in depth the needed generalization to account for emission of uncharged particles… When loss of propellant is taken into account, Frisbee has shown that v_e ~ 0.3c leads to a beamed core rocket facing daunting challenges in reaching a true relativistic cruise speed on a one-way interstellar mission where deceleration at the destination (a “rendezvous” mission) would be involved.

Fuel requirements become critical with lower nozzle efficiencies:

… with a payload of 100 metric tons, a 4-stage beamed core rocket designed for a cruise speed of 0.42c on a 40 light-year rendezvous mission would require 40 million tons of antimatter fuel. If the cruise speed were limited to 0.25c or less, only two stages might be needed, and Frisbee envisaged viable interstellar missions with as few as one beamed core stage; in such scenarios, fuel requirements would be dramatically lower.

All of this at 36 percent nozzle efficiency. The new numbers change the picture, with Keane and Zhang stating “With the new reference point of v_e =0.69c provided by the present Geant-based simulation, true relativistic speeds once more become a possibility using the highest performance beamed core propulsion in the distant future.”

Note the ‘distant future’ caveat, highly significant when you consider our problems in producing antimatter (or harvesting same) and the perhaps even more intractable issues involved in storage.

On Software and Methodology

But even if we can’t put a timeframe on something as futuristic as a beamed core rocket, we can continue to study the concept, and it’s heartening to see Keane and Zhang’s conclusion that the simulation software at CERN has proven robust in meeting this challenge and updating our numbers. Whether or not Keane and Zhang’s methodology is on target may be another issue, as Adam Crowl noted recently in a post to a private mailing list of aerospace engineers. Crowl hastens to add that his computations are provisional, but let me quote (with his permission) where he is right now on the magnetic nozzle efficiency issue:

There’s a problem with using just the exhaust velocity given to *part* of the fuel/propellant. It means the actual mass-ratio for a given delta-vee is quite different to a naive computation using the classic Tsiolkovskii equation. A more useful figure of merit for rockets with mass-loss in addition to reaction mass is specific impulse – momentum change per unit mass of fuel/propellant. Using the equations derived by Shawn Westmoreland and the rather vague particle energies in Zhang & Keane, the effective specific impulse is ~0.28c. Even with a perfect jet efficiency the Isp is just 0.31c.

The antimatter reaction, then, may not offer as much as we hoped:

The 0.81c average particle speed quoted in the paper isn’t as useful as the spread of kinetic energies in the particles produced, or the total kinetic energy in the distribution, but they don’t report either figure. What it does imply is that an antimatter-matter reaction puts about 11% of the mass-energy into the charged particles. Not exactly spectacular.

The chance to go to work on concepts through papers in the preprint process is invaluable, and we’ll see how Crowl’s thinking, as well as Keane and Zhang’s, evolves with further study of the issues in this paper. One thing is for sure: Given the manifest problems of antimatter production and storage, we’ll have no shortage of time in which to consider these matters before the question of actually producing this kind of antimatter rocket becomes pressing.

The paper is Keane and Zhang, “Beamed Core Antimatter Propulsion: Engine Design and Optimization,” accepted by JBIS (preprint).

Antimatter is so tantalizing a prospect for propulsion that every time a new slant on using it appears, I try to figure out its implications for long-haul missions. But the news, however interesting, is inevitably balanced by the reality of production problems. There’s no question that antimatter is potent stuff, with the potential for dealing out a thousand times the energy of a nuclear fission reaction. Use hydrogen as a working fluid heated up by antimatter and 10 milligrams of antimatter can give you the kick of 120 tonnes of conventional rocket fuel. If we could get the cost down to $10 million per milligram, antimatter propulsion would be less expensive than nuclear fission methods, depending on the efficiency of the design.

But how to reduce the cost? Current estimates show that producing antimatter in today’s accelerator laboratories runs the total up to $100 trillion per gram. But when I was researching my Centauri Dreams book, I spent some time going through the collection of Robert Forward’s papers at the University of Alabama-Huntsville, where several boxes of materials are stored in Salmon Library. Forward was constantly working in a number of different fields, always keeping his eye on the latest research, and as part of that effort he produced a series of newsletters on antimatter developments that he circulated among colleagues.

Image: A Penn State artist’s concept of an antimatter-powered Mars ship with equipment and crew landers at the right, and the engine, with magnetic nozzles, at left. Credit: PSU.

Reading through these materials, I came to see that when we quote the $100 trillion per gram figure, we’re talking about antimatter as produced more or less as a byproduct. Forward understood and appreciated the science requirements of particle accelerator labs but also saw that they were hardly the most efficient place to produce antimatter in any quantity. They were not, after all, in the propulsion business. He proceeded to do a study for the US Air Force looking at what might happen if an antimatter facility were actually designed for no other purpose than the creation of antiprotons, finding that the energy efficiency could be raised from one part in 60 million to a part in 10,000, or 0.01 percent.

The cost of building the factory, meanwhile, could be lowered dramatically, to the point where Forward believed our $10 million per milligram would be within reach. This is an interesting figure in several ways. As noted above, it makes antimatter feasible for certain kinds of space missions (assuming equivalent advances in our methods of antimatter storage. But as the price begins to drop, we can expect to find new applications in other areas of research, which should drive demand and spur further work on efficient production. It’s worth remembering that even at today’s prices, antimatter has proven its worth in scientific research and medical uses.

What about other ways of lowering the cost? One possibility is to look beyond slamming high-energy protons into heavy-nuclei targets. Writing with Joel Davis in a book called Mirror Matter: Pioneering Antimatter Physics (Wiley, 1988), Forward looked at options like heavy ion beam colliders, in which beams of heavy ions like uranium could be collided to produce 10¹⁸ antiprotons per second (with acknowledged problems in creating large amounts of nuclear debris). He also considered new generations of superconducting magnets to create magnetic focusing fields near the region where the beams collide, which should make tighter beams and greater antimatter production possible.

I bring all this up because the possibility of harvesting antimatter from natural sources in space, which we talked about last week, has to be weighed against boosting production here on Earth. But Forward’s ideas actually coupled the two notions. He wanted to move antimatter production by humans into space in the form of huge factories. Here’s what he has to say on this in an essay in his book Indistinguishable from Magic (Baen, 1995):

Where will we get the energy to run these magic matter factories? Some of the prototype factories will be built on Earth, but for large scale production we certainly don’t want to power these machines by burning fossil fuels on Earth. There is plenty of energy in space. At the distance of the Earth from the Sun, the Sun delivers over a kilowatt of energy for each square meter of collector, or a gigawatt (1,000,000,000 watts) per square kilometer. A collector array of one hundred kilometers on a side would provide a power input of ten terawatts (10,000,000,000,000), enough to run a number of antimatter factories at full power, producing a gram of antimatter a day.

We’re a long, long way from producing a gram of antimatter a day, of course, which is why studies like the recent one performed by Ronan Keane (Western Reserve Academy) and Wei-Ming Zhang (Kent State University) have such a futuristic air. But it’s important to learn the theoretical constraints on propulsion systems even if the required antimatter isn’t available, and on that score, Keane and Zhang are thinking ahead to the most advanced kind of antimatter of them all, a beamed core drive. To make it work, assuming you have the antimatter available, you need to inject protons and antiprotons into a magnetic nozzle, one that channels charged pions from the matter/antimatter annihilation into a focused beam of powerful thrust.

Although charged pions decay quickly, they can start out at 90 percent of the speed of light. Unfortunately, earlier magnetic nozzle calculations have proven inefficient at channeling these energies, dropping the exhaust velocity down to a third of this value. Tomorrow we’ll look at how a more efficient magnetic nozzle can produce better results, as Keane and Zhang have analyzed using CERN software to simulate what would go on in the hellish interior of a beamed core antimatter engine. But we also need to consider other ways of using antimatter for propulsion, assuming that Forward’s space-borne factories aren’t going to be coming online any time soon.

In Stephen Baxter’s wonderful novel Ark (Roc, 2010), a team of scientists works desperately to come up with an interstellar spacecraft while epic floods threaten the Earth. The backdrop gives Baxter the chance to work through many of our current ideas about propulsion, from starships riding a wave of nuclear explosions (Orion) to antimatter possibilities and on into Alcubierre warp drive territory. I won’t give away the solution, but will say that it partly involves antimatter used in an unorthodox way, and because Baxter’s is a near-term Earth, there simply isn’t enough antimatter to go around. That means getting to Jupiter first to harvest it.

Antimatter in space is an idea that James Bickford (Draper Laboratory) analyzed in a Phase II study for NASA’s Institute for Advanced Concepts, for he had realized that high-energy galactic cosmic rays interacting with the interstellar medium (and also with the upper atmospheres of planets in the Solar System) produce antimatter. In fact, Bickford’s calculations showed that about a kilogram of antiprotons enter the Solar System every second, though little of this reaches the Earth. To harvest some of this incoming antimatter, you need a planet with a strong magnetic field, so Jupiter is a natural bet for Baxter’s scientists, who go there to forage.

The odd thing, though, is that Saturn is actually a better source of antimatter than Jupiter, with 250 micrograms produced by reactions in the rings and injected into the magnetosphere every year. Bickford’s work showed that the process by which galactic cosmic rays produce antimatter isn’t as effective around Jupiter because its magnetic field shields the Jovian atmosphere and lowers the flux. A much larger flux reaches the atmosphere of Saturn. But Bickford also believed that our own Earth would be a good antimatter source, leading to the idea of using a plasma magnet — the scientist discusses using high temperature superconductors to form two pairs of 100-meter RF coils to manage this. The result is a kind of magnetic scoop that could trap antiparticles found in our planet’s radiation belts.

Image: Among sources of naturally occurring antimatter in our Solar System, Saturn may be the most useful. Credit: James Bickford.

Why go to the trouble of collecting antimatter from space? Because antimatter production on the order of one-trillionth of a gram per year, which is about what we can get out of today’s accelerator labs through high-energy particle collisions, isn’t enough to power up a lightbulb for more than a few seconds. Moreover, at today’s prices the stuff costs about $100 trillion per gram. This is why Robert Forward, who used to circulate an antimatter newsletter among colleagues and wrote extensively about its possibilities, proposed that one day we would build antimatter factories in space. Build a large enough solar-powered array and you could, he thought, come up with something on the order of a gram of antimatter per day.

Remember that as little as ten micrograms of antimatter might power a 100-ton payload on a one-year mission to Jupiter and you can see that one gram of antimatter a day is a bountiful supply. But Forward’s antimatter collector array was huge, 100 kilometers to the side, and well beyond today’s engineering. Thus the interest generated by the PAMELA satellite (Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics) last year when it picked up more antiprotons in the region known as the South Atlantic Anomaly than had been expected.

This South Atlantic Anomaly is where the inner Van Allen radiation belt makes its closest approach to the Earth’s surface, which in turn creates a higher flux of energetic particles there. The PAMELA work showed that Bickford’s original NIAC analysis was correct — antimatter is indeed being produced near the Earth. Bickford went on to suggest that we could collect some 25 nanograms per day using his magnetic scoop, a process that if successful would prove orders of magnitude more cost effective than creating antimatter here on Earth.

So would Baxter’s doughty crew be able to harvest their antimatter much closer to home than Jupiter or Saturn? Maybe not. A new paper by Ronan Keane (Western Reserve Academy) and Wei-Ming Zhang (Kent State University) comes into play here. The authors have developed new thinking on antimatter propulsion, specifically on the magnetic nozzles that would be required to make it work. It’s important work and tomorrow I want to get into the propulsion aspects of it, but for today I note their comment on the PAMELA findings and antimatter. Here’s a quote:

The recent PAMELA discovery, in which the observed antiproton flux is three orders of magnitude above the antiproton background from cosmic rays, paves the way for possible harvesting of antimatter in space. Theoretical studies suggest that the magnetosphere of much larger planets like Jupiter would be even better for this purpose. If feasible, harvesting antimatter in space would completely bypass the obstacle of low energy efficiency when an accelerator is used to produce antimatter, and thus could offer a solution to the main difficulties stressed by the skeptics.

The problem with this — and this has been noted by The Physics arXiv Blog and Jennifer Ouellette in recent days — is that PAMELA could come up with only 28 antiprotons over the course of 850 days of data acquisition. There is no question that Bickford is right in seeing how antimatter can be produced locally. In fact, the paper on the PAMELA work says this: “The ?ux exceeds the galactic CR antiproton ?ux by three orders of magnitude at the current solar minimum, thereby constituting the most abundant antiproton source near the Earth.” But does the process produce enough antimatter to make local harvesting a serious possibility?

We need to learn more, obviously, and it’s worth noting, as Keane and Zhang do in their paper, that the Alpha Magnetic Spectrometer was installed on the International Space Station in mid-2011, giving us a much enhanced ability to detect and measure antiparticles in Earth orbit. Antimatter harvesting within the Solar System appears to be a workable concept, but if we’re going to need to go to the gas giants to make it happen, we’re obviously pushing back the time frame on collecting significant quantities that could be used in future propulsion systems.

More on this tomorrow, when we’ll look further at Keane and Zhang’s ideas on antimatter engines and what could make them possible. Their paper is “Beamed Core Antimatter Propulsion: Engine Design and Optimization,” submitted to the Journal of the British Interplanetary Society (preprint). The PAMELA work is Adriani et al., “The discovery of geomagnetically trapped cosmic ray antiprotons,” Astrophysical Journal Letters Vol. 37, No. 2, L29 (abstract / preprint). For a cluster of Bickford references, see Antimatter Source Near the Earth, published here last August.