  Electron holes (EH) are highly stable non-linear structures met omnipresently
in driven collision-less hot plasmas. A mechanism destabilizing small
perturbations into holes is essential for an often witnessed but less
understood sub-critically driven intermittent plasma turbulence. In this paper
we show how a tiny, eddy-like, non-topological seed fluctuation can trigger an
unstable evolution deep in the linearly damped region, a process being
controlled by the trapping non-linearity and hence being beyond the realm of
the Landau scenario. After a (transient) transition phase modes of the
privileged spectrum of cnoidal EH are excited which in the present case consist
of a solitary electron hole (SEH), two counter-propagating "Langmuir" modes
(plasma oscillation), and an ion acoustic mode. A quantitative explanation
involves employing non-linear eigen-modes, yielding a non-linear dispersion
relation with a forbidden regime and the negative energy character of the SEH,
properties being inherent in Schamel's model of undamped Vlasov-Poisson
structures identified here as lowest order trapped particle equilibria. An
important role in the final adaption of nonlinear plasma eigenmodes is played
by a deterministic response of trapped electrons which facilitates transfer of
energy from electron thermal energy to an ion acoustic non-uniformity,
accelerating the SEH and positioning it into the right place assigned by the
theory.
