  In \v{C}erenkov and Smith-Purcell free-electron lasers (FELs), a resonant
interaction between the electron beam and the co-propagating surface mode can
produce copious amount of coherent terahertz (THz) radiation. We perform a
three-dimensional (3D) analysis of the surface mode, taking the effect of
attenuation into account, and set up 3D Maxwell-Lorentz equations for both
these systems. Based on this analysis, we determine the requirements on the
electron beam parameters, i.e., beam emittance, beam size and beam current for
the successful operation of a \v{C}erenkov FEL.
