# Electric field in cyclotron

Recently I've read a little bit about cyclotrons and can't understand one thing. Why does a particle accelerate only in the gap (I mean increasing speed not changing direction) between dees? The second thing is how do the electric field lines in a cyclotron look like, because I've read that there is no electric field inside dee.

This is a typical diagram of a cyclotron.

A horizontal electric field exists only in the space between the dees, while a perpendicular (vertical) magnetic field exists within the dees.

The following points describe the working of a cyclotron:

1. Consider a particle getting emitted from the ion source depicted in the figure. It enter one Dee from its one side. Now, the magnetic field exists vertically, while the motion if the charged particle is horizontal. As a result, the particle has to undergo circular motion inside the Dees. Thus, the particle (let's call it P) traces a circle and comes out from the other side of the Dee.
2. Outside, the vertical magnetic field does not exist, but the horizontal electric field exists. This electric field accelerates P in a horizontal direction towards the other Dee.
3. P enters the second Dee from the other side. Inside the dee, again a magnetic field exists, which forces the particle to trace a circular path and come out of the Dee from the other side.
4. As P comes out, it again gets accelerated by the horizontal electric field that exists outside the Dees, and enter the first Dee through one side.
5. This process continues. As the particle gets accelerated each time, the radius of its circular motion increases. Consequently, the particle traces circles (or rather, semi circles) inside the Dee with increasing nearness to the outer wall of the Dees.
6. Finally, when P gets accelerated enough that the radius of its motion nearly equals the circumference of the Dee, it gets ejected out of the system by a special mechanism.

Now, a problem would arise if there would exist an electric field within the Dees. That electric field would horizontally accelerate the charged particle, and the real purpose of a cyclotron (that is, to accelerate a charged particle to a very high velocity, but within a small region) would not be fulfilled.

Here's another relevant image.

Note: The electric field is an oscillating one, that is, it constantly changes its direction to always accelerate the particle (never to decelerate it). Its oscillation is synced with the time the particle takes to complete a half-circle within the Dee and come out of it.

Hope this helps!

The Dees are hollow metal boxes.... due to electrostatic shielding, Electric field inside Ds remains 0. In the gaps electric field exists and increases velocity slightly every half a cycle.