||An Introduction to Compton Scattering, Page 1
These pages are designed as a brief tutorial on Compton Scattering,
and how we use it to produce x-rays.
An electromagnetic wave packet moves from left to right below (red).
The electron (yellow) is moving at relativistic speeds and collides with
the electromagnetic wave.
However, the electron sees a doppler up-shifted laser pulse in its rest
frame. The wavelength is contracted an amount proportional to the
electron energy, as shown by the solid green line below.
In linear Compton scattering, the electron oscillates in response
to the electric field of the laser pulse at this higher frequency, but
it's instantaneous energy is close to the initial energy (the perpindiular
component of its motion is small). As the electron oscillates, it
radiates (dashed green line) in its rest frame at the same wavelength as
the incident radiation. Back in the laboratory frame however this
radiated electromagnetic has received another doppler shift:
This radiation can have a very small wavelength since it depends on the
square of the electron energy (an additional factor of 0.25 is necessary
to conserve energy and momentum simultaneously and has been ommitted from
this simple calculation). In our simple model, the blue radiation
continues in the direction of the electron while the laser wave is reduced
in amplitude and continues in its original direction. The electron
finishes the interaction with near its initial energy.
For example, using an electron beam with an energy of 5 MeV (or five
million electron volts) in head-on collision with a near-infrared laser
of 800 nm (or a photon energy of 1.55 eV) the Compton backscattered radiation
has an energy of 600 eV, which is in the soft x-ray region.