# Scalar potential of a point charge

By Glenn Decker

Like a shock wave from a supersonic aircraft, synchrotron radiation is emitted as an expanding wave front radiates outward and away from a charged particle as it suddenly transitions from a curved to a straight trajectory. To an observer near the top of the figure, the arrival of the wave front corresponds to a huge electromagnetic impulse of X-ray radiation, similar to a sonic boom. Using devices called undulators at the Advanced Photon Source, the intensity of these impulses can be further enhanced, resulting in very intense X-ray sources.

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Scalar potential of a point charge shortly after exiting a dipole magnet, moving left to right. One can see the synchrotron radiation wave front pull away from the electron (actually positron, since the scalar potential is positive). It's only moving 0.9 times the speed of light though. Otherwise the height of the wavefront diverges towards infinity while its width shrinks to zero. The observer is moving along with the positron, which is why it stays in the middle.