A method for the calculation of electron energy-straggling spectra

To calculate electron beam dose distributions accurately, numerical methods of electron transport calculations must account for the statistical variation (or "straggling") in electron energy loss. This paper shows that the various energy straggling theories that are applicable to short path lengths all derive from a single statistical model, known as the compound Poisson process. This model in turn relies on three assumptions: (1) the number of energy-loss events in a given path length is Poisson distributed; (2) events are mutually independent; and (3) each event has the same probability distribution for energy loss (i.e., the same energy-loss cross section). Applying the principles of the compound Poisson process and using fast Fourier transforms, a new method for calculating energy-loss spectra is developed. The spectra calculated using this method for 10, 20, and 30 MeV electrons incident on graphite and aluminum absorbers agreed with Monte Carlo simulations (EGS4) within 1% in the spectral peak. Also, stopping powers derived from the calculated spectra agreed within 1.2%, with stopping powers tabulated by the International Commission on Radiation Units and Measurements. Several numerical transport methods "propagate" the electron distribution (in position, direction, and energy) over small discrete increments of path length. Thus the propagation of our calculated spectra over multiple path length increments is investigated. For a low atomic number absorber (graphite in this case), calculated spectra agreed with EGS4 Monte Carlo simulations over the full electron range, provided the path length increments were sufficiently small (less than 0.5 g/cm2). It is concluded from these results that numerical methods of electron transport should restrict the size of path length increments to less than 0.5 g/cm2 if energy straggling is to be modeled accurately.