We can simplify the process as follows:

H₂ + e^-  →  H₂⁺ + 2e^-

H₂^+ ₊ e^-  →  H⁺ + H + e^-

H _⁺ e^-  →  H⁺ + 2e^-

---

 H₂   →   2 H⁺ + 2e^-

---

For the LHC beam, we need:

2808 bunches x 1.15·10¹¹ = 3·10¹⁴   protons per beam

or,  6·10¹⁴  protons for the two beams   (1)

(We are using as protons per bunch the value initially planned for the LHC. With the upgrades and improvements made during successive long shutdowns (LS), this value has been increasing.)

A single cubic centimetre of hydrogen gas at room temperature contains

with  P = 10⁵ Pa   ,,   V = 10^-6 m³   ,,   T=293 K

using   P·V = n·R·T  -   

n = 4·10^-5 moles   ,,     N = 4·10^-5 x 6·10²³ = 2.4·10¹⁹ molecules  

So,  about 5·10¹⁹ atoms of hydrogen      (2)

Taking into account (1) and (2), the LHC can be refilled about 100000 times with just one cubic centimetre of gas – and it only needs refilling twice a day!

The particles are accelerated by a 90 kV supply and leave the Duoplasmatron with 1.4% speed of light, i.e. ~ 4000 km/s.

 

 

Then they are sent to a radio frequency quadrupole, QRF -an accelerating component that both speeds up and focuses the particle beam. From the quadrupole, the particles are sent to the linear accelerator (LINAC2).

 

---

A small commercial hydrogen cylinder contains about 5 kg of gas. So the amount of hydrogen molecules is:

n =  5000/2 = 2500 moles

2500  x 6·10²³ = 1.5·10²⁷ molecules

N = 2 x 1.5·10²⁷ = 3·10²⁷ atoms

Taking into account that the process yields about 70% protons we have:

  0,7 x 3·10²⁷ = 2.1 ·10²⁷atoms

With (1), this cylinder can be used:

2.1·10²⁷ / 6  ·10¹⁴= 3.5·10¹²  times

Since the LHC is filled every ten hours, this cylinder could be used for:

10 x 3.5·10¹²  = 3.5·10¹³ hours

So, about 4 ·10⁹ years

The hydrogen will diffuses out of the bottle faster.

---

A we said at the top, a new ion source (providing in this case H^-) is already working in the new linear accelerator, Linac4.

---

1.34 x 10²⁰ protons were accelerated in the accelerator complex in 2016. This might sound like a huge number, but in reality it corresponds to a minuscule quantity of matter, roughly equivalent to the number of protons in a grain of sand. In fact, protons are so small that this amount is enough to supply all the experiments. The LHC uses only a tiny portion of these protons, less than 0.1%, as shown in the diagram.

 

Taken from the Annual Report 2016 - CERN Document Server