Cyclotron
charged particles by using a high frequency alternating voltage across a magnetic field to spiral the beam out and eventually deflect it once the beam's radius equals its container's. At this point the particles' speed is generally very high, approaching the speed of light. The cyclotron was invented by Ernest Lawrence in 1929, who used it in experiments which required particles of speeds of up to 1 MeV. Cyclotrons are used today in the treatment of cancer, as the particles produced ionize tumors and help to stop or slow cancerous growth.
Problems solved by the cyclotron:
The cyclotron was designed to address the limitations of the linear accelerator, which works by accelerating particles in a straight line through evacuated tubes that contain a series of ring electrodes. These electrodes switch from positive to negative voltage repeatedly. A serious disadvantage is that in order to accelerate particles faster, impractically long tubes were becoming necessary. (The largest such linear accelerator is the Stanford Linear Accelerator (SLAC), about two miles or 3.2 km long.) Cyclotrons work by accelerating particles in a circular path, allowing much more distance to be covered with a compact accelerator.
Limitations of the cyclotron:
While a significant technical achivement at the time, the configuration of the device limits its cost effectiveness at higher power. These limitations were addressed with the invention of the synchrotron.
How the cyclotron works:
In the cyclotron a magnetic field is applied perpendicular to a disk-shaped vacuum chamber containing two hollow D shaped semi-circular electrodes. The straight portions of these hollow electrodes are open and face each other. A current of electrons or ions flowing perpendicular to a magnetic field experiences a force that is perpendicular to its direction of motion. (This force is used to practical effect in electric motors.) With charged particles free to move in a vacuum (unlike in a motor where electrons are constrained to the wires), the particles in motion will follow a circular path. If the particles loose energy while circulating they will spiral inward. If the device is capable of applying energy to the particles they will spiral outward. In the cylotron a high frequency alternating voltage applied across the "D" electrodes causes the particles to accelerate when passing through the gap betwen the elecrodes. The perpendicular magnetic field forces causes them to travel in a circular path through the D chambers. The particles accelerate only when passing the gap between the two Ds.
|
|
|
A large cyclotron magnet at the Lawrence Hall of Science.
The black portions are the iron pole pieces and continue across below ground level.
The electromagnet coils were within the white cylinders. The vacuum chamber
would be placed in the horizontal gap between the poles of the magnet
|
|
|
|
A pair of Dee electrodes at the Lawrence Hall of Science.
These would be contained within the vacuum chamber.
The serpentine pipes are for cooling liquid.
|
Mathematics of the cyclotron:
The centripetal force is provided by the transverse magnetic field B, and the force on a particle travelling in a magnetic field (which causes it to curve) is equal to Bqv. So,
- <math>\frac{mv^2}{r} = Bqv<math>
(Where m is the mass of the particle, q is its charge, v is its velocity and r is the radius of its path.)
Therefore,
- <math>\frac{v}{r} = \frac{Bq}{m}<math>
v/r is equal to angular speed, ω, so
- <math>\omega = \frac{Bq}{m}<math>
And, the frequency
- <math>f = \frac{\omega}{2 \times \pi}<math>
Therefore,
- <math>f = \frac{Bq}{2 \times \pi \times m}<math>
This shows that for a particle of constant mass the frequency does not depend on the radius of the particle's orbit. As the beam spirals out its frequency does not decrease and it must continue to accelerate, as it is travelling more distance in the same time. As particles approach the speed of light they acquire additional mass, requiring modifications to the frequency or the magnetic field during the acceleration. This is accomplished in the synchrocyclotron.
Related technologies:
The spiraling of electrons in a vacuum chamber within a transverse magnetic field is used in the magnetron, a device for producing high frequency radio waves.
- See also Particle accelerator, Linear accelerator, cyclotron radiation, synchrocyclotron, synchrotron
