  There are implementations and proposals for using microwave or optical
radiation for electron acceleration, undulation, deflection, and spatial as
well as temporal focusing. Using terahertz (THz) radiation in such applications
can be superior to microwave or optical radiation since THz pulses can be
generated with significantly smaller temporal jitter to the electron bunch to
be manipulated as compared to microwave pulses, and contrary to the optical
pulses, the much larger wavelength of THz pulses compares well with typical
sizes of electron bunches. Recently generation of ultrashort THz pulses with 1
MV/cm focused electric field was demonstrated, and it is predicted that THz
pulses with even 100 MV/cm focused field will be possible. According to the
first results of our analytical and numerical studies this field strength is
high enough for manipulation of relativistic electron beams by polarised THz
pulses in various geometries. It is possible, e.g., to construct a 30 cm long
THz undulator for saturated FEL working at 9.6 nm wavelength using electron
bunches with 100 MeV energy and 0.42 nC charge.
