# 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 *E*_{TOT} (i.e. the kinetic energy plus the rest mass energy) of the electron: *E*_{TOT} = *m*_{e}*c*^{2}, where *m*_{e} 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.