Why did we need a 8.3 T magnetic field in the LHC beam pipe?

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SUMMARY

The LHC beam pipe requires a magnetic field of 8.3 Tesla, which is determined by the number of dipole magnets (1232) and their effective length. The calculation involves considering the effective circumference and the distribution of the magnetic field along the length of each magnet. The discrepancy between the calculated 5.4 Tesla and the required 8.3 Tesla arises from not accounting for the full operational parameters of the LHC, including the need for quadrupoles and the non-circular tunnel design. Understanding these factors is crucial for accurate magnetic field assessments in particle accelerators.

PREREQUISITES
  • Understanding of particle physics and beam dynamics
  • Familiarity with magnetic field calculations in accelerators
  • Knowledge of the LHC design and its components, including dipole and quadrupole magnets
  • Basic principles of ultra-relativistic momentum calculations
NEXT STEPS
  • Research the design and function of dipole and quadrupole magnets in particle accelerators
  • Learn about the calculations involved in determining magnetic fields in circular accelerators
  • Study the impact of synchrotron radiation on particle beams in accelerators
  • Explore the historical context and design evolution of the LHC and its predecessors, such as LEP
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Physicists, engineers, and students involved in particle accelerator design, as well as anyone interested in the operational principles of the Large Hadron Collider.

curious.cat
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I tried to work backwards and verify the magnetic field required by the LHC beam pipes. A circumference of 27km implies a radius R=4300 m. The beam energy E is 7 TeV per proton beam. Considering approximation E approximately equal to pc to get momentum (ultra-relativistic case). Plugging into p=qBr, I am getting a magnetic field of 5.4T as opposed to 8.3T. Clearly, I am doing something wrong. Could someone please point out where I am faltering? Thank you very much.
 
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The LHC tunnel is not a perfect circle. It was built for LEP, where long straight sections are needed for electron/positron acceleration (to counter synchrotron radiation losses). And even in the curves, the dipole field is not everywhere as you need quadrupoles and a few more elements in the ring.
 
Thank you so much for your reply. :) Actually, I was wondering more along the lines of why 8.3, it seems like a weird number. Is there some calculation after which we arrive at this figure?
 
Count the number of dipole magnets in the ring (1232), look up their effective length (the field is not present at full strength along the whole length), take the product as effective circumference, and you should get some number close to 8.3 T. Even with the full length of 15 meters per magnet you get a reasonable agreement.
 
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Thank you so much!
 

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