Taking a closer look at LHC

Simple movement

Eeach bunch travels at almost the speed of light (v = 0,999999991·c ) :

v = 0,999999991 x 299792458 ⇒ v = 299792455 m/s

So each one will go around

299792455 / 26659 = 11245 laps per second

During the 20 minutes needed to reach the final energy, the protons cover a distance further than from Earth to the Sun and back.

11245 x 20 x 60 x 27 = 3.64·10⁸km

The Frequency of the circular movement already calculated is: f = 11,245 kHz

And the Period is: T = 1/f ≈ 9·10^-5 s

Protons will be accelerated to v~c. While travelling they will permanently be under a centripetal acceleration produced by Lorentz Force.

Let´s calculate this centripetal acceleration:

a ≈ c²/r ⇒ a_c ≈ 2.3·10¹³ m/s²

Therefore 2·10¹²times the acceleration of gravity.

It's been said before that the distance between the two bunches will be: d = 7, 48 m

So the “time between bunches” -bunch spacing- will be

t = distance / velocity
t = 7,48 / 3·10⁸

t = 24,95·10^-9s ⇒ t = 24,95 ns

which is a very important parameter.

Another interesting exercise is to calculate how many laps the protons travel before falling due to gravity.

h = ½g·t² ⇒ t = (2h/g)^1/2

where h is the pipe radius (~ 28 mm)

so: t = (2·0,028/9,81)^1/2

t ≈ 76 ms

Divided by the period:

nº of laps = 76·10^-3/8,9·10^-5

n = 850 laps

Therefore, we must not only correct the electromagnetic alterations but we must also correct those due to gravity. The magnetic multipoles will correct those alterations.

AUTHORS

Xabier Cid Vidal, PhD in experimental Particle Physics for Santiago University (USC). Research Fellow in experimental Particle Physics at CERN from January 2013 to Decembre 2015. Currently, he is in USC Particle Physics Department ("Ramon y Cajal", Spanish Postdoctoral Senior Grants).

Ramon Cid Manzano, secondary school Physics Teacher at IES de SAR (Santiago - Spain), and part-time Lecturer (Profesor Asociado) in Faculty of Education at the University of Santiago (Spain), until his retirement in 2020. He has a Degree in Physics and in Chemistry, and is PhD for Santiago University (USC).

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