Borderlands of Science

by Charles Sheffield

  Forward also offers an ingenious way of stopping the sail at its destination. The circular sail is constructed in discrete rings, like an archery target. As the whole sail approaches its destination, one inner circle, 320 kilometers across and equal in area to one-tenth of the original sail, is separated from the outer ring. Reflected laser light from the outer ring serves to slow and halt the inner portion at the destination star, while the outer ring flies on past, still accelerating. When exploration of the target stellar system is complete, an inner part of the inner ring, 100 kilometers across and equal in area to one-tenth of the whole inner ring, is separated from the rest. This "bull's-eye" is now accelerated back towards the Sun, using reflected laser beam pressure from the outer part of the original inner ring. The travel time to Alpha Centauri, including slowing-down and stopping when we arrive, is 8.6 years (Earth time) and 7 years (shipboard time). Note that we have reached speeds where relativistic effects make a significant difference to perceived travel times.

  Could we build such a ship, assuming an all-out worldwide effort?

  Not yet. The physics is fine, but the engineering would defeat us. The power requirement of the laser is thousands of times greater than the total electrical production of all the nations on Earth. The space construction capability is also generations ahead of what can reasonably be projected for the next half century. We are not likely to go to the stars this way. Something better will surely come along before we are ready to do it. I feel this way about some other ideas, discussed later in this chapter.

  8.15 The Bussard Ramjet. This is a concept introduced by Robert Bussard in 1960. It was employed in one of science fiction's classic tales of deep space and time, Poul Anderson's Tau Zero (Anderson, 1970).

  In the Bussard ramjet, a "scoop" in front of the spaceship funnels interstellar matter into a long hollow cylinder that comprises a fusion reactor. The material collected by the scoop undergoes nuclear fusion, and the reaction products are emitted at high temperature and velocity from the end of the cylinder opposite to the scoop, to propel the spacecraft. The higher the ship's speed, the greater the rate of supply of fuel, and thus the greater the ship's acceleration. It is a wonderfully attractive idea, since it allows us to use reaction mass without carrying it with us. There is interstellar matter everywhere, even in the "emptiest" reaches of open space.

  Now let us look at the "engineering details."

  First, it will be necessary to fuse the fuel on the fly, rather than forcing it to accelerate until its speed matches the speed of the ship. Otherwise, the drag of the collected fuel will slow the ship's progress. Such a continuous fusion process calls for a very unusual reactor, long enough and operating at pressures and temperatures high enough to permit fusion while the collected interstellar matter is streaming through the chamber.

  Second, interstellar matter is about two-thirds hydrogen, one-third helium, and negligible proportions of other elements. The fusion of helium is a complex process that calls for three helium nuclei to interact and form a carbon nucleus. Thus the principal fusion reaction of the Bussard ramjet will be proton-proton fusion. Such fusion is hindered by the charge of each proton, which repels them away from each other. Thus pressures and temperatures in the fusion chamber must be extremely high to overcome that mutual repulsion.

  Third, there is only about one atom of interstellar matter in every cubic meter of space. Thus, the scoop will have to be many thousands of kilometers across if hydrogen is to be supplied in enough quantity to keep a fusion reaction going. It is impractical to construct a material scoop of such a size, so we will be looking at some form of magnetic fields.

  Unfortunately, the hydrogen of interstellar space is mainly neutral hydrogen, i.e., a proton with an electron moving around it. Since we need a charged material in order to be able to collect it electromagnetically, some method must first be found to ionize the hydrogen. This can be done using lasers, beaming radiation at a carefully selected wavelength ahead of the ramjet. It is not clear that a laser can be built that requires less energy than is provided by the fusion process. It is also not clear that materials exist strong enough to permit construction of a magnetic scoop with the necessary field strengths.

  The Bussard ramjet is a beautiful concept. Use it in stories by all means. However, I am skeptical that a working model will be built any time within the next couple of centuries, or perhaps ever.

  8.16 Hybrids. For completeness, we will also mention three other systems. One has an onboard energy source and uses external reaction mass, the other two have onboard reaction mass and use external energy.

  8.17 Laser-powered rockets. These rockets carry reaction mass, but that mass does not produce the energy for its own heating and acceleration. Instead, the energy is provided by a power laser, which can be a considerable distance from the target spaceship.

  This concept was originally proposed by Arthur Kantrowitz as a technique for spacecraft launch. It is attractive for interplanetary missions, although for laser power to be available at interstellar distances it is necessary to build a massive in-space power laser system.

  The requirement for onboard storage of reaction mass is also huge. Even when all of this has been done, the EJV does not exceed maybe 200 kms/second. This system sounds fine for launches, less good for in-space use. Although we never named it as such, this is what Jerry Pournelle and I used as the launch system in our novel Higher Education (Sheffield and Pournelle, 1996).

  Note that laser power could be used equally well to provide the energy for other propulsion systems, such as the ion drive. This removes the bulky onboard equipment that otherwise severely limits ship acceleration.

  8.18 Ram Augmented Interstellar Rocket (RAIR). The RAIR employs a Bussard ramscoop to collect interstellar matter. However, instead of fusing such matter as it flashes past the ship, in the RAIR an onboard fusion reactor is used to heat the collected hydrogen and helium, which then exits the RAIR cylinder at high speed.

  Certainly, this eliminates one of the central problems of the Bussard ramjet—namely, that of fusing hydrogen quickly and efficiently. It also allows us to make use of interstellar helium. However, the other problems of the Bussard ramjet still exist. One little-mentioned problem with both the RAIR and the original Bussard ramjet is the need to reach a certain speed before the fusion process can begin, since below that speed there will not be enough material delivered to the fusion system. The acceleration to reach that minimum velocity is itself beyond today's capabilities.

  8.19 The vacuum energy drive. The most powerful theories in physics today are quantum theory and the theories of special and general relativity. Unfortunately, those theories are not totally consistent with each other. If we calculate the energy associated with an absence of matter—the "vacuum state"—we do not, as common sense would suggest, get zero. Instead, quantum theory assigns a specific energy value to a vacuum.

  In classical thinking, one could argue that the zero point of energy is arbitrary, so we could simply start measuring energies from the vacuum energy value. However, if we accept general relativity that option is denied to us. Energy, of any form, produces spacetime curvature, and we are therefore not allowed to redefine the origin of the energy scale. Once this is accepted, the energy of the vacuum cannot be talked out of existence. It is real, and when we calculate it we get a large positive value per unit volume.

  How large?

  Richard Feynman addressed the question of the vacuum energy value and computed an estimate for the equivalent mass per unit volume. The estimate came out as two billion tons per cubic centimeter. The energy in two billion tons of matter is more than enough to boil all Earth's oceans.

  Is there any possibility that the vacuum energy could be tapped for useful purposes? Robert Forward has proposed a mechanism, based upon a real physical phenomenon known as the Casimir Effect. I think it would work, but the energy produced is small. The well-publicized mechanisms of others, such as Harold Puthoff, for extracting vacuum energy leav
e me totally unpersuaded.

  Science fiction that admits it is science fiction is another matter. According to Arthur Clarke, I was the first person to employ the idea of the vacuum energy drive in fictional form, in the story "All the Colors of the Vacuum" (Sheffield, 1981). Clarke employed one in The Songs of Distant Earth (Clarke, 1986). Not surprisingly, there was a certain amount of hand-waving on both Clarke's part and mine as to how the vacuum energy drive was implemented. If the ship can obtain energy from the vacuum, and mass and energy are equivalent, why can't the ship get the reaction mass, too? How does the ship avoid being slowed when it takes on energy, which has an equivalent mass that is presumably at rest? If the vacuum energy is the energy of the ground state, to what new state does the vacuum go, after energy is extracted?

  Good questions. Look on them as an opportunity. There must be good science-fictional answers to go with them.

  8.20 Launch without rockets. The launch of a rocket—any rocket—is certainly an impressive sight and sound. All that noise, all that energy, thousands of tons of fuel going up in smoke (literally) in a few minutes.

  But does it have to be that way? Let us invoke a classical result from mathematics: The work done carrying a test particle around a closed curve in a fixed potential field is zero.

  Around the Earth there is, to good accuracy, a fixed potential field. A spaceship that goes up to orbit and comes back down to the same place is following a closed curve. Conclusion: we ought to be able to send a test particle (such as a spacecraft, which on the scale of the whole Earth is no more than a particle) to orbit and back, without doing any work.

  Let's do it, in several different ways.

  8.21 The beanstalk. Suppose we have a space station in geostationary orbit, i.e. an equatorial orbit with period exactly 24 hours. A satellite in such an orbit hovers always over the same point on the Earth's equator. Such orbits are already occupied by communications satellites and some weather satellites.

  Now suppose a strong loop of cable runs all the way down to the surface of Earth from the space station. The cable must be long as well as strong, since geostationary orbit is more than 35,000 kilometers above the surface. We defer the question as to how we install such a thing. (A geostationary satellite has a period of 24 hours, and hovers above a fixed point on the equator. A geosynchronous satellite simply has a period of 24 hours, but can be inclined to the equator and reach to any latitude.)

  Attach a massive object (say, a new communications satellite) to the cable down on the surface. Operate an electric motor, winding the cable with the attached payload up to the station. We will have to do work to accomplish this, lifting the payload against the downward gravitational pull of the Earth. We do not, however, have to lift the cable, since the weight of the descending portion of the loop will exactly balance the weight of the ascending portion.

  Also, suppose that we arrange things so that, at the same time as we raise the payload up from the surface, we lower an equal mass (say, an old, worn-out communications satellite) back down to the surface of the Earth. We will have to restrain that mass, to stop it from falling. We can use the force produced by the downward pull to drive a generator, which in turn provides the power to raise the payload. The only net energy needed is to overcome losses due to friction, and to allow for the imperfect efficiency of our motors and generators that convert electrical energy to gravitational energy and back.

  The device we describe has been given various names. Arthur Clarke, in The Fountains of Paradise (Clarke, 1979), termed it a space elevator. I, in The Web Between the Worlds (Sheffield, 1979), called it a beanstalk. Other names include skyhook, heavenly funicular, anchored satellite, and orbital tower.

  The basic idea is very simple. There are, however, some interesting "engineering details."

  First, a cable can't simply run down from a position at geosynchronous height. Its own mass, acted on by gravity, would pull it down to Earth. Thus there must be a compensating mass out beyond geosynchronous orbit. That's easy enough; it can be another length of cable, or if we prefer it a massive ballast weight such as a captured asteroid.

  Second, if we string a cable from geostationary orbit to Earth it makes no sense for it to be of uniform cross section. The cable needs to support only the length of itself that lies below it at any height. Thus the cable should be thickest at geosynchronous height, and taper to thinner cross sections all the way down to the ground.

  What shape should the tapering cable be? In practice, any useful cable will have to be strong enough to stand the added weight of the payload and the lift system, but let us first determine the shape of a cable that supports no more than its own weight. This is a problem in static forces, with the solution (skip the next half page if you are allergic to equations):

  A(r)=A(R).exp (K.f(r/R).d/TR)

  In this equation, A(r) is the area of the cable at distance r from the center of the Earth, A(R) is the area at distance R of geosynchronous orbit, K is the Earth's gravitational constant, d is the density of cable material, T is the cable's tensile strength, and f is the function defined by:

  f(x)=(3/2-1/x-x2/2)

  The form of the equation for A(r) is crucial. First, note that the taper factor of the cable, which we define as A(r)/A(R), depends only on the ratio of cable tensile strength to cable density, T/d, rather than actual tensile strength or density. Thus we should make a beanstalk from materials that are not only strong, but light. Moreover, the taper factor depends exponentially on T/d. If a cable originally had a taper factor from geosynchronous orbit to Earth of 100, and if we could somehow double the strength-to-density ratio, the taper factor would be reduced to 10. If we could double the strength-to-density again, the taper factor would go down to 3.162 (the square root of 10). Thus the strength-to-density ratio of the material used for the cable is enormously important. We note here the presence of the exponential form in this situation, just as we observed it in the problem of rocket propulsion.

  We have glossed over an important point. Certainly, we know the shape of the cable. But is there any material with a large enough strength-to-density ratio? After all, at an absolute minimum, the cable has to support 35,770 kilometers of itself. The problem is not quite as bad as it sounds, since the Earth's gravitational field diminishes as we go higher. If we define the "support length" of a material as the length of uniform cross section able to be supported in a one-gee gravitational field, it turns out that the support length needed for the beanstalk cable is 4,940 kilometers. Since the actual cable can and should be tapered, a support length of 4,940 kilometers will be a good deal more than we need. On the other hand, we must hang a transportation system onto the central cable, so there has to be more strength than required for the cable alone.

  Is there anything strong enough to be used as a cable for a beanstalk? The support lengths of various materials are given in TABLE 8.1 (p. 227).

  The conclusion is obvious: today, no material is strong enough to form the cable of a beanstalk from geostationary orbit to the surface of the Earth.

  However, we are interested in science fiction, and the absolute limits of what might be possible. Let us recall Chapter 5, and the factors that determine the limits to material strength. Examining TABLE 5.1 (p. 122), we see that solid hydrogen would do nicely for a beanstalk cable. The support length is about twice what we need. It would have a taper factor of 1.6 from geosynchronous orbit to Earth. A cable one centimeter across at the lower end would mass 30,000 tons and be able to lift payloads of 1,600 tons to orbit.

  Unfortunately, solid metallic hydrogen is not yet available as a construction material. It has been made as a dense crystalline solid at room temperature, but at half a million atmospheres pressure. We need to have faith in progress. There are materials available, today, with support lengths ten times that of anything available a century ago.

  Beanstalks are easier for some other planets. TABLE 8.2 (p. 228) shows what they look like around the solar system, assuming the hydrogen cable as our con
struction material.

  Mars is especially nice. The altitude of a stationary orbit is only half that of the Earth. We can make a beanstalk there from currently available materials. The support length is 973 kilometers, and graphite whiskers comfortably exceed that.

  Naturally, the load-bearing cable is not the whole story. It is no more than the central element of a beanstalk that will carry materials to and from orbit. The rest of the system consists of a linear synchronous motor attached to the load-bearing cable. It will drive payloads up and down. Some of the power expended lifting a load is recovered when we lower a similar load back down to Earth. The fraction depends on the efficiency of conversion from mechanical to electrical energy.

  So far we have said nothing about actual construction methods. It is best to build a beanstalk from the top down. An abundant supply of suitable materials (perhaps a relocated carbonaceous asteroid) is placed in geostationary orbit. The load-bearing cable is formed and simultaneously extruded upward and downward, so that the total up and down forces are in balance. Anything higher than geosynchronous altitude exerts a net outward force, everything below geosynchronous orbit exerts a net inward force. All forces are tensions, rather than compressions. This is in contrast to what we may term the "Tower of Babel" approach, in which we build up from the surface of Earth and all the forces are compressions.

  After extruding 35,770 kilometers of cable downward from geostationary orbit, and considerably more upward, the lower end at last reaches the Earth's equator. There it is tethered, and the drive train added. The beanstalk is ready for use as a method for taking payloads to geosynchronous orbit and beyond. A journey from the surface to geosynchronous height, at the relatively modest speed of 300 kilometers an hour, will take five days. That is a lot slower than a rocket, but the trip should be far more restful.