Neutrons from DD fusion in the interelectrode space of a table-top, low-energy, nanosecond vacuum discharge with a deuterium-loaded Pd anode have been demonstrated earlier. In addition, the principal role of a virtual cathode and the corresponding deep potential well formed in the interelectrode space are recognized under detailed particle-in-cell simulations of the discharge experimental conditions using a fully electrodynamic code. PIC modelling has allowed the identification of the scheme of small-scale experiments with a rather old branch of plasma physics as the inertial electrostatic confinement fusion. The goal of this work is to present and discuss in detail the available experimental results on deuteron oscillations followed by pulsating DD neutron yield in this scheme based on nanosecond vacuum discharge. PIC simulations of some experimental regimes of pulsating neutron yield are also shown and discussed, as well as comparisons with an available similar scheme of periodical oscillating plasmas spheres for fusion. KEYWORDS inertial electrostatic confinement, neutron yield, virtual cathode 1 Contrib. Plasma Phys. 2018;58:952-960 www.cpp-journal.org