# Energy of the particles in the particle accelerator

Recently I came across something and I was surprised. I always thought that huge amount of energy is required to accelerate particles in the accelerator in the particle physics.But looks like no. The peak energy of proton beams at the LHC now is around 7 trillion electron Volts (TeV), which is only like 0.00000121J. So energy involved in particles accelerators is not that much then or am I missing something.? May be since the mass of these partciles is so small, their velocity needs to really high to get this much energy and may be that is the big deal.?

• 7 TeVs are over 11 ergs! 7000 times more than the mass of a proton is not a lot? At the moment of impact, energywise, the protons are mostly kinetic energy. How do you define "that much"? Commented Mar 28, 2019 at 0:14
• @CosmasZachos I think the OP means that LHC energy is not that high compared to other energy scales in nature, for instance in this list (which includes the LHC value too) here - en.wikipedia.org/wiki/Orders_of_magnitude_(energy) Commented Mar 28, 2019 at 2:06
• Similarly, energy of superlasers is not "that much" either. The key point is not the absolute amount of energy, but it's intensity, concentration in the small amount of matter, like in LHC, or in small volume and time window, like the laser power of the fusion projects. Commented Mar 28, 2019 at 6:43
• Imagine energy needed to accelerate 1 g of protons. You would need energy equivalent to anihilation of 2x3.5 kg of matter and antimatter. Or fusion of about 1000 kg of hydrogen to helium, if I remember correctly . Commented Mar 28, 2019 at 6:49
• In one of his books, Sean Carroll mentions that the total energy of all the 500 trillion protons is comparable to that of an "onrushing locomotive engine".
– user191954
Commented Mar 28, 2019 at 8:10

## 3 Answers

Yes, you are missing something. First, 7 TeV is the energy of each proton. The LHC beam contains 300 trillion protons! Second, the protons continuously lose energy as they radiate synchrotron radiation, so you have to continuously put in energy just to keep them going around at the same speed.

• $300\cdot10^{12}$ particles times $0.00000121J$ gives $363 MJ$... Commented Mar 28, 2019 at 6:58
• "Second, the protons continuously lose energy [...] so you have to continuously put in energy just to keep them going around at the same speed." And you have to keep the magnets energized and coolant for the superconducting parts chilled and so on. The power cost is so substantial that the operators of major accelerators call the electric utilities to let them know in advance when they are going to fire up the machine in earnest so that the power company can make sure they have enough reserve capacity on-line to manage the demand (they might very well bring an additional power plant up). Commented Mar 29, 2019 at 3:16

A particle accelerator does not work with one particle at a time. At any moment, there will be billions of particles distributed into a beam (usually with bunches in it). Because they are charged, the particles in the beam represent a current. Electrical power is (current x voltage) and as such the beam packs enough wallop to tear holes in the beam tube and wreak havoc upon the equipment nearby if it gets out of control.

From Wikipedia: "While operating, the total energy stored in the magnets is 10 GJ (2,400 kilograms of TNT) and the total energy carried by the two beams reaches 724 MJ (173 kilograms of TNT)"