When collectively accelerated deuterons in pulsed electron beam machines interact with structural materials and insulators, they produce neutrons that can be used for diagnostic purposes. This paper describes a method for synthesizing neutron spectra that such devices might produce. It involves averaging experimental nuclear reaction data over angle and over energy to approximate the distributions in angle and in energy of deuterons as they impinge upon materials. Neutron time-of-flight (TOF) spectra were obtained using the Lawrence Livermore Laboratory tandem Van de Graaff accelerator and a 16-detector TOF spectrometer. Spectra were recorded at each of 16 angles for deuterons having energies of 2.5, 3.0, and 3.5 MeV on thick targets of carbon, aluminum, Teflon, CH2, and CD2. When summed over 4π sr at constant neutron energy to approximate (for example) the neutron spectrum from isotropic mono-energetic deuterons, the 19F(d,n) and 27Al(d,n) spectra still show well-resolved high-energy peaks at each bombarding energy. The synthesized TOF spectra that would be observed for such a case with pulse mode detectors and those that would be observed with current mode scintillation detectors are presented.