THE EGS5 CODE SYSTEM

2.15.6 Electron Step-Size SelectionUser control of multiple scattering step-sizes in EGS4 was accomplished through the specificationof the variable ESTEPE, the fractional kinetic energy loss desired over the steps. Because of thecomplete decoupling of the energy loss and elastic scattering models in EGS5, however, there aretwo separate step-size mechanisms, one based on energy loss and controlling energy hinge steps, andone based on scattering strength and controlling multiple-scattering hinge steps. Of the two, themultiple-scattering step is almost always the more limiting because it is what drives the accuracy ofthe transport mechanics model. As stated earlier, energy hinges are required primarily to provideaccurate numerical integration of energy-dependent quantities. Because hard collisions impose defacto energy hinges whenever they are encountered, for situations in which their cross sections arelarge because the PEGS thresholds AE and AP are small, the numerous hard collisions often providethe full accuracy required in energy integration, thus rendering energy hinges superfluous. Only incases where hard collision probabilities are small and material cross sections, stopping powers, etc..,vary rapidly with energy do energy hinge steps actually need to be imposed, and for such instances,a mechanism has been developed by which these hinge steps are automatically determined in PEGS,as described below.2.15.7 Energy Hinge Step-Size Determination in PEGSAs noted above, in the dual hinge formalism of EGS5, the energy steps provide no function otherthan assuring accurate numerical integration over energy-dependent variables (such as energy loss,scattering strength, etc.). For any such quantity f which varies with energy through a step of totallength t, if the energy hinge occurs at a distance h, the EGS5 random energy hinge methodologygives for the integration of f over distance variable s through tF (t:h) =∫ t0ds f(s) (2.376)= hf(E 0 ) + (t − h)f(E 1 )where E 0 is the initial energy and E 1 the energy at the end of the energy hinge step t. Asimplemented in EGS5, the energy hinges distances are uniformly distributed in energy, so if ζ is arandom number, we have h = ζ∆E| dEdx |−1 and (t − h) = (1 − ζ)∆E| dEdx |−1 , giving us in practiceF (t:h) = ζ∆E f(E 0 )dE−1∣ dx ∣ + (1 − ζ)∆E f(E 1 )dE−1∣E 0dx ∣(2.377)E 1Since the energy hinges are uniformly distributed over t, the average values of the integratedquantities are given byF (t) ==∫ t0∫ 10dh F (t:h) p(h) (2.378)(∣ ∣∣∣ dE−1)dζ ζ∆E f(E 0 )dx ∣ + (1 − ζ)∆E f(E 1 )dE−1∣E 0dx ∣E 1108