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Build the ultimate particle collider in YOUR solar system!
THE AMATEUR SCIENTIST
How to build a Planck-mass accelerator in your solar system.
by Antoni Akahito
Since the cave dwellers 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=mc.sup.2 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 10.sup.43 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 Panck-mass accelerator
simulates the big bang.
Beside such a machine, existing accelerators pale into insignificance.
Consider the proton. Its mass is about 10.sup.-24 gram, orders of
magnitude below the sensitivity of the best laboratory balances.
Through E=mc.sup.2 it harbors an equivalent energy of about one
billion electron volts (or one giga electron 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.sup.-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 10.sup.6 TeV. Particles created in cosmic-ray
collisions would weigh in at about 10.sup.-15 gram.
Grand unified theories (GUT'S), however, which profess to combine the
strong, weak and electromagnetic forces into one strong-electroweak
forces, are thought to begin operating at about 10.sup.12 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 10.sup.16 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 10-5 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
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. "Superc in the context of
accelerators has very much the same ring as the term "postmodern" in
literature. What does "postmodern" 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 machine of 10.sup.16 TeV, it will have to do; as 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 10.sup.12 to
10.sup.13 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 10.sup.13 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
10.sup.13 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 10.sup.12
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
It does correspond, however, to approximately 4 X 10.sup.30 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 10.sup.13 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
laboratory. A proton collider therefore circulates 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 non-colliding-beam synchrotron to
yield a pair of 20 TeV particles from a single proton smashing into
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 University's 10-GeV 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).sup.4, where E is
the particle energy and m is its rest mass--in other words, very
rapidly. By the time you reached only 10.sup.4 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 10.sup.27 times the size of the
Because synchrotron radiation losses go as (E/m).sup.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 10.sup.13 times less. But the factor of E.sup.4 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 10.sup.7 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 10.sup.14 times the size of the
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 10.sup.6 TeV per
centimeter. SLAC provides an "energy gradient" of roughly 10.sup.-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 10.sup.13 TeV per centimeter.
And so there were 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 10.sup.6 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.sup.-7 TcV per centimeter, however, this calls for an
accelerator 100,000 light-years 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 10.sup.6 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
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 CO.sub.2 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.sub.-4 TeV per centimeter, only a
million times less than our goal.
At this stage the amateur must overcome a seriius obstacle. Electrons
are bound to atoms with energies of about 10 electrons volts. Atomic
dimensions are of order 10.sub.-8 centimeter. One therefore expects
that field gradients larger than, say, 10 eV per 10.sub.-8 centimeter
will tear electrons from their nuclei. In terms of our units this
upper limit is about 10.sup.-3 TeV per centimeter, about 100 times
larger than the SLAC 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.sup.-5 TeV per centimeter;
10.sup.-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 amateu 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 10.sup.6 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. Eventually, of course, one will
want to go for the theoretical limit of 10.sup.6 TeV per centimeter,
at which a fully operational electron UC would be only 10.sup.10
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 10.sup.24.,
something more than the U.S. budget deficit (actually about 10.sup.11
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
grandchildrenhs 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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