The hadron collider is 27kms in size. How much does upping the scale of size help with research?

If we made a collider that wrapped around the planet would it be significantly more powerful than the Hadron?
You can think of the LHC as a giant microscope. The smaller the scale you want to study, the larger the energies are that are required to probe it. In order to obtain those energies, you need to make particles travel at increasingly relativistic speeds. To keep the particles in the LHC travelling inside the ring, you need to curve their path with magnetic fields. The velocity that a charged relativistic particle will travel at is v=rqB/γm, so the energy is E~pc=γmvc=rqBc where γ is the Lorentz factor, v is velocity, m is rest mass, q is charge, and B is magnetic field. Even the superconducting magnets used in the LHC can only produce a field of about 13T, so once you can no longer increase B, you can increase r.

Given the current record for LHC magnetic field strength, this gives you a theoretical maximum energy per nucleon of about 16.7TeV. A collider that wrapped around the planet using the same magnetic field strength would be able to produce energies of 24829TeV. However, these increasing energies give declining returns, as we think we have a "mostly complete" model of particle physics, and the energies required to probe more fundamental physics, such as string theory, are (arguably) thought to be many orders of magnitude larger than this.

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