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 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 ⇒ 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 / velocityt = 7,48 / 3·108 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 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.
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
It's been said before that the distance between the two bunches will be : d = 7, 48 m
t = distance / velocityt = 7,48 / 3·108
so: t = (2·0,028/9,81)1/2
t ≈ 76 ms
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.
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