Synchrotron Radiation Cone

What you are seeing: a relativistic electron of Lorentz factor $\gamma$ orbiting in a magnetic field $\vec B$ . Its radiation is beamed into a forward cone of half-angle $\sim 1/\gamma$ pointing along the instantaneous velocity. The bottom panel is the observed pulse profile and synchrotron spectrum with peak at $\nu_c = (3/2) \gamma^3 \nu_L$

Figure 1. Electron in B field beams synchrotron radiation into a forward cone of half-angle 1/gamma. Method: closed-form Rybicki-Lightman formulas + Westfold spectral envelope.

log10 gamma1.5

log10 B (T)-4.0

animation speed2

view tilt (deg)40

WHAT TO TRY

Raise the Lorentz factor gamma: the radiation beams into an ever-tighter forward cone of half-angle 1/gamma, the searchlight that sweeps past as the electron orbits.
Raise the magnetic field B: the critical frequency nu_c and the total synchrotron power P_sync both climb steeply, which is why strong-field sources blaze across the spectrum.
Watch the spiraling electron: its acceleration is centripetal, so the beamed cone rotates with it, the emission that lights up radio galaxies and the Crab nebula.