Learning Objectives

By the end of this section, you will be able to do the following:

State the principle of a cyclotron
Explain the principle of a synchrotron
Describe the voltage needed by an accelerator between accelerating tubes
State Fermilab's accelerator principle

The information presented in this section supports the following AP® learning objectives and science practices:

1.C.4.1 The student is able to articulate the reasons that the theory of conservation of mass was replaced by the theory of conservation of mass-energy. (S.P. 6.3)
4.C.4.1 The student is able to apply mathematical routines to describe the relationship between mass and energy and apply this concept across domains of scale. (S.P. 2.2, 2.3, 7.2)
5.B.11.1 The student is able to apply conservation of mass and conservation of energy concepts to a natural phenomenon and use the equation E= mc² to make a related calculation. (S.P. 2.2, 7.2)

Before looking at all the particles we now know about, let us examine some of the machines that created them. The fundamental process in creating previously unknown particles is to accelerate known particles, such as protons or electrons, and direct a beam of them toward a target. Collisions with target nuclei provide a wealth of information, such as information obtained by Rutherford using energetic helium nuclei from natural $α$ radiation. But if the energy of the incoming particles is large enough, new matter is sometimes created in the collision. The more energy input or $Δ E,$ the more matter $m$ can be created, since $m = Δ E / c^{2} .$ Limitations are placed on what can occur by known conservation laws, such as conservation of mass-energy, momentum, and charge. Even more interesting are the unknown limitations provided by nature. Some expected reactions do occur, while others do not, and still other unexpected reactions may appear. New laws are revealed, and the vast majority of what we know about particle physics has come from accelerator laboratories. It is the particle physicist's favorite indoor sport, which is partly inspired by theory.

Early Accelerators

An early accelerator is a relatively simple, large-scale version of the electron gun. The Van de Graaff—named after the Dutch physicist—which you have likely seen in physics demonstrations, is a small version of the ones used for nuclear research since their invention for that purpose in 1932. For more, see Figure 16.7. These machines are electrostatic, creating potentials as great as 50 MV, and are used to accelerate a variety of nuclei for a range of experiments. Energies produced by Van de Graaffs are insufficient to produce new particles, but they have been instrumental in exploring several aspects of the nucleus. Another, equally famous, early accelerator is the cyclotron, invented in 1930 by the American physicist, E. O. Lawrence (1901–1958). For a visual representation with more detail, see Figure 16.8. Cyclotrons use fixed-frequency alternating electric fields to accelerate particles. The particles spiral outward in a magnetic field, making increasingly larger radius orbits during acceleration. This clever arrangement allows the successive addition of electric potential energy and so greater particle energies are possible than in a Van de Graaff. Lawrence was involved in many early discoveries and in the promotion of physics programs in American universities. He was awarded the 1939 Nobel Prize in Physics for the cyclotron and nuclear activations, and he has an element and two major laboratories named for him.

A synchrotron is a version of a cyclotron in which the frequency of the alternating voltage and the magnetic field strength are increased as the beam particles are accelerated. Particles are made to travel the same distance in a shorter time with each cycle in fixed-radius orbits. A ring of magnets and accelerating tubes, as shown in Figure 16.9, are the major components of synchrotrons. Accelerating voltages are synchronized—occur at the same time—with the particles to accelerate them, hence the name. Magnetic field strength is increased to keep the orbital radius constant as energy increases. High-energy particles require strong magnetic fields to steer them, so superconducting magnets are commonly employed. Still limited by achievable magnetic field strengths, synchrotrons need to be very large at very high energies, since the radius of a high-energy particle's orbit is very large. Radiation caused by a magnetic field accelerating a charged particle perpendicular to its velocity is called synchrotron radiation in honor of its importance in these machines. Synchrotron radiation has a characteristic spectrum and polarization, and can be recognized in cosmic rays, implying large-scale magnetic fields acting on energetic and charged particles in deep space. Synchrotron radiation produced by accelerators is sometimes used as a source of intense energetic electromagnetic radiation for research purposes.

The image shows a table-top-sized electrical machine. It has a cubic base out of which comes a clear vertical tube about half-a-meter long. Inside the tube a conveyer belt is seen running up and down the tube. On top of the tube is a metallic sphere maybe thirty centimeters in diameter.

Figure 16.7 An artist's rendition of a Van de Graaff generator.

The image shows a disc-shaped cyclotron consisting of two horizontal semicircular plates that are separated by a gap. An alternating voltage is put across the gap, and an electric field is shown going from the left semicircular plate across the gap to the right semicircular plate. A magnetic field pierces the plates from top to bottom. A dotted line labeled external beam spirals outward from the center of the cyclotron, making four revolutions inside the semicircular plates before reaching the outer edge

Figure 16.8 Cyclotrons use a magnetic field to cause particles to move in circular orbits. As the particles pass between the plates of the Ds, the voltage across the gap is oscillated to accelerate them twice in each orbit.

Modern Behemoths and Colliding Beams

Physicists have built ever-larger machines, first to reduce the wavelength of the probe and obtain greater detail, then to put greater energy into collisions to create new particles. Each major energy increase brought new information, sometimes producing spectacular progress, motivating the next step. One major innovation was driven by the desire to create more massive particles. Since momentum needs to be conserved in a collision, the particles created by a beam hitting a stationary target should recoil. This means that part of the energy input goes into recoil kinetic energy, significantly limiting the fraction of the beam energy that can be converted into new particles. One solution to this problem is to have head-on collisions between particles moving in opposite directions. Colliding beams are made to meet head-on at points where massive detectors are located. Since the total incoming momentum is zero, it is possible to create particles with momenta and kinetic energies near zero. Particles with masses equivalent to twice the beam energy can thus be created. Another innovation is to create the antimatter counterpart of the beam particle, which thus has the opposite charge and circulates in the opposite direction in the same beam pipe. For a schematic representation, see Figure 16.10.

The first image shows a circular ring made up of about thirty blue tubes whose diameters are much less than the diameter of the ring. The tubes are arranged end-to-end, so that a line joining their axes forms the ring. The second image shows a close-up view of three consecutive tubes, which we shall call tubes one, two, and three. Tube one is labeled plus, tube two is labeled minus, and tube three is labeled plus. An arrow labeled E points from tube one to tube two, and between these two tubes is a sphere

Figure 16.9 (a) A synchrotron has a ring of magnets and accelerating tubes. The frequency of the accelerating voltages is increased to cause the beam particles to travel the same distance in shorter time. The magnetic field should also be increased to keep each beam burst traveling in a fixed-radius path. Limits on magnetic field strength require these machines to be very large in order to accelerate particles to very high energies. (b) A positive particle is shown in the gap between accelerating tubes. (c) While the particle passes through the tube, the potentials are reversed so that there is another acceleration at the next gap. The frequency of the reversals needs to be varied as the particle is accelerated to achieve successive accelerations in each gap.

On the left side of the image is a pair of equal-diameter, horizontal rings, with one labeled proton source and the other labeled anti proton source. The rings look like they are made of a hose; that is, their cross section is circular and they appear hollow. In the proton-source ring blue arrows appear indicating counterclockwise motion inside the hose. In the anti-proton-source ring, red arrows appear indicating clockwise motion inside the hose. A section of hose tangentially leaves each ring to tangent

Figure 16.10 This schematic shows the two rings of Fermilab's accelerator and the scheme for colliding protons and antiprotons, not to scale.

Detectors capable of finding the new particles in the spray of material that emerges from colliding beams are as impressive as the accelerators. While the Fermilab Tevatron had proton and antiproton beam energies of about 1 TeV, so that it can create particles up to $2 TeV/ c^{2},$ the Large Hadron Collider (LHC) at the European Center for Nuclear Research (CERN) has achieved beam energies of 3.5 TeV, so that it has a 7-TeV collision energy; CERN hopes to double the beam energy in 2014. The now-canceled Superconducting Super Collider was being constructed in Texas with a design energy of 20 TeV to give a 40-TeV collision energy. It was to be an oval 30 km in diameter. Its cost as well as the politics of international research funding led to its demise.

In addition to the large synchrotrons that produce colliding beams of protons and antiprotons, there are other large electron-positron accelerators. The oldest of these was a straight-line or linear accelerator, called the Stanford Linear Accelerator (SLAC), which accelerated particles up to 50 GeV as seen in Figure 16.11. Positrons created by the accelerator were brought to the same energy and collided with electrons in specially designed detectors. Linear accelerators use accelerating tubes similar to those in synchrotrons, but aligned in a straight line. This helps eliminate synchrotron radiation losses, which are particularly severe for electrons made to follow curved paths. CERN had an electron-positron collider appropriately called the Large Electron-Positron Collider (LEP), which accelerated particles to 100 GeV and created a collision energy of 200 GeV. It was 8.5 km in diameter, while the SLAC machine was 3.2 km long.

The schematic shows a linear accelerator about three kilometers long with magnets along its path. Electrons and positrons coming from different sources are accelerated down the linear accelerator, then are deviated by magnets to the right and left, respectively, to follow paths that circle around to meet head-on at a large device labeled mark two particle detector.

Figure 16.11 The Stanford Linear Accelerator was 3.2 km long and had the capability of colliding electron and positron beams. SLAC was also used to probe nucleons by scattering extremely short wavelength electrons from them. This produced the first convincing evidence of a quark structure inside nucleons in an experiment analogous to those performed by Rutherford long ago.

Example 16.2 Calculating the Voltage Needed by the Accelerator Between Accelerating Tubes

A linear accelerator designed to produce a beam of 800-MeV protons has 2,000 accelerating tubes. What average voltage must be applied between tubes—such as in the gaps in Figure 16.9—to achieve the desired energy?

Strategy

The energy given to the proton in each gap between tubes is ${PE}_{elec} = qV$ where $q$ is the proton's charge and $V$ is the potential difference, or voltage, across the gap. Since $q = q_{e} = 1.6 \times 10^{- 19} C$ and $1 eV = (1 V) (1.6 \times 10^{- 19} C)$ , the proton gains 1 eV in energy for each volt across the gap that it passes through. The AC voltage applied to the tubes is timed so that it adds to the energy in each gap. The effective voltage is the sum of the gap voltages and equals 800 MV to give each proton an energy of 800 MeV.

Solution

There are 2,000 gaps and the sum of the voltages across them is 800 MV; thus,

16.6

V_{gap} = \frac{800 MV}{2,000} = 400 kV .

Discussion

A voltage of this magnitude is not difficult to achieve in a vacuum. Much larger gap voltages would be required for higher energy, such as those at the 50-GeV SLAC facility. Synchrotrons are aided by the circular path of the accelerated particles, which can orbit many times, effectively multiplying the number of accelerations by the number of orbits. This makes it possible to reach energies greater than 1 TeV.

16.3 Accelerators Create Matter from Energy

16.3 Accelerators Create Matter from Energy

Learning Objectives