Physicists use particle accelerators to explore matter on the smallest scale.
Charged particles such as electrons or protons are accelerated by an electric field to speeds almost equal to the speed of light. They are made to collide with one another and in such collisions some of the kinetic energy is turned into matter - new particles are created.
The simplest particle accelerator is the electron gun. The electrons are produced by heating a cathode. The electrons 'boil' off from the cathode and are accelerated towards an anode with a small hole in it. Many of the electrons pass through the hole forming an electron ray (cathode ray). The energy of the electrons is found using Energy = eV.
Electron guns are useful for producing electrons of relatively low energy for laboratory work. There are two designs of particle accelerators used for producing particles of a much higher energy for research purposes: the linear accelerator and cyclotron.
In a linear accelerator (LINAC) the charged particles are accelerated in a straight line (whereas in a circular accelerator magnetic fields are used to move the particles in a circular trajectory - see the cyclotron next). The diagram below shows the principle of operation of a LINAC.
An alternating p.d. is connected across adjacent cylindrical electrode tubes. Charged particles are accelerated across the gaps between electrodes. By the time the particle reaches the next gap the polarity of electric field has reversed and so the particle is accelerated once more.
LINACs have an important advantage over circular accelerators. When a charged particle is moved in a circular path it radiates energy (synchrotron radiation) so that a lot of the input energy is wasted. There is no such waste in a linear accelerator. However, the length of a LINAC limits the energy achieved.
One of the most powerful linear accelerators is located at the Stanford Linear Accelerator Centre, California. This accelerator is 3km long and accelerates electrons up to an energy of 50 GeV.
The length limitation can be overcome by making the charged particles follow a circular path. In a cyclotron charged particles are accelerated across the gap between two 'D' shaped electrodes. Meanwhile a perpendicular magnetic field moves the particles in a circle. The radius of the circle increases after each successive acceleration, so the path spirals out from the source at the centre to the target on the outside.
We will now derive the unique frequency f at which the accelerating voltage must alternate if the polarity of the D's is to reverse each time the charged particle reaches the gap.
Force on charge q moving at velocity v perpendicular to mag. field of strength B is:
F = Bqv
This provides the centripetal force necessary for circular motion, so:
The time for orbit is therefore:
Thus the frequency of the a.c. (cyclotron resonance frequency) is:
So F is constant if Bm q and m do not alter and independent of v and r.
The relatively small size of cyclotrons makes them useful for producing energetic particles for medical treatments and testing advanced industrial materials. As the speed of the particles approaches that of light, however, the relativistic mass increase becomes significant and this results in the charges arriving too late to be accelerated across the gap. This puts a limit of about 1 GeV on the energy achievable.
Synchrotrons overcome this problem: the frequency of the alternating voltage increases to match the flight time of the particles. In a synchrotron an increasing magnetic field confines a beam of accelerated charged particles to an orbit of fixed radius. Synchrotrons are very large and very expensive machines but they are capable of much higher energies than cyclotrons.
The mass spectrometer was developed in the early part of the last century to determine the comparative masses of ionised atoms and, later, the relative abundances of isotopes. It works using many of the principles described above for the particle accelerators described above. The simplified diagram below shows the main parts of a mass spectrometer.
The device vaporises a sample under study (A) and then ionises the atoms with a beam of electrons (B). The ions are then accelerated by an electric field (C) and pass through a velocity selector to ensure that they are all moving at the same velocity (D). In the separation chamber (E) the ions are subjected to a magnetic field acting into the plane of the diagram. This field forces the ions into circular paths of radius given by
Where M is the mass of the ion, q is its charge, B is the magnetic field strength, r is the radius of the ion's path and v is the ion's velocity.
In practise the ions are all given the same charge, and as the velocity selector ensures that they all move with same speed (in the same magnetic field), the radius of the ion's path is proportional to its mass. If, for example, the source contained the two neon isotopes 22Ne and 20Ne two signals would be detected. The signal from the 20Ne would be closer to the source than the 22Ne.
The mass spectrometer is similar to the LINAC in the way that it accelerates ions. It is also similar to the cyclotron in its used of a magnetic field to produce a circular orbit for the charged particles but of course the particles do not complete any orbits or gain any energy in the separation chamber.
In the late 1970s, the physicists at CERN (European Nuclear Research Centre) came up with a brilliant idea. If you could fire two particles in opposite directions and make them collide, you would effectively double the available energy at a stroke without increasing the maximum kinetic energy of the particles. This is the principle behind the large electron-positron collider (LEP) and in the proton-antiproton super proton synchrotron at CERN. The forces used to accelerate and bend the particles and antiparticles have the same effect on both but they act in opposite directions.
But why are physicists so obsessed with using larger and larger energies?
In order to probe an object you must use waves with a wavelength similar in size to the size of the object under examination. The de Broglie relation allows us to find the wavelength of a particle of a given energy as shown below.
As you can see the wavelength of a particle is inversely proportional to its energy. If you want particles of a very small wavelength (suitable for probing the tiniest pieces of matter) you need very high energies.
The Tevatron at Fermilab is one of the most powerful synchrotrons in the world. It has a circumference of 6km and accelerates protons and antiprotons to 1000 GeV (1 TeV). Calculate the wavelength of the protons produced by this machine. (h = 6.6 x 10-34 Js, c = 3.0 x 108ms-1, e = 1.6 x 10-19 C)