Axial Betatron Motion

Axial Betatron Motion

Author: Tim

This experiment shows the effect that shaping the magnetic field has on focusing the cyclotron’s beam. If the beam wanders off of the mid-plane, the magnetic field pushes it back, but of course it then overshoots and goes below the mid-plane. The magnetic field pushes the beam back up, and so it goes. The beam oscillates about the mid-plane in the vertical (axial) direction as it spirals out in the horizontal plane. These images show that action and is one of the most fundamental accelerator demonstrations this cyclotron provides.

This paper describes the first observation of betatron motion in our cyclotron.

This paper goes more into the details of the betatron motion demonstrations with the 12-Inch Cyclotron

View into the cyclotron chamber through the “rectangular port.”
When beam is on, and the cyclotron is tuned up, the green light from the phosphor screen can be bright enough to shine light out.
This is what the human eye would see, just a dot, or sliver on the edge of the phosphor screen. The beam image is its position profile at that particular radius.
If you set up a camera to take a long exposure and slide the screen in-and-out during beam on time, the vertical motion of the beam will be “painted in.”
A typical setup.
The painted in image as seen from a few steps back.
Here is an older photo of Tim sliding the radial probe during the image acquisition.
Tim’s favorite betatron motion image, this was taken will using the “good” weak focusing pole tips.
This is what a normal ion source looks like during cyclotron operation. Ions are being sprayed into the chamber in the mid-plane.
This was a specially built ion source chimney with a major vertical offset, which intentionally gives the ions a vertical error.
This image is the result of that large initial vertical error while operating with the “good” weak focusing pole tips.
This image is the result of that large initial vertical error while operating with the AKG270 spiral poletips.
Here the cyclotron is outfitted with the “bad” weak focusing pole tips.
The “bad” weak focusing poletips cause the beam to severely axially “blow up” and strike the cyclotron chamber DEE or lids and be lost. This is known as the Walkinshaw resonance.