Earlier, in a nanosecond vacuum discharge (NVD) with a deuterated Pd anode, the appearance of DD neutrons was observed not only at the well-studied quasi-stationary stage, where a
virtual cathode (VC) appears in the interelectrode space, but also at the very initial stage of the
discharge. An analysis of the experiment shows that the autoelectron beam can play the role of
a kind of trigger for starting DD syntheses processes on the surface or in the bulk of the Pd anode, but its mechanism at the initial stage of the discharge remained unclear. In this work, we performed PiC modeling of the possible partial penetration of a beam of autoelectrons into hollow anode Pd tubes. This leads to the formation of very small short-lived VCs inside individual Pd tubes, where, starting from a current of 100 A, DD microsynthesis is possible. It is shown that in devices with oscillating ions the favorable scaling of the DD fusion power, which increases with decreasing VC radius, can be retained up to rVC 0.02 cm.