Calculating LHC Forces on a Proton

• teve
In summary, the radial force needed to keep a proton going in a circular path at 7 Tev or a Lorentz factor of 7500 is about 2e-6 Newtons.

teve

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?

Hi teve,

There was a recent thread by upurg which addressed the radial component of the question:

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.

DaleSpam said:
There was a recent thread by upurg which addressed the radial component of the question:

The last post of that thread suggests the radial force is just mv^2/r, but the velocity is multiplied by the Lorentz factor. Is this correct?

Then with the LHC Lorentz factor 7500 and radius 4300m, the radial force on a proton is
((1.67e-27)(7500c)^2)/4300 = 2e-6 Newtons. For 2808 bunches with 1.15e11 protons each (from wiki) and a 27km circumference that's about 25 kN/m of inward radial force. That's 50 kN for 2 beams.

I roughly estimate the weight of the dipole magnets at 4000 kg/meter. From further rough calculations I find that the dipole magnets have to be bolted down or they could tip over (if they were free standing). Is that right?

1. How do you calculate the forces on a proton in the LHC?

To calculate the forces on a proton in the LHC, you would use the equation F=qE, where F is the force, q is the charge of the proton, and E is the electric field strength. You would also need to consider the magnetic field in the LHC, using the equation F=qvB, where v is the velocity of the proton and B is the magnetic field strength. These two forces combined will give you the total force acting on the proton in the LHC.

2. What is the significance of calculating the forces on a proton in the LHC?

Calculating the forces on a proton in the LHC is important because it helps us understand the behavior of particles in high-energy environments. The LHC is used to study the fundamental building blocks of matter and the forces that govern them, so understanding the forces acting on protons in this environment is crucial for furthering our understanding of the universe.

3. How are the forces on a proton in the LHC different from those in regular environments?

The forces on a proton in the LHC are much stronger than those in regular environments. This is because the LHC accelerates particles to extremely high speeds and collides them at high energies, creating intense electric and magnetic fields that can exert significant forces on the protons.

4. Can the forces on a proton in the LHC be controlled?

Yes, the forces on a proton in the LHC can be controlled by adjusting the electric and magnetic fields in the accelerator. This allows scientists to carefully manipulate the particles and study their behavior under different conditions.

5. How does the calculation of forces on a proton in the LHC contribute to scientific research?

The calculation of forces on protons in the LHC is essential for understanding the fundamental laws of physics and studying the behavior of matter at the smallest scales. It also has practical applications, such as in the development of new technologies and medical treatments that utilize particle accelerators.