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 synchrotron spectrum peaks near the critical energy E_c = (3/2) ℏ γ² (eB/m_e) sin α. Half the total radiated power falls below E_c and half above. It sets the characteristic frequency of the emission — radio for low γ or weak B, X-ray for high γ or strong B.

What is the pitch angle?

The pitch angle α is the angle between the electron's velocity vector and the magnetic field direction. The radiated power and critical frequency both scale as sin α. For an isotropic distribution of electrons, the average is sin α = π/4, but 90° (perpendicular) is the standard single-particle assumption.

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

Name: Synchrotron Radiation Energy Calculator
Availability: InStock
Author: Nham Vu

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.

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Summary

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

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: 2026-07-22 · Reviewed by Nham Vu