# What is the average radius of a betatron vacuum chamber?

1. Jun 4, 2012

### youngT-Stark

My friend and I were discussing particle accelerators (betatrons to be exact) and we began to argue about the size of the core magnets and vacuum chamber. He said that an average torodial vacuum chamber is 0.5m. I have seen old photos of them and said thats more likely to be the diameter. I have reviewed several patents on betatrons, read three books on particle accelerator physics, and havent managed to find out how large a vacuum chamber is. If anybody can give me a rough estimate or other parameters so i could figure it out, I would be very appreciative.

Or for that matter, any parameters of a betatron would do the trick.

2. Jun 5, 2012

### Bob S

There are three important parameters that provide guidance on calculating the radius of the betatron orbit.

1) The typical energy of a small betatron was probably in the range of 20 MeV. The largest ever built, at the University of Illinois, was about 300 MeV.

2) The B field at the orbit is half the average B field inside the orbit.

3) The rigidity of an electron beam is $$B\rho=\frac{\beta \gamma}{c}m_{o} c^2 \text { Tesla meters}$$So assuming the peak field at the orbit is 0.5 Tesla at 20 MeV, we get a rigidity of 0.067 Tesla meters, and an orbit radius of 0.13 meters. For the Illinois betatron, it would be about 2 meters. See photo on page 19 of http://www.lhep.unibe.ch/img/lectureslides/5_2007-11-12_AcceleratorPhysicsIII.pdf [Broken]

Last edited by a moderator: May 6, 2017
3. Jun 5, 2012

### youngT-Stark

Thanks, that is a huge help.