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Old cyclotron magnet from the Lawrence Hall of Science

A Cyclotron is a particle accelerator that is much smaller than normal accelerators. The cyclotron fixes the problems the limitations of linear accelerators give. It is basically a linear accelerator in a magnetic field to bend the path into a circular pattern. Dr. Ernest Lawrence designed it based on a German paper outlining the theory and construction of a linear accelerator. This design is now used to make the new larger and more powerful accelerators. Unlike the large particle accelerators, a cyclotron in only about 100 feet in diameter, so it can easily fit into a large building. Cyclotrons have a limit to the acceleration they can impart on a particle because of special relativity.


A superconductor cyclotron's magnet

The cyclotron is a smaller particle accelerator. It can be built so small it can fit into a person's pocket. The cyclotron consisted of two semicircular areas that contain a magnetic field. These areas are called dees[1]. The dees are charged with electricity to make an electromagnetic field in them. Between the two dees, there is a gap with a vacuum in it[2].

A modern cyclotron has a physical weight of fifty-five tons. Its dimensions are generally 100 feet by 100.5 feet by 39 feet (30.5 meters by 30.6 meters by 11.9 meters). The power supply for a cyclotron has a radio frequency controller so the change from positive and negative charges in the cyclotron can be controlled precisely. All cyclotrons now have computers to optimize the acceleration of particles. The dees are made from low carbon steel with a nickel plated pole. The dees house two annealed copper coils. The coils have fiber-glass and epoxy resin to insulate them. The vacuum between the two dees is contained by an aluminum tank sealed by polyurethane rings. Ions are made in the cyclotron using a tungsten filament. This has a plasma filter on it to better the conditions for negative ions to be made[2].


The main use of cyclotrons is to study subatomic particles by smashing atoms together. This gives scientists a cheaper alternative to large particle accelerators. It also can fit in a small footprint[3]. One example is a team of scientists in Germany that used a cyclotron to research super-heavy isotopes. The cyclotron they used was known as a superconductor cyclotron. In their studies, they collided aluminum and magnesium and their findings put into question the theories about atomic stability[4]. For many decades, the cyclotron was the major method of making high-energy beams for nuclear physics[5].

The cyclotron can be used for medical uses. Some of these are proton tumor and cancer killing[5]. University of Pennsylvania has plans to make a center that will treat cancer using protons accelerated with a cyclotron. Rather than the traditional treatment that uses X-rays, this would use protons that do not scatter as easily. This fact makes the beam of protons easier to aim more precisely minimizing the side effects of the treatment[6].

Since the cyclotron is much smaller than other particle accelerators, it is more readily used to bombard other atoms. This results in positron emitting isotopes that can be used in PET imaging[5](Positron emission tomography imaging[7]).


An old cyclotron that is small

The cyclotron was designed and made by Ernest Lawrence. He based the designs on a German scientific paper he read in 1929 that outlined the principle the cyclotron works on. The paper also described a device that consisted of a glass tube and used a high voltage RF (radio frequency) to accelerate ions from one side of it. He thought that the this design could be changed to use one electrode and make the path of the particle's travel to be circular using magnetic fields[8].

A doctoral student started to help Dr. Lawrence in 1930 to make the first cyclotron. To make the first one, they used a four inch magnet, one hollow D-shaped electrode, a filament, a collector cup, and a brass, circular container to hold all of the apparatus in a vacuum. Once the first cyclotron was finished, they put hydrogen gas in it. The gas was ionized and it went through the accelerator and they went into the collector cup. It showed a current proving Dr. Lawrence's theory. In the years to come, Dr. Lawrence and his assistant made an eleven inch cyclotron. By 1932, cyclotrons could accelerate a proton to one million electron volts[8] (1.602 X 10-19 Joules[9]). That was the first time in physics history that happened[8].

With the discovery of special relativity, the limit of what cyclotrons can accelerate particles was found. According to the theory of special relativity (particularly the mass to energy equivalence E=mc2), as the particles gain energy, they gain mass as well. Since the RF voltage is constant, the accelerating particle will accelerate slower each time around the cyclotron. At a point in the particle's travel, it will stop accelerating because the particle will not be synchronized. This is fixed in modern cyclotrons by changing the RF frequency to match the change in the inertia due to relativity. The real name of modern cyclotrons is syncro-cyclotron or syncrotron[8] (a normal particle accelerator[10]).

How it Works

The diagram of a cyclotron from Dr. Lawrence

A cyclotron works similarly to how an electric motor works. The current of the ions or electrons flow in a magnetic field that is perpendicular to their vector of travel. These particles move in a circular pattern that spirals from the center to the exit point of the cyclotron if it is accelerating the particle. If it does not, the particles spiral inwards. This acceleration is achieved when the two dees are connected to a DC power supply that can alternate the negative and positive current synchronized with the phase of the orbiting particles in the cyclotron[10].

Mathematics proof

Cyclotrons work using the magnetic field (B) perpendicular to the particle's vector of travel. The centripetal force created is equal to Bqv.

{\tfrac  {mv^{2}}{r}}=Bqv

(m is the mass of the particle, q is the charge of the particle, v is the velocity, and r is the radius of the orbit of the particle) Rearranged

{\tfrac  {v}{r}}={\tfrac  {Bq}{m}}

v/r equals angular velocity, so \omega

\omega ={\tfrac  {Bq}{m}}

the frequency is

f={\tfrac  {\omega }{2\pi }}

In conclusion

f={\tfrac  {Bq}{2m\pi }}

This shows that the frequency of the particle does not depend on the radius of the orbit the particle takes. So the particle has to accelerate if the frequency does not change and the radius increases. This is because the particle has to travel the increased distance in the same time. This concept works until the particle gets to around one third of the speed of light due to the mass-energy equivalency[10].


  1. Davidson. The Cyclotron Webphysics. Web. Dec 13, 2011.
  2. 2.0 2.1 McClain, Bonny. Cyclotron Made How. Web. Jan 24,2012.
  3. Jessa, Tega. cyclotron Universe Today. Web. Jan 29, 2012.
  4. Borland, Jeff. Scientists Use Superconducting Cyclotron to Make Super-Heavy Metals Wired. Web. Jan 29, 2012.
  5. 5.0 5.1 5.2 Unknown Author. cyclotron Web. Jan 29,2012
  6. Wolverton, Mark. How to Use a Cyclotron Particle Accelerator to Fight Cancer Popular Mechanics. Web. Jan 29, 2012.
  7. Unknown. Fact Sheet: What is PET? SNM.Web. March 4,2012.
  8. 8.0 8.1 8.2 8.3 Olsen, Christopher. A Brief Historical Review of the Invention of the Cyclotron Rutgers Cyclotron. Web. Jan 24,2012.
  9. Unknown Author. Electron Volt Web. Jan 29, 2012.
  10. 10.0 10.1 10.2 Unknown Author. Cyclotron Physics Daily. Web. Jan 29, 2012.