Beyond the God Particle (28 page)

However, there is another and very important thing we can do: by cleverly using magnetic fields to bend charged beam particles in a circle, we can build a much higher energy particle accelerator than a linac that is more compact in size and therefore usually less expensive. Such circular machines, called cyclotrons and synchrotrons, exploit circular orbits of charged particles moving in magnetic fields to cause the particles to pass many times through the same RF cavity and receive many kicks in energy. The magnetic field simply holds the particle in its circular orbit.

As the beam particle's energy increases, and if the magnetic field is held constant, the particle will stray into a larger and larger radius orbit. To hold the particles in the same orbit, the magnetic field must also increase with the beam energy. This is the principle of a particle accelerator called a
synchrotron
. As there are limits to the highest electric fields we can create, there are also limits to how large a magnetic field we can create. This translates into the requirement of very large-diameter circular orbits for very high-energy particles. For example, the Tevatron achieved a 1 TeV (one trillion electron volts) beam energy for protons and antiprotons, and was a circular ring about 1 mile in diameter; the LHC is designed to achieve a 7 TeV beam particle energy, uses slightly stronger magnets, but is about 5.3 miles in diameter.

ELECTRIC CURRENTS PRODUCE MAGNETIC FIELDS

As we've seen, electric fields are generated
by electric charges and cause electric charges to accelerate. Likewise, magnetic fields are generated by electric currents, and they in turn cause electric currents to deflect in direction or move in a circle.

Moving electric charges are called electric currents. André-Marie Ampère discovered that magnetic fields are produced by electric currents, and that electric currents are affected by magnetic fields.
¹²
Electric charges that are not moving do not produce magnetic fields and are not affected by them. Electric currents in matter, such as in copper or aluminum wire, consist of the most loosely bound electrons moving through the material to produce the current. As far as the electric charge goes, this is an electrically neutral situation—all positive electric charges are sitting at rest, such as the atomic nuclei with most of the electrons remaining attached to the atoms. The looser electrons can be coaxed to move through the material by a battery and become an electric current. The stationary charges associated with the atoms do nothing but keep the material electrically neutral, so that the net electric charge of the material is zero even though it may be carrying a large electric current.

In a simple experiment, two wires with constant electrical currents flowing in them, when placed parallel and near to each other, will be seen to attract or repel each other.
¹³
If the currents are moving in opposite directions, the wires repel each other; if they are moving in the same direction, the wires attract each other. This is a direct observation of the connection of magnetism to electrical currents. The wires are electrically neutral (no net electric charges, hence no electric fields are present), but it is the electric currents that produce the magnetic forces between the wires. One wire carrying a constant electrical current will also cause a compass needle to deflect.

The ancients, like many people today who are not familiar with magnetism, viewed it as a mysterious, almost magical, property of certain materials, such as iron or “lodestone” (which contains iron). The Chinese were the first to note the existence of magnetism and apply it to build a compass.
¹⁴

An electron by itself, unattached to an atom, produces its own tiny magnetic field due to its intrinsic spin. In most materials the electrons are paired, in opposite spins and opposite orbital motions, and the magnetic field of one electron is canceled by an opposite magnetic field produced by the other electron in the pair. The atoms in materials such as iron, cobalt, and nickel have unpaired electrons. As a result, though each atom of these
elements acts like a very small magnet, if all the magnetic fields of all the atoms are aligned together, the effects can add up to make a large macroscopic magnetic field. In iron, the little individual atomic magnets within the material interact with one another in such a way that they have a tendency to line up in a common direction. This forms a “magnetic domain,” in which clusters of millions of atoms align to produce a common magnetic field. Finally, with a little more coaxing, usually an external applied magnetic field, the domains themselves can be coaxed into alignment, and then you have a powerful magnetic field emanating from a bar of iron. The physics at the atomic level of all of this is quite subtle, complex, and an interesting subject to study—so, yes, in a sense magnetism is a mysterious and special property of certain materials, but it isn't magic.

FIGURE 8.31. Bar Magnet.
The magnetic field of a bar magnet.

The poles of a magnet are called north (N) and south (S). If a small iron bar magnet is hung from its middle by a string, it becomes a compass needle, and its N end will point northward, thus its S end points southward. The N end of a magnet will repel the N end of another magnet, S will repel S, but N and S attract each other. Hence, N and S are like positive and negative charges (we call N and S magnetic monopoles). However, we can never have an isolated N without, somewhere, having a compensating S; all magnets are therefore “dipoles,” i.e., having two opposite poles, with equal but opposite N and S. This is a consequence of the magnetic field being set up by electrical currents, rather than having magnetic charges, or “magnetic monopoles,” as their sources.
¹⁵
Either pole of a magnet will induce magnetization in a nearby magnetic material. Therefore, either pole can attract iron-containing objects, such as paper clips, because the magnet will induce magnetization in the paper clip. The paper clip becomes itself a temporary magnet, with its N pole facing an S pole, or vice versa.

If we arrange a flat white sheet of paper over a bar and sprinkle over the paper little iron filings, the filings will align with the magnetic field and allow us to visualize the magnetic field itself!
¹⁶

CYCLOTRONS

We'll only mention cyclotrons in passing, since they are rather passé in modern particle physics, and will instead refer the interested reader to the extant literature, e.g., search online for “cyclotrons” or see the
Wikipedia
entry.
¹⁷
The idea of a cyclotron is to accelerate charged particles but to hold them in circular spiral motion with a
constant magnetic field
. For example, we can inject particles into the center of a circular machine with a perpendicular magnetic field. We give the particles a little kick in energy, and they will move in a circle. Each time the particles complete one full turn, they are given another “kick” of energy from the same electric field, and then the cycle repeats. As the particle receives each kick in energy, it will tend to spiral outward into a circular orbit with a larger radius.

The cyclotron was invented in 1932 by Ernest Lawrence of the University of California, Berkeley, with much of the development in collaboration with his student, M. Stanley Livingston. The cyclotron was an
improvement over the linac of the 1920s, when it was invented, being more compact and cost-effective due to the circular repetitive acceleration process.

For several decades, cyclotrons were the best source of high-energy beams for nuclear physics experiments; several cyclotrons are still in use for this type of research. Cyclotrons are still actively used in medical applications to treat cancer and to produce radioactive isotopes for medical imaging. Ion beams from cyclotrons can be used, as in proton therapy, to penetrate the body and kill tumors by radiation damage, while minimizing damage to healthy tissue along their path. Cyclotron beams can be used to bombard other atoms to produce short-lived positron-emitting isotopes suitable for PET imaging.

SYNCHROTRONS

The most advanced circular accelerator, and the one used most commonly in particle physics, is the synchrotron. The first electron synchrotron was constructed by Edwin McMillan in 1945, although the principle had already been published in a Soviet journal by Vladimir Veksler.
¹⁸
The first proton synchrotron was designed by Sir Marcus Oliphant and built in 1952. Protons, and even muons, can be accelerated to very high energies in large rings without appreciable synchrotron radiation loss. The Large Hadron Collider and former Tevatron were both proton synchrotrons (the Tevatron also circulated and accelerated antiprotons in the opposite direction in the machine).

In a synchrotron, particles are held in a fixed circular orbit. Each time they complete a cycle in the machine they receive a kick of energy from RF cavities. As the energy of the particles increases, the magnetic field is also slightly increased to maintain the same orbit. This allows the vacuum beam pipe that contains the motion of the particles to be a very large circular shape, rather than a large disk, as in the cyclotron. The smaller cross-section beam pipe allows for the magnetic fields to be localized within the pipe. These factors allow us to build very high-energy machines that are far less expensive than cyclotrons or linacs.

Synchrotrons “hit a wall” when they are used to accelerate electrons.
Owing to its small mass, an electron tends to radiate photons copiously when placed in a circular orbit at high energies. This is called “synchrotron radiation.” To achieve high energies an electron synchrotron has to be quite large, or else most of the acceleration energy will be radiated away. The Large Electron–Positron Collider (LEP) at CERN that collided electrons with positrons was a synchrotron that occupied the large tunnel that today houses the LHC, with a diameter of about 5.3 miles. LEP pushed the limit of achievable synchrotron energy with a beam of electrons circulating in one direction and positrons in the other, each beam having about 100 GeV of energy per particle (hence 200 GeV total; LEP went a bit above this energy scale in its last days). Energies of about 45 GeV per particle create a total energy in the collision of 90 GeV, allowing direct production of the Z
⁰
boson. The synchrotron energy loss per orbit at LEP was about 0.2 percent. At the highest energies, about 100 GeV per beam, the electrons lost about 2 percent of their energy every time they orbited in the machine due to the synchrotron radiation. Synchrotron radiation itself is useful, however, in many applications, particularly in the study of chemical and biological reactions. Large circular electron machines are often designed to be sources of the high-energy photons from synchrotron radiation, or “synchrotron light sources.”
¹⁹

MAGNETIC LENSING

Recall that a lens can, ideally, focus all the photons that are moving parallel to the axis of the lens to a point. It turns out that we cannot make a magnetic field that focuses charged particles exactly like a lens. With a “quadrupole magnet,” however, we can focus the electrons that are moving in one plane—let's say the “horizontal plane,” but then we end up defocusing by the same amount in the perpendicular, or vertical plane. If we rotate the quadrupole about its axis by 90
^o
we will get exactly the opposite: particles in the vertical plane are now focused, while those in the horizontal plane are defocused.
²⁰

However, here we exploit the fabulous trick that was used by microscope and telescope lens makers to correct for chromatic aberration. We can have one quadrupole that focuses (defocuses) in the horizontal (vertical)
plane, followed by a second quadrupole, rotated by 90 degrees, that that focuses (defocuses) in the vertical (horizontal) plane. However, recall that when a focus lens (F) is followed by some space (O), which is then followed by defocus (D) and more space (O), the net effect is to focus. That is, a compound lens that is focus-space-defocus-space, or “FODO,”
is net focusing
(see
figure 7.27
caption)! We can therefore keep a tightly focused beam orbiting within our synchrotron by repeating this arrangement: FODOFODOFODO…. This technique is called
alternate gradient focusing
. This was the breakthrough that led to large synchrotrons, such as the first Alternating Gradient Synchrotron (AGS) at Brookhaven National Laboratory, then eventually to the Tevatron and LHC.
²¹

Synchrotrons are unable to accelerate particles from rest, and they require a sequence of pre-acceleration stages. This can be done by a chain of other accelerators, like linacs or other smaller synchrotrons, and an initial kick from something simpler, like a high voltage.