Synchrotron radiation

Synchrotron radiation is the electromagnetic radiation emitted when a relativistic charged particle is bent by a perpendicular magnetic field and therefore undergoes perpendicular acceleration at fixed speed. Because the acceleration is perpendicular to velocity, the Liénard-generalised Larmor formula evaluates to P = q²c β⁴ γ⁴/(6πε₀R²), where R is the radius of curvature and γ = (1 − β²)^(−1/2) is the Lorentz factor. The γ⁴ scaling means radiation losses are negligible at non-relativistic energies but catastrophic at γ > 10⁴ — the fundamental reason circular electron colliders (like LEP at CERN) hit energy walls below the TeV scale while proton colliders (heavier by 1836, radiating 1836⁴ ≈ 10¹³ times less per unit acceleration) do not.

The spectrum is broadband, peaking near the critical frequency ω_c = (3/2) γ³ c/R. Above ω_c the spectrum falls exponentially, below ω_c it rises as ω^(1/3). Because of relativistic beaming, the emission at each instant is confined to a narrow forward cone of half-angle 1/γ — the laboratory-frame observer sees a short pulse each time the tangent to the orbit sweeps past, and the Fourier transform of this short pulse is what produces the broad spectrum. First observed as a blue-white arc leaking out of General Electric's 70 MeV synchrotron in April 1947, the phenomenon now powers dedicated synchrotron light sources (Diamond, ESRF, APS, NSLS-II) that produce brilliant, tunable, polarised, collimated beams from infrared to hard X-rays for crystallography, spectroscopy, and imaging. Astrophysically, synchrotron radiation is the dominant non-thermal emission mechanism from supernova remnants (Crab Nebula), radio galaxies, AGN jets, and the polarised radio emission of the Milky Way's magnetised interstellar medium. The pulsar mechanism — relativistic electrons accelerated along curved open-field lines of a rotating neutron star — is a close relative.