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CERN's SPS accelerator can accelerate protons to an energy of at most 7*10-8 J. From there the protons are transferred into the LHC, used to produce neutrinos, or used in one of the other experiments around SPS.
The energy in the SPS is limited because the SPS must be able to keep the protons on their circular track using strong magnets. If you would try to increase the energy then the protons wouldn't stay in the beam pipe and more and crash into the outer wall, getting lost in the process.
The LHC can reach a higher energy than the SPS because it is larger and has stronger magnets. It could be used to create neutrinos at higher energy - but similar to the SPS, the neutrino energy could not exceed the proton energy, so you get at most 1.0*10-6 J (and usually much less). Stronger magnets might double that in the future, but it will stay a tiny energy in macroscopic terms.
Note that I didn't use speed values anywhere: You can find the corresponding speed for each energy, but in practice this doesn't matter. The energy is a more useful quantity, then you don't have to count digits in things like "0.999999995 times the speed of light".
- It can transfer these protons to the LHC, where they are accelerated to an energy of at most 1.0*10-6 J.
- It can shoot these protons onto a fixed target, the collisions create some pions with an energy of at most 7*10-8 J. Energy is conserved - the pions can't have more energy than the protons used to make them. The pions then decay, among the decay products are neutrinos with an energy of at most 7*10-8 J - again, this limit is given by conservation of energy. "At most" because some energy will go into other particles produced in both processes.
The energy in the SPS is limited because the SPS must be able to keep the protons on their circular track using strong magnets. If you would try to increase the energy then the protons wouldn't stay in the beam pipe and more and crash into the outer wall, getting lost in the process.
The LHC can reach a higher energy than the SPS because it is larger and has stronger magnets. It could be used to create neutrinos at higher energy - but similar to the SPS, the neutrino energy could not exceed the proton energy, so you get at most 1.0*10-6 J (and usually much less). Stronger magnets might double that in the future, but it will stay a tiny energy in macroscopic terms.
Note that I didn't use speed values anywhere: You can find the corresponding speed for each energy, but in practice this doesn't matter. The energy is a more useful quantity, then you don't have to count digits in things like "0.999999995 times the speed of light".