Understanding the interaction of a kilojoule picosecond laser pulse with long-scale-length preplasma or homogeneous near-critical-density (NCD) plasma is crucial for guiding experiments at national short-pulse laser facilities. Using full three-dimensional particle-in-cell simulations, we demonstrate that in this regime, cross-filament stochastic acceleration is an important mechanism that contributes to the production of superponderomotive high-flux electron beams. Since the laser power significantly exceeds the threshold of the relativistic self-focusing, multiple filaments are generated and can propagate independently over a long distance. Electrons jump across the filaments during the acceleration and their motion becomes stochastic. We find that the effective temperature of electrons increases with the total interaction time following a scaling like ${T}_{\mathrm{eff}}\ensuremath{\propto}{\ensuremath{\tau}}_{i}^{0.65}$. By irradiating a submillimeter-thick NCD target, the space charge of electrons with energy above 2.5 MeV reaches tens of microcoulombs. Such high-flux electrons with superponderomotive energies significantly facilitate applications in high-energy-density science, nuclear science, secondary sources, and diagnostic techniques.
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