Described herein are neutron generators that employ direct field ionization of ionizable fusion gases, as well as well-logging tools and methods that utilize such neutron generators. In various embodiments, the neutron generator includes a cylindrical field-ionization structure distributed around the inner surface of a tubular housing, and a cylindrical ion-accelerating grid disposed about the longitudinal axis concentrically to the field-ionization structure. Ions generated by the field-ionization structure may accumulate inside the ion-accelerating grid, from which they can be axially extracted and accelerated towards a fusion target. Additional tools, systems, and methods are disclosed.