Friday, May 18, 2012

Physics Context: Special Relativity in the Design of Particle Accelerators

I hear some questions of some students in a Senior High School when a teacher teach about the Special Relativity of Einstein."What is the use of this consept?" So, I want to ask that student back, if it was my chance, I'll say what do you think? You do not know? Are you realy want to know? Let's check it out!
One of the use of the Special Relativity is in the application of "Particle Accelerator". Particle accelerator, any device that produces a beam of fast-moving, electrically charged atomic or subatomic particles. Physicists use accelerators in fundamental research on the structure of nuclei, the nature of nuclear forces, and the properties of nuclei not found in nature, as in the transuranium elements and other unstable elements. Accelerators are also used for radioisotope production, industrial radiography, radiation therapy, sterilization of biological materials, and a certain form of radiocarbon dating. The largest accelerators are used in research on the fundamental interactions of the elementary subatomic particles.

Particle accelerators exist in many shapes and sizes (even the ubiquitous television picture tube is in principle a particle accelerator), but the smallest accelerators share common elements with the larger devices. First, all accelerators must have a source that generates electrically charged particles—electrons in the case of the television tube and electrons, protons, and their antiparticles in the case of larger accelerators. All accelerators must have electric fields to accelerate the particles, and they must have magnetic fields to control the paths of the particles. Also, the particles must travel through a good vacuum—that is, in a container with as little residual air as possible, as in a television tube. Finally, all accelerators must have some means of detecting, counting, and measuring the particles after they have been accelerated through the vacuum.

The key feature of any particle accelerator is the accelerating electric field. The simplest example is a uniform static field between positive and negative electric potentials (voltages), much like the field that exists between the terminals of an electric battery. In such a field an electron, bearing a negative charge, feels a force that directs it toward the positive potential (akin to the positive terminal of the battery). This force accelerates the electron, and if there is nothing to impede the electron, its velocity and its energy will increase. Electrons moving toward a positive potential along a wire or even in air will collide with atoms and lose energy, but if the electrons pass through a vacuum, they will accelerate as they move toward the positive potential.

The difference in electric potential between the position where the electron begins moving through the field and the place where it leaves the field determines the energy that the electron acquires. The energy an electron gains in traveling through a potential difference of 1 volt is known as 1 electron volt (eV). This is a tiny amount of energy, equivalent to 1.6 × 10−19 joule. A flying mosquito has about a trillion times this energy. However, in a television tube, electrons are accelerated through more than 10,000 volts, giving them energies above 10,000 eV, or 10 kiloelectron volts (keV). Many particle accelerators reach much higher energies, measured in megaelectron volts (MeV, or million eV), gigaelectron volts (GeV, or billion eV), or teraelectron volts (TeV, or trillion eV).

Some of the earliest designs for particle accelerators, such as the voltage multiplier and the Van de Graaff generator, used constant electric fields created by potentials up to a million volts. It is not easy to work with such high voltages, however. A more-practical alternative is to make repeated use of weaker electric fields set up by lower voltages. This is the principle involved in two common categories of modern particle accelerators—linear accelerators (or linacs) and cyclic accelerators (principally the cyclotron and the synchrotron). In a linear accelerator the particles pass once through a sequence of accelerating fields, whereas in a cyclic machine they are guided on a circular path many times through the same relatively small electric fields. In both cases the final energy of the particles depends on the cumulative effect of the fields, so that many small "pushes" add together to give the combined effect of one big "push".

The repetitive structure of a linear accelerator naturally suggests the use of alternating rather than constant voltages to create the electric fields. A positively charged particle accelerated toward a negative potential, for example, will receive a renewed push if the potential becomes positive as the particle passes by. In practice the voltages must change very rapidly. For example, at an energy of 1 MeV a proton is already traveling at very high speeds—46 percent of the speed of light—so that it covers a distance of about 1.4 metres (4.6 feet) in 0.01 microsecond. (One microsecond is a millionth of a second.) This implies that in a repeated structure several metres long, the electric fields must alternate—that is, change direction—at a frequency of at least 100 million cycles per second, or 100 megahertz (MHz). Both linear and cyclic accelerators generally accelerate particles by using the alternating electric fields present in electromagnetic waves, typically at frequencies from 100 to 3,000 MHz—that is, ranging from radiowaves to microwaves.

An electromagnetic wave is in effect a combination of oscillating electric and magnetic fields vibrating at right angles to each other. The key with a particle accelerator is to set up the wave so that, when the particles arrive, the electric field is in the direction needed to accelerate the particles. This can be done with a standing wave—a combination of waves moving in opposite directions in an enclosed space, rather like sound waves vibrating in an organ pipe. Alternatively, for very fast-moving electrons, which travel very close to the speed of light (in other words, close to the speed of the wave itself), a traveling wave can be used for acceleration (Sutton, 2012).