What is synchrotron radiation?

Synchrotron radiation is electromagnetic radiation emitted by relativistic charged particles (usually electrons) accelerating along curved paths in a magnetic field. It produces a broad spectrum peaking at the critical frequency, and is responsible for non-thermal radio through X-ray emission in many astrophysical objects.

What is the Lorentz factor γ?

γ = E_total / (m_e c²) is a dimensionless measure of the electron energy relative to its rest energy (0.511 MeV). At γ = 1 the electron is at rest; cosmic ray electrons in a pulsar nebula can reach γ ~ 10⁷–10⁸.

What is the critical photon energy?

The critical energy E_c = (3/2) ℏ γ² (eB/m_e) sin α sets the characteristic spectral scale. The single-electron spectral-power curve peaks near 0.29 E_c, rather than E_c being a median-energy boundary.

What is the pitch angle?

The pitch angle α is the angle between the electron's velocity vector and the magnetic field. Critical frequency scales as sin α, while single-particle total power scales as sin²α. For an isotropic distribution, ⟨sin²α⟩ = 2/3; 90° is the maximum-emission single-particle case.

What magnetic field units should I use?

Interstellar and intergalactic fields are typically quoted in microgauss (μG), galactic fields in tens of μG, neutron star surfaces in teragauss (TG). The calculator accepts μG, G, and T and converts internally to SI.

Why does the power scale as γ²?

Synchrotron power P ∝ γ² B² because both the magnetic energy density and the relativistic beaming of radiation increase with γ². Higher-energy electrons therefore radiate far more power, which also leads to faster cooling (shorter synchrotron lifetime) at higher energies.

Synchrotron Radiation Energy Calculator

Enter electron energy (or Lorentz factor) and magnetic field strength to get synchrotron radiation power and critical photon energy.

Electron & Field Parameters

Electron Energy Input Mode

Electron Energy (MeV)

Electron rest energy = 0.511 MeV. Enter total energy.

Magnetic Field Strength

Pitch Angle α (degrees)

Angle between electron velocity and B field. 90° = perpendicular (maximum emission).

Results

Results will appear here after calculation.

Copied!

Summary

Synchrotron radiation is emitted when relativistic electrons spiral around magnetic field lines. For a specified single-particle pitch angle, this calculator uses P = 2σ_T c γ²β²U_B sin²α and ν_c = (3/2)γ²(eB/2πm_e)sin α. For an isotropic pitch-angle distribution, ⟨sin²α⟩ = 2/3, reducing the averaged power coefficient to 4/3.

How it works

Enter the electron energy in MeV, or switch to Lorentz factor γ directly.
Enter the magnetic field strength in microgauss (μG), gauss (G), or tesla (T).
Set the pitch angle α between the electron velocity and the magnetic field (default 90°).
The calculator derives γ, the magnetic energy density U_B, and the cyclotron frequency.
Synchrotron power P and critical photon energy E_c are computed from the standard formulae.
Results are shown in physical units: watts, eV/keV, and the corresponding photon frequency.

Use cases

Estimate X-ray emission from a pulsar wind nebula given its B-field and electron energy.
Find the critical frequency of a radio galaxy jet emitting at a known magnetic field.
Convert between electron Lorentz factor and synchrotron peak photon energy.
Determine whether a given astrophysical source emits in radio, optical, X-ray, or gamma-ray.
Check synchrotron cooling timescales for high-energy electrons in a supernova remnant.
Explore how emission shifts to higher energies as B-field or electron energy increases.
Cross-check synchrotron formulae for accelerator physics or plasma physics coursework.

Frequently Asked Questions

Last updated: 2026-06-19 · Reviewed by Nham Vu