or scattering interactions between the beam and the target. Dispersion relation When a charged particle travels above a periodic grating (or periodic media inhomogeneity), a current is induced on the surface of the grating. This induced current then emits radiation at the discontinuities of the grating due to the scattering of the Coulomb field of the induced charges at the grating boundaries. The dispersion relation for the Smith–Purcell effect (SPE) is given as follows: , where the wavelength is observed at an angle to the direction of the electron beam for the order reflection mode, and is the grating period and is the relative electron velocity (). This relation can be derived through considering energy and momentum conservation laws. References Quantum optics