Publications Details

PROBABILITY DISTRIBUTION FUNCTIONS OF THE NUMBER OF SCATTERING COLLISIONS IN ELECTRON SLOWING DOWN

Franke, Brian C.; Prinja, Anil K.

The probability distribution of the number of collisions experienced by electrons slowing down below a threshold energy is investigated to understand the impact of statistical distribution of energy losses on computational efficiency of Monte Carlo simulations. A theoretical model based on an exponentially peaked differential cross section with parameters that reproduce the exact stopping power and straggling at a fixed energy is shown to yield a Poisson distribution for the collision number distribution. However, simulation with realistic energy-loss physics, including both inelastic and bremsstrahlung energy loss interactions, reveal significant departures from the Poisson distribution. In particular, the low collision numbers are more prominent when true cross sections are employed while a Poisson distribution constructed with the exact variance-to-mean ratio is found to be unrealistically peaked. Detailed numerical investigations show that collisions with large energy losses, although infrequent, are statistically important in electron slowing down.