A numerical model and scaling relationship for energetic electron beams propagating in air

Scaling relationships for energy loss and scattering are combined with a particle code to construct a purely algebraic expression for the energy deposited by an energetic electron beam injected into field-free homogeneous air. An algebraic formulation is possible because the mean free paths for the major collisional processes depend similarly on density and energy above 1 keV. Accordingly, the spatial behavior of an initially cold pencil beam is approximately self-similar when expressed in terms of the nominal beam range, provided the beam energy at injection exceeds several keV. Since a warm and broad beam can always be decomposed into a series of cold pencil beams, the total energy deposited can be obtained through a simple sum. With such a model, the ionization and excitation generated by a beam can be computed quickly and easily at every point in space. Similar formulations can be developed for other media using particle codes or experimental data. In liquids or solids, the energy deposited is quickly converted to heat and ultimately to melting and/or vaporization of the material. [DOI: 10.1063/1.2986657]