Cyclotron

Operation

In a cyclotron the magnetic field is applied perpendicularly in an open stope in the shape of disc, which contains two semicircular electrodes in form of D. the rectilinear portions of these electrodes face. The flow of electrons or ions crossing a perpendicular magnetic field is subjected to a force perpendicular to the direction of the movement (this principle is used for the operation of the electrical motors). Here, in the vacuum, these particles charged follow a circular course. If the particles lose energy they will follow an interior spiral. If the apparatus is able to increase their energy they will follow a spiral expanding. It is this principle which is used in a cyclotron. A high frequency alternating voltage is applied to the electrodes in D, which accelerates the particles with each one of their passages of the one with the other.

Frequency of the cyclotron

The centripetal Force is provided by the transverse magnetic field B , and forces it which applies to a particle crossing a magnetic field (what causes the circular trajectory) is equal to Bqv . By expressing the equality with the Centrifugal force, one obtains.

m v ² /r = B q v according to Newton which says that the sum of the forces applied is equal to m has and thus, the force of Lorentz ( B q v ) is equal to m has (in a uniform circular motion, acceleration a = v ² /r )

(Where m is the mass of the particle, Q its load, v its speed and R the ray of its trajectory.)

Consequently,

v/r = B q/m

v/r is equal to the angular velocity, ω , which gives

ω = B q/m

There is also the frequency F ,

f = ω/(2 π)

Therefore,

f = B Q (2 π m)

That shows that for a particle of constant mass, the frequency does not depend on the ray of the orbit of this particle. While the ray increases, the frequency does not decrease, but the particle accelerates, which makes him traverse an additional distance to each turn, for the same period. However, when it approaches speed of light, a relativistic effect saves to him an additional mass, which requires an adjustment of the frequency of the electric field, operation which is carried out in a Synchrocyclotron.

Utility

A cyclotron is a particle accelerator of approximately 6 m3, being able to allow the production of four radioelements: oxygen 15 (¹⁵O), carbon 11 (¹¹C), nitrogen 13 (¹³N), and fluorine 18 (¹⁸F).

Fluorine 18 (isotope with short half-life: 2 hours) allows to manufacture fluorodésoxyglucose (FDG), a radioactive sugar which will be fixed on the cancerous zones. A Tomography by Emission of Positrons (Mtoe) will make it possible to detect in a particularly fine way certain cancers then to treat them at very early stages.

The current technology of manufacture of the cyclotrons is currently quasi monopolized by the Belgian company of origin IBA, (spin-off of the catholic Université of Leuwen, founded in 1986 per Yves Jongen) whose seat is located at Leuwen-the-New.

See too

External bonds

site of company IBA

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