Lienard-Wiechert Beaming and Synchrotron Lobe

What you are seeing: the angular distribution of radiation from a charge accelerated either parallel to or perpendicular to its velocity. As $\gamma \to \infty$ the radiation collimates into a forward cone of opening angle $\sim 1/\gamma$ , which is the synchrotron beaming effect. The cyan circle marks the $1/\gamma$ opening angle.

Figure 1. Relativistic beaming of the radiation lobe.

γ (Lorentz)3.0

geometry

WHAT TO TRY

Raise the Lorentz factor gamma: the radiation lobe collapses from a broad pattern into a tight forward searchlight of half-angle 1/gamma. Relativistic beaming is what makes synchrotron sources so directional.
Switch the geometry between acceleration parallel to v and perpendicular to v: the parallel case (linear accelerator) and the perpendicular case (synchrotron) beam into different shapes, both forward-collimated at high gamma.
Drag to orbit the camera: the lobe is a 3D solid of revolution about the velocity, so spinning it shows the forward pencil that a distant observer catches only as the beam sweeps past.