What determines the strength of a magnetic field in a cyclotron?

[Aidan Davis]

In a cyclotron, I understand that a uniform magnetic field is used, oriented perpendicular to the plane in which the particles accelerate. This field is created by two cylindrical permanent magnets whose opposite poles face each other,as I understand it. What formula(e) determine the strength (flux density) of the field, based on parameters such as radius, height, separation distance, material, and temperature. The plane of acceleration for the particles is assumed to be the halfway point between the two magnets.
I could not find a full concise answer for this online, and since I have few resources outside of that, this is my go to when google fails. Thanks for the help.

 

[SlowThinker]

I believe you can use simply the formula for long solenoid, supposing that the particle beam fits between 2 turns of the wire somewhere in the middle. The gap is probably as thin as possible, and obviously there is no material in it.
I'm not sure if the coils have ferrite or air cores (seems to have air cores), or if the magnets are actually straight or toroids. A few minutes of Googling didn't find it but the information should be out there somewhere...

 

[Aidan Davis]

I believe you can use simply the formula for long solenoid, supposing that the particle beam fits between 2 turns of the wire somewhere in the middle. The gap is probably as thin as possible, and obviously there is no material in it.
I'm not sure if the coils have ferrite or air cores (seems to have air cores), or if the magnets are actually straight or toroids. A few minutes of Googling didn't find it but the information should be out there somewhere...

Ah, a solenoidal electromagnet could be used as opposed to permanent magnets, as it would, through variations in current, allow for adjustments in the flux density in the field to give optimum particle energy.
Does a cyclotron like this exist or do they all have permanent magnets?