### Re: How small could the magnets of a 10 in. cyclotron be? (approximately)

Date: Fri Aug 27 10:16:42 1999
Posted By: Georg Hager, Grad student, Theoretical Particle Physics
Area of science: Physics
ID: 934388454.Ph
Message:

Greetings! Sorry that this is so late.

You ask how big (or small) the magnets of a ten-inch cyclotron would have to be. That depends on several factors:

1. What kind of particles are accelerated in the cyclotron?
2. To what maximum energy do you want to accelerate them?
3. What are the other boundary conditions that have to be taken into account? (like maxiumum AC frequency, maximum amplitude etc.)
Assuming that you can assure the homogeneity of the magnetic field and the proper frequency stability of your RF source, you should be able to calculate the necessary magnetic field strength for your setup (just equal the Lorentz force on the particles with the centripetal force due to the circular motion). The angular frequency, for instance, would be qB/m, where q is the charge of the particles, B is the field strength and m is the particle mass. Knowing roughly the frequency of your AC source, you can come up with the field strength (for relativistic particle velocities, of course, you are in a bit of trouble here due to the relativistic mass increase; let us just assume that the velocities you wish to attain are less than 0.1c).

Of course, your magnets would have to have at least the diameter of your cyclotron `D's, because you want the magnetic field to extend through all the space the particles might traverse. So the real question is, are you able to build magnets that can provide the required magnetic field strength and still have a homogeneous field? Assuming that all you have at your disposal are usual copper wire coils with currents of the order of amperes running through them, and maybe iron cores with a magnetic susceptibility of roughly 1000, you might be able to reach magnetic fields of the order of Teslas. That should be about the limit for `home-made' equipment.

Some more info on a specific cyclotron can be seen at this site. I hope I have provided valuable information to you.

Bye,
Georg.

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