SINCE THE CAVE DWELLER first collided flint against flint to produce fire, natural philosophers have had to resort to ever higher energies in their quest to unlock nature's minutest secrets. The Superconducting Supercollider is the latest instrument to be brought to bear in the physicist's eternal search for truth, but with the site allocation already taken care of, it is long past time to look toward the next step in mankind's greatest journey. Since one can expect congressional fluctuations to obstruct the progress of science for some years to come, this month I wish to encourage proponents of small scale science-amateurs in particular-to grasp the torch and construct a Planck-mass accelerator.

The Planck mass, or Planck energy (the equivalence of mass and energy by E=mc² makes the terms interchangeable), is the largest energy that physics as now constituted can deal with in any sensible fashion. It is the energy an average particle had second after the big bang when the forces of quantum mechanics and gravity are thought to have been unified. A Theory of Everything, of which current superstring theories may be dim precursors, would explain the unification and in fact could be experimentally tested by a Planck-mass accelerator. In principle there is little difference between such a machine and its ancestors: protons or electrons are accelerated up to Planck energies and collided head on. During the collisions the projectiles convert their energy into Planck-mass particles, particles that existed at the earliest instants of creation. Boiled down to its essentials, a Planck-mass accelerator simulates the big bang.

Beside such a machine, existing accelerators pale into insignificance. Consider the proton. Its mass is about 10^-24 gram, orders of magnitude below the sensitivity of the best laboratory balances. Through E= mc² it harbors an equivalent energy of about one billion electron volts (or one gigaelectron volt, abbreviated GeV). The world's largest accelerator, Fermilab's Tevatron, can accelerate protons to energies of 2,000 GeV, now usually abbreviated as 2 TeV for two tera electron volts. The Tevatron, then, can impart to protons about 2,000 times their rest mass in energy. If two such protons are collided together in the Tevatron, the energy can be used to create new particles with masses of approximately 10^-21 gram, still far below the sensitivity of any laboratory balance. The Superconducting Supercollider (ssc) is designed for 20-TeV operation, only 10 times higher than Tevatron energies.

Cosmic rays do somewhat better: the highest-energy cosmic rays, believed to be produced by astronomical objects such as Cygnus X-3, are measured at roughly 10⁶ TeV. Particles created in cosmic-ray collisions would weigh in at about l0^-15 gram.

Grand unified theories (GUT's), however, which profess to combine the strong, weak and electromagnetic forces into one strong-electroweak force, are thought to begin operating at about 10¹² TeV. This is a million times higher than the most energetic cosmic rays and 100 billion times higher than the expected attainments of the ssc.

Still, we are going for the Max. The Planck energy, where the Theory of Everything is presumed to come into play, corresponds to approximately l0¹⁶ TeV. This is 10 billion times more energetic than the most energetic cosmic ray. It is 1,000 trillion times more energetic than the particles that will be produced by the ssc. It corresponds to a mass of about 1O^-5 gram, which can be measured on today's laboratory balances.

The first and most difficult step in building the Planck-mass accelerator is finding a name for it. The Superconducting Supercollider has already overburdened the growing list of endeavors anointed with the adjective "super" (now elevated to the rank of nonhyphenated prefix): superconductors, supersymmetry, superparticles, superstrings, supercomputing centers and Supertuesdays. The Superconducting Supercollider has even managed to usurp two supers in as many words and has acquired a three-initial abbreviation in the bargain.

It is certainly easy to be sympathetic: the ssc will be 87 kilometers in circumference and will cost $5 billion (barring overruns). Still, all this is vaguely unsatisfactory. "Super" in the context of accelerators has very much the same ring as the term "postmodern" in literature. What does "post modern" become after 10 years? If an accelerator designed for 20 TeV is to be anointed with the adjective "super," then in the next generation we shall be forced to go to "Hypercollider," and then no doubt to "Superhypercollider" and "Hypercolossalcollider,' at which point accelerator naming begins to sound like Sneak Previews. Clearly what is super today is superfluous tomorrow. Therefore for the Planck-mass accelerator I suggest "Ultimate Collider," or uc. Modest though two initials may be to describe a ma chine of 10¹⁶ TeV, it will have to do; a I have said, according to our present conceptions of space and time, it does not make any sense to talk about anything larger.

The second step in designing the uc is to consider what kind of power source will be needed to accelerate protons or electrons up to the Planck energy and create Planck-mass particles. A simple arithmetic calculation reveals the first obstacle: the entire energy of a one-megaton atomic bomb converted into planckons (as I shall call them) will produce about three million. Three million planckons may seem like a lot, but it is negligible compared with the beam intensities achieved by today's accelerators. Machines such as Fermilab's Tevatron are typically capable of delivering 10¹² to 1O¹³ particles per second to the target. Consequently, to achieve today's beam intensities, the amateur will need the energy equivalent of roughly a million one-megaton bombs exploding per second.

This computation assumes, obviously, that 100 percent of the energy of the atom bomb goes into making planckons,

which is overly optimistic. The actual efficiency of present-day accelerators is difficult to judge. A beam intensity of 1013 particles per second at an energy of 20 TeV represents a power of about 30 megawatts. If, as planned, a 300-megawatt power plant is to be built for the ssc, a 10¹³ particle-per-second beam intensity implies an efficiency of 10 percent; the rest is lost to refrigeration of the magnets, transmission lines and so on. If the beam intensity is only 10¹² particles per second, the ssc will be about 1 percent efficient. Of course, with room-temperature superconductors (which the do-it-yourselfer can fashion empirically in the kitchen) refrigeration losses can be considerably reduced, if not eliminated entirely.

Nevertheless, I want to be on the safe side, and so I shall assume that the prototype uc will have an efficiency of only 1 percent. With a 1 percent efficiency, the power source for the uc will have to provide the equivalent of 100 million one-megaton bombs per second during operations. This is far above the megatonnage available in today's arsenals.

It does correspond, however, to approximately 4 x 10³⁰ ergs per second, or only about a thousandth the luminosity of the sun, which is well within the range of a science-oriented society. The amateur, then, should begin by placing a system of solar collectors in orbit around the sun. If they are placed at the radius of Mercury's orbit, the combined collection area should be at least 4 x 10¹³ square kilometers, about 660 times the surface area of Jupiter. The solar energy should then be transformed into microwaves, for example, and beamed to the accelerator proper. A large capacitor bank is recommended, for it will significantly reduce the required collection area. (Canal Street in Manhattan has traditionally been a good hunting ground for junk parts.)

Having solved the problem of energy supply, the next task is to look into the design of the accelerator itself. Today's machines are predominantly of two types: linear accelerators, or linacs, and synchrotrons. As its name implies, a linear accelerator accelerates particles along a straight line. The world's largest linac currently is the Stanford Linear Accelerator-universally known as SLAC-with a length of three kilometers. The way a linac accelerates electrons, say, is fairly straightforward. A high-frequency alternating electric field, at approximately 1,000 megahertz, is passed down a microwave guide. The phase of the field is arranged so that it will push the electrons down the cavity. In other words, the electron is accelerated by getting it to ride the crest of a wave. A linac has the disadvantage that it can accelerate a particle only once-from beginning to end. The final energy of the particle is limited by the amount of energy the accelerator can impart to it on a single pass.

In contrast, a synchrotron accelerates particles repeatedly around a single circular track. Synchrotrons are thus capable of much higher energies for a given length than the linear accelerator is, and largely for this reason the ssc has been designed as a synchrotron. It will also utilize an increasingly popular technique known as colliding beams, which is why "collider" follows the second "super" in ssc. According to relativity, the energy available to create new particles is much greater when two protons or two electrons collide head on than it is when they hit a stationary target in the laboculates two beams of protons in opposite directions until they attain the required energy and then forces them into a head-on collision. In the ssc the full 40 TeV of the two protons is then available to create new particles, each with an energy of 20 TeV. For a noncolliding-beam synchrotron to yield a pair of 20-TeV particles from a single proton smashing into a laboratory target, it would have to accelerate the proton to an energy of approximately 800,000 TeV.

For that reason colliding-beam synchrotrons are now considered the wave of the future. Unfortunately simple considerations show that synchrotrons-be they stationary-target or colliding-beam-cannot be the basis of the Ultimate Collider (without significant difficulties); the amateur is urged to avoid them.

According to a century-old result of Maxwell's theory of electromagnetism, any accelerating charged particle radiates energy. One of the basic problems any accelerator designer faces is knowing how much energy the electrons will lose as they hurtle down SLAC's vacuum chamber, or how much energy protons will give off as they circulate in the ssc's storage rings. Left to themselves, these circulating protons would sooner or later radiate away all their energy and stop. And so some fraction of the energy input of an accelerator simply goes into replacing the energy the particles lose as they are accelerated.

The amount of energy lost in an accelerator depends very crucially on the design. Synchrotrons are prey to an illness appropriately termed synchrotron radiation: the radiation emitted by any charged particle in a circular orbit. In Cornell Universities 10GeV synchrotron, a 10.5-MeV boost is given to an electron on each turn, but the losses from synchrotron radiation on each turn are about 8.85 MeV. And so, you see, at high energies most of the energy goes not into accelerating particles but into making up radiation losses. Unfortunately synchrotron radiation goes up as (E/m)⁴, where E is the particle energy and m is its rest mass-in other words, very rapidly. By the time you reached only 10⁴ TeV- 5,000 ssc energies-an electron circulating in a synchrotron of 100-kilometer radius would be radiating away a Planck mass of energy on every turn.

Radiation losses are, however, inversely proportional to the radius of the accelerator; an obvious strategy, then, is to make the radius of the accelerator larger. This is not very feasible. The radius necessary to keep a Planck-energy electron radiating at less than one Planck energy per turn is roughly 10²⁷ times the size of the observable universe.

Because synchrotron radiation losses go as (E/m)⁴, such losses are less severe for protons, which are much heavier than electrons. Specifically, the proton is almost 2,000 times more massive than the electron, and so at a fixed energy synchrotron radiation losses are about 10¹³ times less. But the factor of E⁴ means that once a proton is accelerated to an energy 2,000 times higher than that of an electron, radiation losses will be the same: in an accelerator with a radius of 100 kilometers, at about 10⁷ TeV radiation losses exceed one Planck mass per turn. To keep the radiation losses from Planck-energy protons within acceptable bounds, one would need to construct a synchrotron with a radius 10¹⁴ times the size of the observable universe.

Luckily for the amateur, there is a solution to the problem. Radiation losses in a linear accelerator turn out to be vastly less severe than those associated with synchrotrons. In a linac the power lost to radiation can always be kept below the input power simply by keeping the energy given to the electrons below the order of 10⁶ TeV per centimeter. SLAC provides an "energy gradient" of roughly 10^-7 TeV per centimeter, which is 13 orders of magnitude below the upper bound. Protons, because they are heavier, are again subjected to a less stringent limit, in this case about 10¹³ TeV per centimeter.

And so there we are. To be conservative, the Ultimate Collider prototype should be constructed as a linac. As long as we keep the energy gradient below the limit of 10⁶ TeV per centimeter, we can attain arbitrarily high energies. What is more, we want to make it a colliding linac-two linear accelerators run in opposite directions to capitalize on the full energy available in head-on collisions.

The first obvious feasibility test is to scale up SLAC to Planck energies. At 10^-7 TeV per centimeter, however, this calls for an accelerator 100,000 lightyears long, somewhat greater than the size of the galaxy. A collider would be twice as long, with the laboratory area presumably at the center. Such unwieldy proportion makes data collection inconvenient; an experimenter after throwing the "on" switch, would have to wait 200,000 years for the results.

Again we are saved by the fact that radiation losses in linacs are so small. If we choose to construct a machine with an energy gradient of 100 TeV per centimeter-still far below the limit of 10⁶ TeV per centimeter-the length of the uc is reduced enough so that it would fit within the orbit of Pluto. At first glance an energy gradient of 100 TeV per centimeter-which is one billion times as large as the gradient at SLAC-strikes one as large, if not impossible. SLAC'S accelerating field is produced by a bank of more than 200 high-frequency oscillators known as klystrons, and they produce about the maximum gradient attainable by conventional methods. The thought of increasing 200 klystrons to 200 billion does not seem very fruitful.

But the klystron is not the only device capable of generating large amounts of power. The highest power available today actually comes from lasers. Even a commercially available CO₂ laser can result in gradients 10 times as high as those at SLAC, and the HELIOS laser at the Los Alamos National Laboratory is already up by a factor of 1,000. Some investigators are now talking about future laser-driven machines with gradients of 10^-4 TeV per centimeter, only a million times less than our goal.

At this stage the amateur must overcome a serious obstacle. Electrons are bound to atoms with energies of about 10 electron volts. Atomic dimensions are of order 10^-3 centimeter. One therefore expects that field gradients larger than, say, 10 eV per 10^-3 centimeter will tear electrons from their nuclei. In terms of our units this upper limit is about 10^-3 TeV per centimeter, about 100 times larger than the smc gradient. Even smaller values-values too small for the uc by a factor of 100,000 or one million- would without doubt cause serious damage to the accelerator's support structure.

The amateur must therefore look to new media to construct the Ultimate Collider. One promising device is a laser-plasma accelerator [see "Plasma Particle Accelerators," by John M. Dawson; SCIENTIFIC AMERICAN, March]. In plasmas, or highly ionized gases, electrons are already detached from their nuclei and so they cannot be further disrupted. Accelerating fields in experimental "beat wave" accelerators have already reached 10^-5 TeV per} centimeter; 10^-2 TeV per centimeter is, theoretically possible with currently , attainable plasma densities, which are obtained from hydrogen. This is only 10,000 times below what is required for the prototype uc. Going to denser materials, such as platinum, would increase the acceleration gradient to about a TeV per centimeter, or about 100 times below the goal. White-dwarf or neutron-star material, which is on the order of 10,000 times denser than platinum, could yield plasma densities and gradients that exceed the required magnitude.

The accelerating chambers of present plasma accelerators are only several millimeters long at best. Consequently the amateur will probably have to run a number of machines in "tandem" in order to produce the required energy.

Based on this picture, for the uc prototype one can imagine the rotating neutron star in Cygnus X-3-which spews out 10⁶ TeV cosmic rays-harnessed to serve as a booster for the main accelerator (although I am not sure this would be very cost effective). A string of giant lasers stretching across the solar system would then take the particles up to the Planck energy. Admittedly this is an unwieldy prototype, but the creative amateur will no doubt find acceleration mechanisms that are even more efficient than the plasma accelerator and is encouraged to pursue them. EventualIy, of course, one will want to go for the theoretical limit of 10⁶ TeV per centimeter, at which a fully operational electron UC would be only 10¹⁰ centimeters long-about a fourth of the distance to the moon. A proton collider could be shorter by a factor of several million-for an accelerator length of order 10 meters.

The final question remains: funding. At the projected ssc price of $250 million per TeV, the uc would cost only $2.5 x 10²⁴, something more than the U.S. budget deficit (actually about 10¹¹ times the gross world product) but already a bargain considering potential spin-offs. Surely, though, one can expect that with increased technological sophistication this cost will decrease to give us the ultimate in big bangs for the buck. In any case, one cannot put a price tag on the philosophical benefit and change in world outlook that such a project will give to our grandchildren and our grandchildren's grandchildren, for with the help of the Ultimate Collider they will have the best chance of understanding the Moment of Creation.

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