One of the main problems for inertial electrostatic confinement devices with electron injection is the space charge neutralization. This work is devoted to the analysis of the problem of plasma quasineutrality in the scheme of plasma oscillatory confinement based on nanosecond vacuum discharge (NVD). Electrodynamics modeling of the processes of aneutronic fusion of proton–boron showed that the plasma in the NVD, and especially on the discharge axis, really corresponds to a quasineutral regime, which is rather different from the well-known scheme of periodically oscillating plasma spheres (POPS). In this case, small oscillations in the NVD are a mechanism of resonant ion heating, unlike coherent compressions in the original POPS model. The scaling of the fusion power turns out to be close to the fusion scheme with POPS, but differs significantly in the values of the parameter of quasineutrality and the compression ratio.