  A new scheme for amplification of coherent gamma rays is proposed. The key
elements are crystalline undulators - single crystals with periodically bent
crystallographic planes exposed to a high energy beam of charged particles
undergoing channeling inside the crystals. The scheme consists of two such
crystals separated by a vacuum gap. The beam passes the crystals successively.
The particles perform undulator motion inside the crystals following the
periodic shape of the crystallographic planes. Gamma rays passing the crystals
parallel to the beam get amplified due to interaction with the particles inside
the crystals. The term `gamma klystron' is proposed for the scheme because its
operational principles are similar to those of the optical klystron. A more
simple one-crystal scheme is considered as well for the sake of comparison. It
is shown that the gamma ray amplification in the klystron scheme can be reached
at considerably lower particle densities than in the one-crystal scheme,
provided that the gap between the crystals is sufficiently large.
