  The nonlinear development of the strong Buneman instability and the
associated fast electron heating in thin current layers with
$\Omega_e/\omega_{pe} <1$ are explored. Phase mixing of the electrons in wave
potential troughs and a rapid increase in temperature are observed during the
saturation of the instability. We show that the motion of trapped electrons can
be described using a Hamiltonian formalism in the adiabatic approximation. The
process of separatrix crossing as electrons are trapped and de-trapped is
irreversible and guarantees that the resulting electron energy gain is a true
heating process.
