An improved electron window is provided for use with a diverging electron beam for use in remediation of hazardous volatile organic compounds. The electron window comprises a support grid having a plurality of circular holes disposed in a diverging bolt circle pattern. Individual electrons of the diverging electron beam pass through respective ones of the plurality of holes. A barrier is provided on a downstream side of the support grid so that the individual electrons pass through the barrier. The circular holes are each of substantially uniform diameter. The diverging bolt circle pattern further comprises a single one of the holes substantially centered on the support grid, and a plurality of groups of the holes concentrically disposed around the single one of the holes. Each of the groups of the holes is disposed in a circular pattern. A number of the holes defined within successive ones of the plurality of groups of holes increases arithmetically as an associated diameter of the circular patterns increases. Also, an associated angle of the holes defined within successive ones of the plurality of groups of holes increases as an associated diameter of the circular patterns increases. The diverging electrons are transmitted through the support grid at a maximum rate of efficiency without undesired interception with the surfaces of the grid holes.