LHC Span Calculator
Calculate LHC beam parameters: momentum, bending radius, Lorentz factor, velocity, revolution frequency, and rigidity from beam energy and magnetic field.
About This Calculator
The LHC Span Calculator computes key beam parameters for the Large Hadron Collider from user-supplied beam energy and magnetic dipole field. Using the relativistic energy-momentum relation E^2 = p^2c^2 + m0^2c^4 and the synchrotron formula p = 0.3BR, it derives momentum, bending radius, Lorentz factor gamma, velocity beta, revolution frequency, and beam rigidity. The calculator supports the full LHC energy range from 0.5 TeV injection to 14 TeV design energy, with magnetic fields from 1 to 10 T covering all operational scenarios.
Particle accelerator physics governs every result. The bending radius tells you how tightly the dipole magnets must curve the beam path; the Lorentz factor shows relativistic mass increase; the revolution frequency indicates how many times per second a proton completes the 27 km ring. These parameters are fundamental to understanding synchrotron design, magnet specifications, and beam dynamics in the world's most powerful particle collider.
Regional Notes
Global: The LHC is a CERN facility in Switzerland. Beam parameters follow universal relativistic physics and are independent of region. Defaults reflect the LHC Run 2/3 operating point: 6.5 TeV beam energy with 8.33 T dipole field (design value). Results apply equally to any synchrotron or particle accelerator worldwide.
India: Indian scientists and institutes (TIFR, BARC, SINP) contribute to LHC experiments CMS and ALICE. The calculator uses SI units consistent with Indian physics education and research standards.
US: US institutions (Fermilab, Brookhaven, MIT, Caltech) are major LHC collaborators. The formula p = 0.3BR is standard in US accelerator physics curricula at institutions like USPAS.
UK: UK universities (Oxford, Cambridge, Imperial, Liverpool) are key LHC participants. CERN hosts significant UK-funded research infrastructure. All units are SI as used in UK physics departments.
Frequently Asked Questions
What is the LHC beam energy in TeV?
The LHC operates at 6.5 TeV per beam giving a 13 TeV center-of-mass collision energy. The design energy is 7 TeV per beam for 14 TeV collisions achieved with 8.33 T superconducting dipole magnets in the 27 km ring.
How do superconducting magnets bend the LHC beam?
LHC dipole magnets use 8.33 T superconducting NbTi coils at 1.9 K to bend protons via the Lorentz force. The bending radius follows p equals 0.3 times B times R where momentum in GeV/c relates directly to field and radius.
How fast do protons travel in the LHC?
At 6.5 TeV protons travel at 0.999999964 c or about 11 000 revolutions per second around the 27 km ring. The Lorentz factor gamma exceeds 6900 meaning the protons are over 6900 times heavier than their rest mass.
What is beam rigidity in accelerator physics?
Beam rigidity B rho is the product of magnetic field and bending radius measuring how stiff the beam is. For the LHC at 6.5 TeV the rigidity is about 21600 Tm calculated as momentum in GeV/c divided by 0.3.
How does magnetic field affect the LHC bending radius?
Higher magnetic fields allow tighter bending radii for the same beam energy. Doubling the field halves the required radius. The LHC uses 1232 dipole magnets each 14.3 m long to achieve the 2804 m bending radius.
What is the LHC circumference and revolution frequency?
The LHC circumference is 26659 meters. At 6.5 TeV protons circle the ring about 11245 times per second taking 89 microseconds per revolution. Each beam contains up to 2808 bunches of 100 billion protons.
How to calculate momentum from beam energy?
Use the relativistic energy-momentum relation E squared equals p squared c squared plus m0 squared c to the fourth. For LHC protons at 6.5 TeV the momentum is approximately 6500 GeV/c since the rest mass 0.938 GeV is negligible.