# What were the maximal collision energy of the LHC if it were rewired to $e^{-}-e^{+}$ collisions?

Yes, I know, that it weren't a large hadron collider then.

No, I don't think, that the creators of the LHC didn't know what they do.

I am just curious.

How could it be calculated? A such rewiring of the LHC (also, making it capable to work with electron-positron pairs) weren't a little bit cheaper as the now planned next linear collider?

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The machine in that same tunnel before the LHC was built was called LEP2. It was an electron-positron machine. It ran at much lower energy. –  dmckee May 23 '14 at 15:13
–  dmckee May 23 '14 at 15:15
@dmckee Yes, but it didn't use superconductive coils, so it had much weaker magnetic fields. This was the cause, why LHC was needed. –  peterh May 23 '14 at 15:15
@dmckee Not exactly, I am asking exactly for the maximal collision energy and how can it to be calculated. –  peterh May 23 '14 at 15:16
There is never anything as simple as "the" maximum energy. It depends on your magnets and on your klystrons and on your budget. And the answer to the above is the answer to this question because it would be energy limited. As far as "how can it to be calculated." goes, I have to ask if you know anything about how these things are put together because this is an engineering limit that depends on packing a lot of klystrons into the space left over after you have packed in a lot of magnets--it's not a physics 101 project. –  dmckee May 23 '14 at 15:21

This has been proposed by a group of physicists, they called it LEP3.( LHC is in the tunnel of LEP and LEP2)

LEP3 would operate at 240 GeV at center of mass, and comprise two separate accelerator rings that would smash electrons and positrons rather than protons and protons, as with the LHC. In their study, the 20 authors call the concept for LEP3 "highly interesting" and that it deserves more detailed study. "Now is the right moment to get this on the table," says theorist John Ellis from Kings College London in the UK, who is an author of the preliminary study and hopes that it will trigger debate among physicists as to how to study the new boson in detail.

This would be enough to attain the Higgs region and get accurate values for standard model parameters. We had stopped at ~210 center of mass in LEP2 , and just missed the Higgs.

There is a proposal for a new tunnel for e+e- called TLEP. See this talk for a presentation .

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I don't know how to calculate the exact value, but I'm sure it will be much less than the current 8 TeV (scheduled 14 TeV) with protons - the problem is that the bremsstahlung losses scale with $\frac 1 m$, which makes it hard to accelerate electrons to high speeds. If it would be advantageous the CERN would have upgraded the LEP instead of building the LHC as it's the same tunnel...

To estimate the energy you might try to find out how much energy per orbit can be added to the particle and calculate how much energy per orbit is lost due to bremsstrahlung.

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