7.6 Producing synchroton radiation in a laboratory
Synchrotron radiation can, of course, be produced in a laboratory by arranging for electrons to be deflected by a magnetic field. Figure 13 shows a beam of synchrotron radiation produced at the European Synchrotron Radiation Facility (Figure 14).
The spectrum of synchrotron emission produced by a single electron has the shape shown in Figure 15: a broad spectrum with a maximum at frequency max.
where B is the magnetic field strength perpendicular to the velocity of the electron, and is the Lorentz factor, given by
The Lorentz factor, which is one of the fundamental ingredients of special relativity, is proportional to the total energy ETOT (i.e. the kinetic energy plus the rest mass energy) of the electron: ETOT = mec2, where me is the electron rest mass. Hence we could alternatively write
The power, P, emitted in synchrotron radiation from a single electron depends on the energy of the electron. If we assume that the electron is highly relativistic (i.e. ~ c) the power emitted is
We have dropped the subscript ‘TOT’, but are still referring to the total energy of the electron.