Taking a closer look at LHC
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 = 3.64·108 km
The Frequency of the circular movement already calculated is: f = 11,245 kHz
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 ⇒ ac ≈ 2.3·1013 m/s2
Therefore 2·1012 times 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 = 24,95·10-9 s ⇒ 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
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 (Spanish Postdoctoral Junior Grants Programme).
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). He has a Degree in Physics and in Chemistry, and is PhD for Santiago University (USC).
CERN and the Environment
For the bibliography used when writing this Section please go to the References Section