An Introduction to Compton Scattering, Page 2

As seen on the previous page, Compton scattering of lasers from relativistic electron beams provides a means of producing high energy electromagnetic radiation. What does this radiation look like, and how efficient is the process?

When an electron radiates in response to low amplitude sinusoidal motion, the radiation forms a dipole pattern. Below, the electron has been wiggled up and down.

ELECTRON FRAME:

But this pattern is severly distorted when the electron has a relativistic velocity, as observed in the laboratory. In particular, when the acceleration is transverse (up and down) to the direction of motion (to the left), this dipole pattern is observed as:

LAB FRAME:

As on the previous page, the blue (up-shifted) radiation is primarily in the direction of the electron motion, and in fact is constrained in a cone which has an angle which decreases as the electron energy increases. This relativistic collimation means that the Compton source has very low divergence, almost like a laser. The distorted dipole patterns are shown below for
different electron energies:

At an electron energy of 5 MeV, gamma = 10 (for example, generated in our compact X-band photoinjector) and the scattered x-ray photons appear as a beam in the laboratory. The reason for this collimation can be thought of as the result of the electron-laser photon collission process: the scattered photons have much less momentum than the incident relativistic electrons and so (like a freight train colliding with a small car) the lower momentum particles are carried along with the relatively massive electrons. (At extremely high scattered photon energies this trend can reverse, and the electron can have its path considerably deflected during the scattering process but that is not important to the Compton Light Source developed by our group.) In three dimensions, these patterns look like:

Left: dipole at rest with a single wavelength of ligh radiated uniformly; Right: dipole pattern in lab frame with gamma = 1.01 with higher energy radiation (blue) collimated in front of the low energy radiation (red).

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