X-ray generation by the Smith-Purcell effect

Smith-Purcell (S-P) radiation is produced when electrons graze the surface of a grating. Calculations based on the theory of diffraction radiation show that, given severe restrictions on ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$-beam quality, S-P radiation is highly efficient. Efficient S-P x-ray generation requires relativistic ${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ beams having a transverse momentum and dimension whose product approaches the Heisenberg uncertainty limit.