Editing Cyclotron (section)

==== Synchrocyclotron ====
{{main|Synchrocyclotron}}
Since <math>\gamma</math> increases as the particle reaches relativistic velocities, acceleration of relativistic particles requires modification of the cyclotron to ensure the particle crosses the gap at the same point in each RF cycle. If the frequency of the accelerating electric field is varied while the magnetic field is held constant, this leads to the ''synchrocyclotron''.{{r|wilson}} 

In this type of cyclotron, the accelerating frequency is varied as a function of particle orbit radius such that: 

<math display="block">f(r) = \frac{1}{2\pi \sqrt{\left(\frac{m_0}{q B}\right)^2 + \left(\frac{r}{c}\right)^2}}</math>

The decrease in accelerating frequency is tuned to match the increase in gamma for a constant magnetic field.{{r|wilson}}