# Synchrocyclotron

Sketch of a synchrocyclotron from McMillan's patent.[1]

A synchrocyclotron is a special type of cyclotron, patented by Edwin McMillan, in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles' velocity begins to approach the speed of light. This is in contrast to the classical cyclotron, where this frequency is constant.[1]

There are two major differences between the synchrocyclotron and the classical cyclotron. In the synchrocyclotron, only one dee retains its classical shape, while the other pole is open (see patent sketch). Furthermore, the frequency of oscillating electric field in a synchrocyclotron is decreasing continuously instead of kept constant so as to maintain cyclotron resonance for relativistic velocities. One terminal of the oscillating electric potential varying periodically is applied to the dee and the other terminal is on ground potential. The proton or deuterons to be accelerated are made to move in circles of increasing radii. The acceleration of particles takes place as they enter or leave D. At the outer edge, the ion beam can be removed with the aid of electrostatic deflector. It was possible to produce 200 MeV deuterons and 400 MeV α-particle with the first synchrocyclotron.[citation needed]

## Differences to the classical Cyclotron

In a classical cyclotron, the angular frequency of the electric field is given by

${\displaystyle \omega ={\frac {qB}{m}}}$,

Where ${\displaystyle \omega }$ is the angular frequency of the electric field, ${\displaystyle q}$ is the charge on the particle, ${\displaystyle B}$ is the magnetic field, and ${\displaystyle m}$ is the mass of the particle. This makes the assumption that the particle is classical, and doesn't experience relativistic phenomena such as length contraction. These effects start to become significant when ${\displaystyle v}$, the velocity of the particle greater than ${\displaystyle \approx {\frac {c}{3}}}$. To correct for this, the relativistic mass is used instead of the rest mass, to do this, a factor of ${\displaystyle \gamma }$ multiplies the mass. Such

${\displaystyle \omega ={\frac {qB}{m\gamma }}}$,

Where,

${\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}$,

This is then the applied frequency angular frequency to the particles as they are accelerated around the synchrocyclotron.

A part of the former Orsay synchrocyclotron

The chief advantage of the synchrocyclotron is that there is no need to restrict the number of revolutions executed by the ion before its exit. As such, the potential difference supplied between the dees can be much smaller.

The smaller potential difference needed across the gap has the following uses:

1. There is no need for a narrow gap between the dees as in the case of conventional cyclotron, because strong electric fields for producing large acceleration are not required. Thus only one dee can be used instead of two, the other end of the oscillating voltage supply being connected to earth.
2. The magnetic pole pieces can be brought closer, thus making it possible to increase greatly the magnetic flux density.
3. The frequency valve oscillator is able to function with much greater efficiency.