Electric field distributions within lightning protection volume of a single lightning rod are studied for the case of a vertical downward leader. The boundaries of volumes with the electrical strength exceeding its critical value for ionization in air are determined, for the rod itself and for objects within its lightning protection (LP) volume. Distance from the leader channel related to the initial achievement of this critical electric strength is found. Simulations are performed using a software based on a FEM (Finite Element Method) for the leader parameters (charge, dimensions, etc.) related to return stroke peak currents of 5 and 30 kA, a rod height of 18.2 m and its tip radius of 1 cm, distances from the channel to rod of 0.5, 30 m and larger, an object height of 5.3 m, widths of 2 and 10cm, and considering different values for the top edge radius (0.1,1 and 5 cm). Results show a significant extent of possible ionization zones within the LP volume. The proposed approach allows preliminary estimating the dimensions of such zones for protected objects of various types (including those in electric power systems, explosive materials storages, etc.), and its development can also be used for the improvements of LP norms and for the analysis of conditions related to upward discharge initiation, and of safety aspects. (C) 2011 Elsevier B.V. All rights reserved.