If we ignore relativistic effects, magnetic field will take the following value:

B = (v*m)/(r*q) Where v is linear electron speed, r is the synchroton radius and m q are the electron mass and electric charge respectively.

If we include relativistic effects, I think special relativity cannot explain this experiment because the difference of speed is not the same seen from the electron’s instantaneous inertial frame of reference (IFR) than from the laboratory’s IFR. That is because of Thomas Precession.

Nonetheless, I have been working with a model that is able to determine magnetic field needed to keep electrons in UCM when they reach relativistic speeds. The result I get is the next:

B = (v*m)/(r*q) * ( 2*k^2/(k+1) )^(1/2) k = 1/(1-v^2)^(1/2)

If you know, theoretically or experimentally, the magnetic field need to keep the UCM you will make me a great favour telling me it so I will know if my model is working or not.