# LHC forces on a proton

I posted an LHC question a while back but did not get a reply. I'll ask a somewhat different, simplified and more specific question. I hope I am asking the question correctly.

How much inward radial force is needed to keep a proton going in a 27 km circular path at 7 Tev or a Lorentz factor of 7500? What is the relativistic formula for it? Is it just mv^2/r with m being relativistic mass?

Supposedly the proton will slow down since it radiates as it is accelerating circularly, so a tangential force behind it is also needed to keep it at 7 Tev. What is this force and the formula for it?

Dale
Mentor
2020 Award
Hi teve,

Wrt the tangential force required, I don't know the answer there. I guess you could look into bremsstrahlung radiation and find out what direction it points and how much energy it has, then you would have to correct for that with incoming radiation of equal 4-momentum.