Taking a closer look at LHC

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FORCES

CENTRIPETAL FORCE

The necessary force on each proton travelling at almost the speed of light will be:

Con v~c :    F_c = mc²/r ⇒   F_c = E/r

To generate this force there are  1232 magnetic dipoles located on the eight archs, each one having a magnetic length of 14,3 m, giving a total implied length:

1232 × 14,3 = 17618 m

Precisely, we can calculate the so-called "bending radius":

r_b =17618/(2π) ⇒ r_b = 2804 m

So,

F_c = 7 TeV /2804 m ⇒ F_c = 1.12·10^-6J /2804 m

F_c = 4·10^-10 N
on each proton.

ACTION AND REACTION

But the accelerator will suffer the same force from each proton.

Considering the two beams with 2808 bunches and the number of protons inside (1,15·10¹¹):

F_T = 2 · 2808 × 1,15·10¹¹× 4·10^-10

F_T  ≈ 260000 N ≈ 26 Tm_Force

So the reaction force over the curved part of the accelerator will be equivalent to 26 tonnes of force.

And the most incredible is that this force is created in interaction with 6·10¹⁴ protons with a rest mass of only 1 ng (one nanogram!).

An other more impresive force acts over the bam pipe because the superconductive currents. which is explained in Section Magnetism II.

The designers have taken these forcee into account because very high precision is required.