A neutron detector comprises at least two conductive cathode sheets lying parallel to one another and coated with neutron reactive material on at least one side thereof; dielectric material separating the cathode sheets and covering less than about 80% of their surface area; and a plurality of anode wires lying generally parallel to the cathode sheets and separated from them by the dielectric, with the distance between adjacent anode wires being no more than twenty times the distance between said cathode sheets. The cathode sheets may be flat or curved; they may be separate plates or they may be successive folds or windings of a single folded or spiral-shaped metal sheet. Related methods for building the detector are disclosed.