Calculator Inputs
Example Data Table
| Particle | Kinetic Energy | Beam Current | Bending Radius | Approx. Beam Power | Approx. Energy Loss/Turn |
|---|---|---|---|---|---|
| Electron | 2 GeV | 0.20 A | 8 m | 3.542127e+04 W | 1.771063e+05 eV |
| Electron | 3 GeV | 0.50 A | 12 m | 2.987652e+05 W | 5.975304e+05 eV |
| Proton | 50 GeV | 0.05 A | 80 m | 3.273113e-05 W | 6.546226e-04 eV |
These rows illustrate typical scaling behavior. Electron beams radiate much more strongly than heavier particles at similar curvature.
Formula Used
The model assumes uniform circular motion in a bending radius ρ. It captures relativistic scaling, beam-current effects, and photon critical energy. It does not include insertion devices, quantum excitation, detailed lattice optics, or transient edge-field corrections.
How to Use This Calculator
- Select a particle preset or choose custom.
- Enter kinetic energy and choose its unit.
- Enter beam current and bending radius.
- Optionally enter magnetic field for consistency checking.
- Set graph points for a denser or lighter energy sweep.
- Press the calculate button to show results above the form.
- Review power, energy loss, field requirement, and critical photon energy.
- Use CSV or PDF export for reporting or documentation.
FAQs
1) What does this calculator estimate?
It estimates synchrotron radiation power for a charged particle beam in circular motion. It also reports gamma, beta, revolution frequency, energy loss per turn, critical photon energy, and a magnetic-field consistency check.
2) How is synchrotron radiation power calculated?
The calculator uses the relativistic circular-motion formula P = [q²c/(6πϵ₀)] × γ⁴β⁴ / ρ². After finding single-particle power, it converts that into per-turn energy loss and total beam power using current and revolution frequency.
3) Why does power increase so sharply with energy?
Power scales approximately with γ⁴ for fixed radius. As beam energy rises, gamma rises too, so radiation grows very quickly. This is why high-energy electron storage rings demand strong RF compensation and careful thermal design.
4) Why do electrons radiate much more than protons?
Electrons have far smaller rest mass, so they reach much higher gamma at the same energy. That makes synchrotron radiation dramatically stronger. Heavy particles like protons or ions lose much less energy under similar bending conditions.
5) Does charge sign matter for radiation power?
No. The sign changes the bending direction, but the power formula contains q², so magnitude matters. A particle and its antiparticle radiate the same power if energy, speed, charge magnitude, and bending radius are identical.
6) What is energy loss per turn?
Energy loss per turn is the radiation energy emitted by one particle during one complete revolution. Storage rings must replace that energy with RF systems, otherwise the beam energy drops every turn.
7) What does critical photon energy mean?
Critical photon energy marks the characteristic point in the synchrotron spectrum. It helps describe how hard or soft the emitted radiation is. Higher critical energy means shorter wavelengths and more penetrating photons.
8) How should I choose the bending radius?
Use the effective bend radius of the dipole path, not the full ring radius unless they are the same in your approximation. Larger bend radius reduces radiation, while tighter curvature increases losses and critical photon energy.