Calculator
Accelerator power and synchrotron loss calculator
LEP2 electrons at 104.5 GeV in a 3096 m bending radius lose about 3.4 GeV per turn. LHC protons at 7 TeV in a 2804 m radius lose about 6.7 keV per turn. Calculate energy loss, radiated beam power and critical photon energy for your beam.
Accelerator power and synchrotron loss calculator
Calculate dipole radiation for one beam in an isomagnetic ring.
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Example: How much synchrotron energy do 7 TeV LHC protons lose per turn at a bending radius of 2804 m and a current of 580 mA?
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Total energy E = gamma mc²; p = sqrt(E² − m²c⁴)/c; p[GeV/c] = 0.2998 B[T] rho[m]. The isomagnetic model uses one bending radius for all dipoles, with no insertion-device radiation. It estimates radiation from one beam, not the facility electricity demand. Critical energy uses the ultrarelativistic approximation.
U0 = e² beta³ gamma⁴/(3 epsilon0 rho); for ultrarelativistic electrons, U0[keV] ≈ 88.46 E⁴[GeV]/rho[m]. P[MW] = U0[keV] I[mA] × 10⁻⁶; Ec = (3/2) hbar c gamma³/rho; f = beta c/C.
Synchrotron loss of well-known rings
Calculated dipole-only comparisons using the listed radius, rather than measured total ring losses. FCC-ee values refer to the CDR baseline. Rings with varying dipole radii need a radiation integral.
| Ring | Particle | E (GeV) | Bending radius (m) | Energy loss per turn (keV) | Critical photon energy (keV) |
|---|---|---|---|---|---|
| LEP2 | Electron | 104.5 | 3096 | 3407000 | 817.6 |
| SPS | Proton | 450 | 741.6 | 0.0004303 | 0.00004403 |
| LHC | Proton | 7000 | 2804 | 6.664 | 0.04383 |
| FCC-ee Z (CDR) | Electron | 45.6 | 10760 | 35550 | 19.55 |
| FCC-ee tt (CDR) | Electron | 182.5 | 10760 | 9120000 | 1253 |
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ScienceShot. Accelerator power and synchrotron loss calculator. https://scienceshot.com/accelerator-power-calculator.
Sources: CODATA 2018, Tiesinga et al. (2021); M. Sands, The Physics of Electron Storage Rings, SLAC-121 (1970); Bailey et al., Synchrotron Radiation Effects at LEP, EPAC 1998 (dipole radius); CERN, The LEP story (2000), record beam energy; P. Lebrun, The Large Hadron Collider, African School of Physics (2014); CERN FCC-ee CDR baseline V1.0 parameters (30 June 2020); H. Bartosik et al., SPS pre-booster option, FCC Week (June 2023), slide 5; CERN Medium Power Converters Section, SPS Complex, energy.
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ScienceShot. (2026). Accelerator power and synchrotron loss calculator [Online calculator]. https://scienceshot.com/accelerator-power-calculator
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author = {{ScienceShot}},
title = {{Accelerator power and synchrotron loss calculator}},
year = {2026},
note = {Online calculator},
url = {https://scienceshot.com/accelerator-power-calculator}
}