synchrotron radiation
/ SIN-kruh-tron /
Whip a relativistic charged particle around a curve with a magnetic field and it hurls out an intense, tightly focused beam of light that sweeps like a lighthouse. Synchrotron radiation is the electromagnetic radiation emitted by charges moving at nearly the speed of light along curved paths, and it is one of the brightest artificial light sources we have.
Any charge in circular motion accelerates centripetally and therefore radiates, but relativity transforms the result dramatically. For a charge of speed v = beta c and Lorentz factor gamma on a circle of radius rho, the radiated power is P = (mu_0 q^2 c^3 / 6 pi) beta^4 gamma^4 / rho^2, equivalently q^2 c beta^4 gamma^4 / (6 pi epsilon_0 rho^2) — the gamma^4 makes it explode for ultra-relativistic particles. The Liénard-Wiechert beaming factor concentrates the emission into a forward cone of half-angle about 1/gamma, so a distant observer sees only brief flashes as the cone sweeps past. The spectrum is broad, extending up to a critical frequency omega_c ~ gamma^3 (c/rho), far above the orbital frequency.
Synchrotron radiation is both a nuisance and a tool. In electron storage rings and circular colliders it is the dominant energy loss (scaling as gamma^4 and forcing ever-larger machines), which is why the highest-energy electron-positron colliders are impractical to build as rings. But that same intense, collimated, tunable X-ray beam, harvested at dedicated synchrotron light sources, drives structural biology, materials science and much more. In astrophysics, synchrotron emission from relativistic electrons lights up the Crab Nebula and radio galaxies.
In a large electron storage ring, each electron loses energy to synchrotron radiation scaling as gamma^4 per turn, and the emitted beam is squeezed into a cone only about 1/gamma radians wide — for a gamma of a few thousand, that is a beam under a milliradian, brighter and more collimated than any laboratory X-ray tube.
Relativistic charge on a curve: power ~ gamma^4, beamed into a ~1/gamma cone, spectrum up to omega ~ gamma^3 c/rho.
The dramatic gamma^4 loss and 1/gamma beaming are purely relativistic; for a slow charge you recover ordinary Larmor radiation with no beaming. Synchrotron radiation refers to charges on curved (magnetic) paths — braking on a straight collision is bremsstrahlung instead.