  We present theoretical studies of high-order harmonic generation (HHG) driven
by plasmonic fields in two-electron atomic systems. Comparing the two-active
electron and single-active electron approximation models of the negative
hydrogen ion atom, we provide strong evidence that a double non-sequential
two-electron recombination appears to be the main responsible for the HHG
cutoff extension. Our analysis is carried out by means of a reduced
one-dimensional numerical integration of the two-electron time-dependent
Schr\"odinger equation (TDSE), and on investigations of the classical electron
trajectories resulting from the Newton's equation of motion. Additional
comparisons between the negative hydrogen ion and the helium atom suggest that
the double recombination process depends distinctly on the atomic target. Our
research paves the way to the understanding of strong field processes in
multi-electronic systems driven by spatially inhomogeneous fields.
