Transformers and Betatrons

[Eeezee]

I'm interested in learning more about how these work. What is an MMF in relation to electric and magnetic fields? What is a 'stable orbit' for a betatron, and what determines this orbit? How are the electrons in a betatron accelerated to such high energies?

I have to give a talk on Betatrons in a few weeks and I want to get some good explanations on how these things work. I have a few textbooks, but none of them really explain a Betatron well. Wangsness' "Electromagnetic Fields" 2nd ed. has an okay explanation in the appendix, but I'm really looking for something more.

 

[Born2bwire]

Griffiths' my friend, Griffiths'. I would assume MMF is magnetomotive force, the magnetic analog of EMF or electromotive force. A betatron is simply a cyclotron. However, in your classic cyclotron, electrons travel in a circular orbit due to a constant magnetic field. The electrons are accelerated by applying high voltages across a gap in the device. The high voltage creates an electric field across the gap in the direction of the electron's velocity and thus applies a Lorentz force. These can be very simple devices. Basically, just two halves of a disc that are separated by a small air gap. The electron starts in the center of the disc and as it accelerates from the electric field that is between the gap of the two halves, it spirals outward (this is because the magnetic field is constant and the magnetic field alone dictates the radial force but this is dependent upon velocity squared and inverse r).

So what if we want the electron to have a stationary orbit? Simple, instead of using an electric field applied in the direction of travel, we increase the magnetic field that is applied perpendicular to the plane of motion. By increasing the magnetic field, we can increase the square of the velocity by which the electron rotates. However, we will also change the radius of the orbit by 1/R. So the trick is to make a magnetic field that varies with /rho in the plane of motion. Problem 7.48 of Griffiths deals with this and the above explanation is just a direct inference of the machine from the problem.

EDIT: Oooh, the betatron appears to have been invented at UIUC. I probably should take a look if they have one on display at Loomis. They have two cyclotrons on display but one of them could be a betatron.

 

[Eeezee]

Argh, that's it, I'm buying a copy of Griiffiths'. For whatever reason our professor decided to change the book last semester to Wangsness, and I really dislike Wagnsness. The book sucks until you get the Poynting vector (and even then, things aren't explained well at all and we had to have the professor go over it)

Is the magnetic field perpendicular to the electron's orbit oscillating or just increasing?

 

[Born2bwire]

Originally posted by: Eeezee
Argh, that's it, I'm buying a copy of Griiffiths'. For whatever reason our professor decided to change the book last semester to Wangsness, and I really dislike Wagnsness. The book sucks until you get the Poynting vector (and even then, things aren't explained well at all and we had to have the professor go over it)

Is the magnetic field perpendicular to the electron's orbit oscillating or just increasing?

Or check it out at your Uni's library. I am not sure how much further help his text would be with the betatron problem. He only discusses it in that one homework problem. One bad thing about the Griffiths text, the edition that we get around campus is very poorly bound. I mean piss-poor. My text is in pieces.

As to the magnetic field, it would have to be increasing. Just take the old cyclotron problem to get a better picture. I have no idea what it is offhand, but the solution is that the B field is proportional to v^2/r.

 

[Gibsons]

I don't mean to derail the topic, but I clicked on this thread expecting to read about Optimus Prime and Megatron.

Thanks for the info on betatrons though, interesting stuff. :thumbsup:

 

[JJ650]

Originally posted by: Gibsons
I don't mean to derail the topic, but I clicked on this thread expecting to read about Optimus Prime and Megatron.

Thanks for the info on betatrons though, interesting stuff. :thumbsup:

LOL! Me too!

 

[Eeezee]

Originally posted by: Gibsons
I don't mean to derail the topic, but I clicked on this thread expecting to read about Optimus Prime and Megatron.

Thanks for the info on betatrons though, interesting stuff. :thumbsup:

Wow... now that I look at it, you're absolutely right. Sorry about that

 

[Born2bwire]

Yep, we do have a betatron on display in Loomis. It's a 24 MeV model and is the larger one that is in the second picture in the link, http://www.physics.uiuc.edu/General_Info/History/Betatron.htm.