Model relativistic beam losses with clear units, constants, and checks built-in today. Compare scenarios, save CSV, print PDF, and validate designs quickly for research.
| Particle | Kinetic energy | ρ (m) | γ (approx.) | Power per particle (W) |
|---|---|---|---|---|
| Electron | 3 GeV | 10 | ~5870 | ~4.0e-05 |
| Electron | 6 GeV | 25 | ~11740 | ~3.0e-05 |
| Proton | 3 GeV | 10 | ~4.2 | ~1e-22 |
Values are illustrative; your settings may differ.
For circular motion where acceleration is perpendicular to velocity, the radiated power follows the Liénard result:
P = (q² c / (6π ε₀)) · (γ⁴ β⁴ / ρ²)
ρ = p/(|q|B) with p = γ m β c.Synchrotron radiation sets real limits on storage-ring performance by draining beam energy continuously. It drives RF system sizing, heat load on vacuum chambers, and shielding decisions. Because power scales steeply with relativistic factor, small energy changes can create large thermal and operational consequences.
The calculator applies the Liénard expression for circular motion, where power grows as γ⁴ and falls as ρ⁻². Doubling energy at fixed radius can increase losses by roughly sixteen times, while doubling the bend radius can cut losses by about four times. This helps compare compact rings with larger lattices.
Bending magnets set curvature through ρ = p/(|q|B). For a given particle and energy, stronger magnetic field reduces radius and therefore increases radiated power. When field is entered, the tool derives ρ from momentum p = γ m β c, ensuring consistent relativistic dynamics across particle species.
Total power is useful, but energy loss per revolution directly informs RF voltage needs. The tool estimates the revolution period from 2πρ/(βc) and multiplies by power to obtain U per turn. Engineers use U to check whether available RF systems can maintain stable orbit and compensate transient disturbances.
Radiation is broadband, yet the spectrum is characterized by the critical angular frequency ωc = (3/2)γ³c/ρ. The calculator converts ħωc to a representative photon energy. This value guides diagnostics and materials choices, since higher critical energies can intensify photo-desorption and raise dose rates in sensitive components.
Electrons radiate strongly because their low mass produces very large γ at modest kinetic energies, making γ⁴ enormous. Protons at the same kinetic energy have γ only a few, so synchrotron losses are often negligible in hadron rings except at extreme energies. The preset options highlight this contrast quickly.
Use the example table as a starting point, then sweep one variable at a time: energy, bend radius, or magnetic field. Keep particle count realistic for total power checks, and export CSV to document trade studies. Export PDF when sharing results with colleagues or attaching quick reports to design notes.
Treat outputs as idealized single-particle estimates scaled by particle count. Real machines include lattice dispersion, insertion devices, and collective effects that modify power distribution, but the same scaling laws remain central. Verify units, avoid unrealistic radii, and use conservative margins when translating power to cooling and shielding requirements. Document assumptions, and cross-check results against reputable accelerator handbooks whenever possible.
It estimates synchrotron radiation power for circular motion, plus revolution period, energy loss per turn, and a representative critical photon energy. Results are provided per particle and scaled totals using a chosen particle count.
For circular motion the power scales approximately with γ⁴. As energy rises, γ increases and the beam becomes more relativistic, so radiative losses grow rapidly even if the bending radius is unchanged.
Use radius mode when lattice geometry is known. Use field mode when you know the dipole field strength. In field mode the tool derives ρ from momentum, charge, and magnetic field for consistency.
Totals are idealized. Real rings redistribute radiation, include insertion devices, and experience collective effects. Use the outputs for first-order budgeting, then refine with lattice-specific tools and measured magnet data.
At the same kinetic energy, electrons achieve a much larger γ because of their small mass. Since power scales strongly with γ, electrons radiate heavily while protons typically radiate negligibly at comparable energies.
Energy loss per revolution is a direct input for RF voltage and power planning. It helps verify that RF cavities can replenish beam energy and maintain stable operation across expected current and energy ramps.
Confirm energy units, radius in meters, and magnetic field in tesla. Avoid unrealistic tiny radii. If results look extreme, switch modes and compare, then export CSV to track changes systematically.
Accurate radiation estimates help design safer, brighter accelerators worldwide.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.