A model of forming deuteron fluxes and neutron generation in an axial plasma diode with two external anodes and a transparent internal hollow cathode is suggested. Such configuration provides longitudinal deuteron oscillations (inertial confinement) and required frequency of collisions with slow deuterons in the cathode plasma. On the basis of the suggested model of neutron generation, the neutron flux generated in the course of D(d, n)3 He nuclear reactions is approximately calculated. The examined diode system seems to be promising for the development of compact controllable neutron sources with increased operation lifetime and transverse size no more than 5 cm.